Keywords: Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems, Control of Mechanical, Electrical and Process Systems, Smart Structures
Abstract: Systematic design of decentralized feedback for coordinated control of multi-agent systems has much to gain from the rigorous examination of the nonlinear dynamics of collective animal behavior. Animals in groups, from bird flocks to fish schools, employ decentralized strategies and have limitations on sensing, computation, and actuation. Yet, at the level of the group, they are known to manage a variety of challenging tasks quickly, accurately, robustly and adaptively in an uncertain and changing environment. In this paper we review recent work on models and methods for studying the mechanisms of collective migration and collective decision-making in high-performing animal groups. Through bifurcation analyses we prove systematically how behavior depends on parameters that model the system and the environment. These connections lay the foundations for proving systematic control design methodologies that endow engineered multi-agent systems with the remarkable features of animal group dynamics.

Keywords: Quantized Feedback and Feedback with Communication Constraints, Hybrid Nonlinear Control Systems, Control of Sampled Data Systems
Abstract: We consider the scenario where a controller communicates with a mobile robot via a network. Our objective is to design the control law such that the robot tracks a given reference trajectory while reducing the usage of the communication channel. For that purpose, we design a nonlinear event-triggered feedback law. We follow an emulation-like approach in the sense that we first synthesize the controller while ignoring the communication constraints and we then derive an appropriate triggering condition. We prove that the states of the robot's model practically converge towards the states of the reference system which generates the desired trajectory to be tracked, using an invariance principle for hybrid systems. The existence of a dwell-time between any two transmissions is discussed. We have implemented the proposed strategy on a benchmark where the controller is located on a remote computer which communicates with the mobile robot via a IEEE 802.11g wireless network. The proposed event-triggering strategy is shown to significantly reduce the need for communication compared to a classical time-triggered setup while ensuring similar, if not better, tracking performances.

Keywords: Stabilization, Lyapunov Methods, Control of Sampled Data Systems
Abstract: Event-triggered control is a sampling strategy that updates the control value only when when some event occurs. This event is usually generated by an event-function that indicates if the control signal must be updated or not. If one excepts self-triggered implementation, event-triggered control requires the evaluation of the event function at each time instant. Unfortunately, in the literature of nonlinear system event-based control, computing the event function is more resource consuming than computing the control itself. Moreover, it requires the knowledge of the Lyapunov function that is not necessarily available. The purpose of this paper is to propose for affine nonlinear systems a new event function that only requires the computation of the control. This reduces the complexity of computing the event and avoids to have the Lyapunov function.

Keywords: Complex Network, Control of Sampled Data Systems, Nonlinear Cooperative Control
Abstract: This paper investigates the problem of event-based control for the synchronization of networks of nonlinear dynamical agents. A distributed model based approach able to guarantee that all the agents converge to an adjustable synchronization region is derived. In such control scheme all the agents use a model of their neighborhood in order to generate triggering instants in which the local controller is updated and, if needed, local information is broadcasted to neighboring agents. The existence of a minimum lower bound between inter-event times is proven both for broadcasted information as well as for control signal updating, thus allowing implementation of the proposed strategy in applications where both the communication bandwidth and the maximum updating frequency of actuators are critical.

Keywords: Control of Sampled Data Systems, Stability, Switching Control
Abstract: In this work, we present a novel self-triggered control which aims at decreasing the number of sampling instants for the state feedback control of perturbed linear time invariant systems. The approach is based on convex embeddings that allow for designing a state-dependent sampling function guaranteeing the system's exponential stability for a desired decay-rate and norm-bounded perturbations. One of the main contributions of this paper is an LMI based algorithm that optimizes the choice of the Lyapunov function so as to enlarge the lower-bound of the sampling function while taking into account both the perturbations and the decay-rate. The advantages of the approach are illustrated with a numerical example from the literature.

Keywords: Control of Sampled Data Systems, Hybrid Nonlinear Systems, Optimal Control
Abstract: Given a predesigned linear state feedback law for a linear plant ensuring (global) exponential stability of the linear closed loop, together with a certain level of performance, we address the problem of recovering (local or global) exponential stability and performance in the presence of plant input saturation and of a communication channel between the controller output and the saturated plant input. To this aim, we adopt Lyapunov-based techniques which combine generalized sector conditions to deal with the saturation nonlinearity and event- triggered techniques to deal with the communication channel. The arising analysis yields an event-triggered algorithm to update the saturated plant input based on conditions involving the closed-loop state. The proposed Lyapunov formulation leads to numerically tractable conditions that guarantee local (or global) exponential stability of the origin of the sampled-data system with an estimate of the domain of attraction.

Keywords: Quantized Feedback and Feedback with Communication Constraints, Hybrid Nonlinear Control Systems
Abstract: We study event-triggered control based on a reduced or simplified model of the plant's dynamics. In particular, we address two time-scale systems and we investigate whether it is possible to synthesize a stabilizing event-triggered controller based only on an approximate model of the slow dynamics given by singular perturbation theory, when the fast one is stable. We highlight specific challenges which arise with the event-triggered implementation: the state of the fast model experiences jumps at transmissions which induces non-trivial difficulties for the stability analysis and the Zeno phenomenon may occur due to the fact that we neglect the fast dynamics. We describe the overall problem as a hybrid singularly perturbed system. We first provide a necessary condition on the triggering condition to avoid the Zeno phenomenon. Afterwards, we propose two strategies which respectively use a dead-zone and a clock variable and which ensure different asymptotic stability properties. The existence of a minimum inter-transmission interval is guaranteed. Our results are illustrated by a physical example.

Keywords: Observability and Observer Design, Performance Issues, Robustness
Abstract: A gradient descent--based nonlinear observer for surface--mount permanent magnet synchronous motors (PMSMs) with remarkable stability properties was recently proposed in [7]. A key assumption for the derivation of the observer is the absence of rotor saliency, which is the case in surface--mount PMSMs. A question of great practical interest is to assess the performance of the observer in the presence of saliency. This is the topic of study of the present paper. It is shown that the robustness of the observer is fully determined by the sinusoidal steady--state values of the currents, providing some guidelines for the selection of their reference values to ensure good position estimation.

Keywords: Stability, Passivity, Variable Structure Control and Sliding Mode
Abstract: Some comparative studies of several nonlinear control techniques applied to dc-dc power converters are developed in this paper, like for instance the Immersion & Invariance, Passivity-Based Control, Feedback Linearization and the Sliding-Mode Control. All these different control strategies are used to drive dc-dc power converters in a dc microgrid. The load, modeled as a Constant Power Load type, is also a major issue of this paper.

Keywords: Model Based Control, Switching Control, Power Systems
Abstract: This paper addresses the voltage imbalance problem of the dc-link capacitors in multilevel power converters. Considering the five-level diode-clamped converter, a mathematical analysis of the capacitor voltage difference dynamics is carried out. It leads to a new problem statement that relates the voltage balancing objective to a problem of ensuring the practical stability of a nonlinear system in the presence of disturbances. Then, exploiting the properties and knowledge of the disturbance patterns, a novel and simple controller is presented. Simulation results are included to validate the performance of the proposed controller.

Keywords: Control of Mechanical, Electrical and Process Systems, Applications of Observer Design, Stabilization
Abstract: A solution to the problem of global exponential tracking without velocity measurement of mechanical systems with friction and possibly unbounded inertia matrix is given in the paper. The proposed controller is obtained combining a new full--information passivity--based controller with a new immersion and invariance observer. The resulting closed--loop system has, in some suitably defined coordinates, a port--Hamiltonian structure with a desired energy function and a uniformly positive definite damping matrix. In this way, global exponential tracking of position and velocity for all desired reference trajectories is ensured.

Keywords: Control of Mechanical, Electrical and Process Systems, Robotics, Lyapunov Methods
Abstract: This work is devoted to a force control strategy of a class of standard mechanical systems in the port-Hamiltonian framework. First, a coordinate transformation is applied to equivalently describe the original port-Hamiltonian system in a port-Hamiltonian form which has a constant mass-inertia matrix in the Hamiltonian. Then, we show how to derive an extended port-Hamiltonian system with structure preservation which can be used for force control purposes. Furthermore, we prove that the closed-loop system is asymptotically stable via a Lyapunov candidate function. Finally, experiments results are provided to show the advantages of the force control strategy in presence of external forces.

Keywords: Passivity, Chemical Process, Lyapunov Methods
Abstract: This paper proposes a thermodynamics based approach for the boundary control of distributed single phase reactive systems in one spatial dimension. More precisely, this approach is motivated by the so-called thermodynamic availability directly derived from the concavity of the entropy function for homogeneous mixtures. On this basis, a general connection to the boundary control is developed for the case of tubular chemical reactors by selecting an appropriate input-output pair. In this control framework, we shall show that to be (strictly) passive, a necessary and sucient condition for the dissipation that is strongly related to the transport phenomena and chemical reaction has to be fullled. Consequently, a proportional boundary feedback control law globally stabilizes the reactor at a desired stationary prole. For a simple study without convection, the dissipation condition holds thanks to the irreversible entropy production.

Keywords: Applications of Observer Design, Biological and Biomedical Systems
Abstract: An observer for the reconstruction of the state of the phenomenological two time-scale model of the microalgae growth, so-called photosynthetic factory model formally described as a bilinear system, is designed. Three states of the model form the probability vector and while one of the states is measurable in real time the second is available only in integrated quantities. The observer designed here uses both information channels to increase precision of the reconstruction. The results are demonstrated on simulations.

Keywords: Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems, Dissipativity, Dynamical Systems Techniques
Abstract: The problem of moment matching with preservation of port Hamiltonian and gradient structure is studied. Based on the time-domain approach to linear moment matching, we characterize the (subset of) port Hamiltonian/gradient models from the set of parameterized models that match the moments of a given port Hamiltonian/gradient system, at a set of finite points.

Keywords: Lyapunov Methods, System Inversion, Chemical Process
Abstract: This paper is concerned with adaptive stabilization of open loop unstable fluidized bed spray granulation with internal product classification by means of nonlinear feedback control. Since the process model is represented by a nonlinear partial integro-differential equation, direct stabilization of the particle size distribution in a L_p or L_∞ norm is difficult. To overcome this problem a stability notion using two generalized distance measures, the discrepancies, is used. It is shown that the adaptive version of the resulting discrepancy based control law is able to cope with uncertainties present in industrial applications.

Keywords: Numerical Methods, Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems, Dissipativity
Abstract: The study of a fractional Burgers equation arising in nonlinear acoustics is presented. The motivation comes from an elementary model of shock waves in brass wind instruments, that proves useful in musical acoustics. Such a model results from the coupling of a conservative nonlinear system with a dissipative term; here the dissipation is represented by a fractional derivative in time, for which equivalent diffusive representations can be efficiently used: in a first part, strong solutions, weak solutions and energy balances are examined. In a second part, ad hoc numerical schemes are derived, in order to capture all the physical phenomena at stake in the original model, and to get rid, as far as possible, of the spurious numerical effects which are highly undesirable: to this end, conservative schemes for hyperbolic conservation laws, diffusive realizations for the fractional derivatives and integrals, and splitting of the two are being used.

Keywords: Passivity, Stabilization, Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems
Abstract: The aim of this paper is to present a simple extension of the theory of linear, distributed, port-Hamiltonian systems to the nonlinear scenario. More precisely, an algebraic nonlinear skew-symmetric term has now been included in the PDE. It is then shown that the system can be equivalently written in terms of the scattering variables, and that these variables are strictly related with the Riemann invariants that appear in quasi-linear hyperbolic PDEs. For this class of PDEs, several results about the existence of solutions, and asymptotic stability of equilibria have already been presented in literature. Here, these results have been extended and applied within the port-Hamiltonian framework, where are suitable of a nice physical interpretation. The final scope is the boundary asymptotic stabilisation of a nonlinear flexible beam with a free-end, and full actuation on the other side.

Keywords: Nonlinear Hybrid Automata, Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems
Abstract: Critical probability of a cellular automaton is investigated via a novel approach of back-ultradiscretization. Specifically, back-ultradiscretization of a gossip protocol provides a conservative yet analytical lower bound, which is usually hard to be evaluated in the form of cellular automata. Comparison of theoretical and numerical values are provided for several representative grids to evaluate efficacy of the proposed approach.

Keywords: Stabilization, Dissipativity, Bilinear Systems
Abstract: Stabilizing a quantum system in a desired state has important implications in quantum information science. In control engineering, stabilization is usually achieved by the use of feedback. The closed-loop control paradigm consists of measuring the system in a non-destructive manner, analyzing in real-time the measurement output to estimate the dynamical state and finally, calculating a feedback law to stabilize the desired state. However, the rather short dynamical time-scales of most quantum systems impose important limitations on the complexity of real-time output signal analysis and retroaction. An alternative control approach for quantum state stabilization, bypassing a real-time analysis of output signal, is called reservoir engineering.

In this paper, we start with a general description of quantum reservoir engineering. We then apply this method to stabilize the ground state (lowest energy state) of a single two-level quantum system. Applying the averaging theorem and some simple Lyapunov techniques, we prove the convergence of our proposed scheme. This scheme has recently been successfully implemented on a superconducting qubit and has led to a fast and reliable reset protocol for these qubits.

Keywords: Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems, Control of Mechanical, Electrical and Process Systems, Smart Structures
Abstract: The random sample consensus (RANSAC) algorithm is frequently used in computer vision to estimate the parameters of a signal in the presence of noisy and even spurious observations called gross errors. Instead of just one signal, we desire to estimate the parameters of multiple signals, where at each time step a set of observations of generated from the underlying signals and gross errors are received. In this paper, we develop the recursive RANSAC (RRANSAC) algorithm to solve the inherent data association problem and recursively estimate the parameters of multiple signals without prior knowledge of the number of true signals. We compare the performance of RRANSAC with several existing algorithms, and also demonstrate the capabilities of RRANSAC in an aerial geolocation problem.

Keywords: Observability and Observer Design, Dynamical Systems Techniques, Backstepping
Abstract: For nonlinear systems affine in the input with state x in R^n, input u in R and output y in R, it is a well-known fact that, if the function mapping (x, u, ..., u^(n-1)) into (u, ..., u^(n-1),y, ..., y^(n-1)) is an injective immersion, then the system can be locally transformed into an observability normal form with a triangular structure appropriate for a high-gain observer. In this technical note we extend this result to the case of systems not necessarily affine in the input and such that the injectivity condition holds for the function mapping (x, u, ..., u^(p-1)) into (u, ..., u^(p-1),y, ..., y^(p-1)) with p >= n. The forced uncertain harmonic oscillator is taken as elementary example to illustrate the theory.

Keywords: Observability and Observer Design, Lyapunov Stability Methods, Control of Sampled Data Systems
Abstract: This paper deals with the design of high gain observers for a class of continuous dynamical systems with discrete-time measurements. Indeed, different approaches based on high gain techniques have been followed in the literature to tackle this problem. Contrary to these works, the measurement sampling time is considered to be variable. Moreover, the new idea of the proposed work is to synthesize an observer requiring the less knowledge as possible from the output measurements. This is done by using an updated sampling time observer. Under the global Lipschitz assumption, the asymptotic convergence of the observation error is established. As an application of this approach, an estimation problem of state of an academic bioprocess is studied, and its simulation results are discussed.

Keywords: Observability and Observer Design, State Estimation and Applications
Abstract: In this paper, a quantitative measure of partial observability is definition for PDEs. The quantity is proved to be consistent in well-posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is introduced. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. The consistency theorem is exemplified using a Burgers' equation.

Keywords: Observability and Observer Design, State Estimation and Applications
Abstract: The objective of this work is to develop some design methods of interval observers for a class of nonlinear continuous-time systems. It is assumed that the estimated system can be represented as a superposition of the nominal subsystem (belonged to the class of uniformly observable systems) and a Lipschitz nonlinear perturbation vanishing at the origin. Then it is shown there exists an interval observer for the system that estimates the set of admissible values for the state consistent with the output measurements. An example of the observer application is given with computer simulation results.

Keywords: Observability and Observer Design, State Estimation and Applications, Geometric Methods
Abstract: In this paper, the design of an unknown input observer is considered. The main contribution consists in the obtention of a sufficient condition to design an observer which estimates a part of the state independently of the knowledge of some inputs. Based on the geometric appraoch, a sufficient condition for the existence of an unknown input observer for state affine systems up to output injection is given. This approach is illustrated in a numerical example.

Keywords: Automotive Systems Marine Systems, Optimal Control
Abstract: Optimal control of nonlinear systems provides a major challenge in control engineering. Constraints on the input signals are common to many real-world applications and render the problem to be tackled even more complicated. This paper proposes a method to map the input constraints by nonlinear functions to the state equations of the system, afterwards an approximation of the solution of the resulting optimization problem is calculated by means of a dynamic extension to the state of the system. The approach is applied in the control of test benches for internal combustion engines, where speed and torque references need to be tracked at the crankshaft of the engine. Simulation results using a high-quality simulator, also regarding effects that have not been included in the model for controller design, show the performance of the proposed approach.

Keywords: Experiment Design, Optimal Control, Aerospace
Abstract: An optimal input design technique for aircraft uncertain parameter estimation is presented in this paper. The original idea is the combining of a dynamic programming method and interval analysis for the optimal input synthesis. This approach does not imply the estimation of a nominal value for parameter and allows to include realistic practical constraints on the input and output variables. The precise description of the approach is followed by an application in aerospace sciences.

Keywords: Optimal Control, Hybrid Nonlinear Systems, Automotive Systems Marine Systems
Abstract: Most energy management systems for hybrid electric vehicles rely on information stored in lookup tables, to define the current mode of operation under certain circumstances. In this paper it is demonstrated how the theory of hybrid optimal control can be used to calculate an initial parameter set for the calibration of parallel hybrid electric vehicles. After solving a hybrid optimal control problem for the fuel optimal operation of the vehicle, taking into account continuous as well as discrete dynamics, the results can be used to automatically calculate lookup-tables for optimal gear shifts, optimal torque-split between motor/generator and internal combustion engine and the determination of the drive mode (electric or hybrid mode). The algorithms proposed are easy in their application and can be used for other hybrid vehicle configurations as well and therefore constitute a valuable tool for the initial calibration.

Keywords: Aerospace and Marine Applications, Automotive Systems Marine Systems, Robotics
Abstract: The L1 adaptive control scheme has proven its effectiveness and robustness in various fields thanks to its particular architecture where robustness and adaptation are decoupled. It was though noted that whenever the trajectory is varying, an inherent lag is present compared to other adaptive schemes due to the presence of a filter in the control architecture. To achieve a better tracking, we propose extending the architecture of the L1 controller by augmenting it with a control input that could take the form of a nonlinear proportional or a proportional integral term. The extended scheme is validated through simulations via an illustrative example as well as experimental results performed on an underwater vehicle.

Keywords: Experiment Design, Geometric Methods, Stabilization
Abstract: This contribution deals with flatness based control of a laboratory model of a gantry crane. The mechanical model has 3DOFs, where a trolley can be moved on a rail, the load is fixed at the end of a rope and can be lifted or lowered by coiling or uncoiling this rope on a cylinder. Under the assumption that the rope is always stretched, the underactuated system is not input to state linearisable but it is flat with the coordinates of the load as flat output. Since the flat output coincides with the variables to be controlled, a flatness based design for trajectory tracking and stabilisation is indicated. The design of the tracking control is accomplished in two steps. First, the system is exactly linearised by a quasi-static state feedback. Subsequently, for the linear system a feedback with integral parts is designed such that the motion of the load is stabilised about the reference trajectories. Moreover, the control law is extended by terms which approximately compensate for the friction occurring at the gantry crane. Finally, the setting of the controller parameters is discussed and measurement results are presented, which demonstrate an excellent tracking behaviour and disturbance attenuation.

Keywords: Geometric Methods
Abstract: We study flatness of two-input control-affine systems, defined on an n-dimensional state-space. We give a complete geometric characterization of systems that become static feedback linearizable after a one-fold prolongation of a suitably chosen control. They form a particular class of flat systems: they are of differential weight n+3. We provide a system of first order PDE's to be solved in order to find all minimal flat outputs. We illustrate our results by two examples: the induction motor and the polymerization reactor.

Keywords: Optimal Control, Necessary Conditions, Geometric Methods
Abstract: This paper provides a detailed discussion of the second covariant derivative of a map and its role in the Lie group projection operator approach (a direct method for solving continuous time optimal control problems).

We begin by briefly describing the iterative geometric optimal control algorithm and summarize the general expressions involved. Particular emphasis is placed on the expressions related to the search direction subproblem, writing them in a new compact form by using a new operator notation.

Next, we show that the covariant derivative of a map between manifolds endowed with affine connections plays a key role in obtaining the required local quadratic approximations for the Lie group projection operator approach.

We present a new result for computing an approximation of the parallel displacement associated with an affine connection which is an affine combination of two (or more) connections. As a corollary, an extremely useful approximation of the parallel displacement relative to the Cartan-Schouten (0) connection on Lie groups is obtained.

Keywords: Geometric Methods, Linear Algebraic Methods
Abstract: We consider left-invariant control affine systems evolving on Lie groups. In this context, feedback equivalence specializes to detached feedback equivalence. We characterize (local) detached feedback equivalence in a simple algebraic manner. We then classify all (full-rank) systems evolving on three-dimensional Lie groups. A representative is identified for each equivalence class. Systems on the Heisenberg group, the Euclidean group, and orthogonal group are treated in full, as typical examples. In these three cases, simple algebraic characterizations of the equivalence classes are also exhibited. A few remarks conclude the paper.

Keywords: Geometric Methods, Dynamical Systems Techniques
Abstract: This paper investigates a class of Lagrangian control systems with n degrees-of-freedom (DOF) and n-1 actuators, assuming that n-1 virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which the reduced dynamics are those of a mechanical system with one DOF and, more generally, under which they have a Lagrangian structure.

Keywords: Linear Algebraic Methods
Abstract: The state realization is called minimal if it is either accessible and observable or its state dimension is minimal. In the linear case those two definitions are equivalent, but not for nonlinear time-invariant systems. It is shown that definitions remain equivalent in case one is searching for minimal realization in a larger class of nonlinear time-varying systems. First, nonlinear realization theory is recasted for time-varying nonlinear systems. A necessary and sufficient realizability condition is given in terms of integrability of certain subspace. The mathematical tools used for this purpose are the algebraic approach of differential forms and the theory of the skew polynomial rings; these tools are again extended from time-invariant to time-varying systems.

Keywords: Geometric Methods
Abstract: In general, controller is designed with respect to one time scale. Time-state control form divides a system into virtual time control part and state control part, and the system is linearized based on two time scales; real and virtual time scales. This paper claims that handling of time scales for a control system should be more flexible, and introduces a multi time-scale transformation as a generalization of time scale transformation. As an example, a mechanical system is linearized under two virtual time scales.

Keywords: Dynamical Systems Techniques, Control of Sampled Data Systems, Fundamental Limitation of Control
Abstract: For nonlinear control systems in discrete time, the global controllability structure within a safe region of the state space is analyzed. The main results characterize those safe regions, where every point can be steered into a relatively invariant subset of complete approximate controllability. Furthermore, for parameter dependent systems, loss of invariance is analyzed.

Keywords: Fundamental Limitation of Control, Stability, Dynamical Systems Techniques
Abstract: In a previous work we developed a convex infinite dimensional linear programming (LP) approach to approximating the region of attraction (ROA) of polynomial dynamical systems subject to compact basic semialgebraic state constraints. Finite dimensional relaxations to the infinite-dimensional LP lead to a truncated moment problem in the primal and a polynomial sum-of-squares problem in the dual. This primal-dual linear matrix inequality (LMI) problem can be solved numerically with standard semidefinite programming solvers, producing a hierarchy of outer (i.e. exterior) approximations of the ROA by polynomial sublevel sets, with a guarantee of almost uniform and set-wise convergence. In this companion paper, we show that our approach is flexible enough to be modified so as to generate a hierarchy of polynomial inner (i.e., interior) approximations of the ROA with similar convergence guarantees.

Keywords: Stabilization, Geometric Methods
Abstract: In this paper, we consider convex optimization problems with constraints. By combining the idea of a Lie bracket approximation for extremum seeking systems and saddle point algorithms, we propose a feedback which steers a single-integrator system to the set of saddle point of the Lagrangian associated to the convex optimization problem. We prove practical uniform asymptotic stability of the set of saddle points for the extremum seeking system for strictly convex as well as linear programs. Using a numerical example we illustrate how the approach can be used in distributed optimization problems.

Keywords: Stability, Lyapunov Methods, Optimal Control
Abstract: Due to its ease of application, the circle criterion has been widely used to guarantee the stability of many anti-windup schemes. While the Popov criterion gives less conservative results, it has been conjectured in the literature that it cannot be used for convex anti-windup synthesis. This paper shows that the conjecture does not necessarily apply in the discrete-time setting. We show how the search for optimal parameters corresponding to the Jury-Lee criterion (a discrete counterpart of the Popov criterion) can be formulated as a convex search via a linear matrix inequality (LMI). The result is then extended to two existing multivariable static anti-windup schemes with stable open-loop plants. Two numerical examples of multivariable anti-windup controller synthesis are provided, and it is shown that in both cases the synthesis using the Jury-Lee criterion can allow better performance than existing methods which use the circle criterion alone.

Keywords: Numerical Methods, Optimal Control, Geometric Methods
Abstract: To identify positive definiteness of functions are important in control theory. However, there does not exist a method to identify the positive definiteness of homogeneous systems with dilation. In this paper, we consider Lipschitz continuous homogeneous functions with dilations. For the functions, we propose a new method to identify the positive definiteness of the functions. Moreover, we apply our proposed method to an optimal homogeneous finite-time control problem. We confirm the effectiveness of the proposed method through the example.

Keywords: Numerical Methods, Computational Efficiency, Parameter Estimation
Abstract: In this paper, we discuss parameter identification for models based on ordinary differential equations in the context of solid oxide fuel cells. In this case, verified methods (e.g. interval analysis), which provide a guarantee of correctness for the computed result, can be of great help for dealing with the appearing uncertainty and for devising accurate control strategies. Moreover, interval arithmetic can be used to discard infeasible areas of parameter space in a natural way and so to improve the results of traditional numerical algorithms. We describe a simulation environment interfacing different verified and floating point based approaches and show how the interchangeability between different techniques enhances parameter identification. Additionally, we give details on possible parallelization of our version of the global interval optimization algorithm on the CPU and the GPU. The applicability of the method and the features of the environment are demonstrated with the help of different fuel cell models.

Keywords: Parameter Estimation, Numerical Methods
Abstract: This paper is concerned with guaranteed parameter estimation in nonlinear dynamic systems in a context of bounded measurement error. The problem consists of finding -- or approximating as closely as possible -- the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds. An exhaustive search procedure is applied, whereby the parameter set is successively partitioned into smaller boxes and exclusion tests are performed to eliminate some of these boxes, until a prespecified threshold on the approximation level is met. In order to enhance the convergence of this procedure, we investigate the use of optimization-based domain reduction techniques for tightening the parameter boxes before partitioning. We construct such bound-reduction problems as linear programs from the polyhedral relaxation of Taylor models of the predicted outputs. When applied to a simple case study, the proposed approach is found to reduce the computational burden significantly, both in terms of CPU time and number of iterations.

Keywords: Robustness, Variable Structure Control and Sliding Mode, Nonlinear Model Predictive Control Theory and Applications
Abstract: In previous work, control-oriented models have been derived for solid oxide high-temperature fuel cell systems. In these models, interval variables have been used to describe uncertainty due to a limited knowledge about system parameters and to handle effects of electric load variations on the temperature distribution in the fuel cell stack module as well as bounded measurement uncertainty. To deal with these types of uncertainty both in the design of robust controllers and during their online usage, interval techniques can be employed successfully. These control procedures make use of the basic principles of either sliding mode control or predictive control. The corresponding algorithms and the prerequisites for their real-time capable implementation using software libraries for interval arithmetic and algorithmic differentiation are described in this paper. Experimental results show the efficiency of these control laws for a fuel cell test rig that is available at the Chair of Mechatronics at the University of Rostock.

Keywords: Stability, Lyapunov Methods, Dynamical Systems Techniques
Abstract: We investigate linear programming relaxations to synthesize Lyapunov functions that establish the stability of a given system over a bounded region. In particular, we attempt to discover functions that are more readily useful inside symbolic verification tools for proving the correctness of control systems. Our approach searches for a Lyapunov function, given a parametric form with unknown coefficients, by constructing a system of linear inequality constraints over the unknown parameters. We examine two complementary ideas for the linear programming relaxation, including interval evaluation of the polynomial form and "Handelman representations" for positive polynomials over polyhedral sets.

Our approach is implemented as part of a branch-and-relax scheme for discovering Lyapunov functions. We evaluate our approach using a prototype implementation, comparing it with techniques based on Sum-of-Squares (SOS) programming. A comparison with SOSTOOLS is carried out over a set of benchmarks gathered from the related work. The evaluation suggests that our approach using Simplex is generally fast, and discovers Lyapunov functions that are simpler and easy to check. They are suitable for use inside symbolic formal verification tools for reasoning about continuous systems.

Keywords: System Inversion, Parameter Estimation, Hybrid Nonlinear Control Systems
Abstract: The paper is devoted to development of control algorithms for nonlinear parametrically uncertain systems. Original system dynamics is approximated by a set of local NARX models combined by a special mixing rule. Algorithm for local models' parameters estimation and structure adjustment has been developed. Proposed approach allows straightforward designing of the combined feedforward/feedback controller.

Keywords: Algebraic Methods, Computational Complexity
Abstract: The paper addresses the problem of dynamic feedback linearization of discrete-time nonlinear control systems. Analogously to the continuous-time case, necessary and sufficient conditions for flatness property are obtained and showed to be equivalent to previously known results on feedback linearizability by endogenous dynamic feedback. An example is added to illustrate the results.

Keywords: Algebraic Methods, Optimal Control
Abstract: Active valves are most effective tools to control gas flow in compressors if fast transitions between the open mode and closed mode are needed. Unfortunately, an accurate model including several nonlinear effects and in particular the resistance and gas flow forces is not available, and this prevents the use of standard model based approaches for time optimal control. However, the repetitive nature of the operation of valves suggests the use of learning methods to track a reference in spite of the insufficient information on the control behavior, thus shifting the problem from the search of the time optimal control to the search of the reference corresponding to its solution. To this end, in this paper, a previously proposed algorithm for the iterative determination of the fastest feasible trajectory is analyzed in terms of convergence conditions and applied to the valve model.

Keywords: Linear Algebraic Methods
Abstract: In this paper the concept of eigenvalues and eigenvectors of nonlinear systems, both continuous- and discrete-time, is suggested. It represents a generalization of the concept known from linear control theory. Some basic properties, like invariance of eigenvalues under a (nonlinear) change of coordinates, possibility to transform the system to the diagonal form and, respectively, to the feedforward form are then shown.

Keywords: Observability and Observer Design, Algebraic Methods
Abstract: In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is no observability criterion for nonlinear systems corresponding to the PBH test. In this study, we generalize the observability PBH test for nonlinear systems using pseudo-linear transformation.

Keywords: Switching Control, Stabilization, Linear Algebraic Methods
Abstract: In this note we prove that if a switched system {cal F} formed by a pair of linear vector fields of R^2 is asymptotically controllable, then the discrete time operator associated to {cal F} admits at least one real eigenvalue lambda, with |lambda|<1. For the particular case at hand, this is an improvement of previous existing results.