Observer analysis and synthesis for perturbed Lipschitz systems under noisy time-varying measurements

International audienceIn this paper the observer synthesis problem is studied for nonlinear Lipschitz systems with noisy time-varying sampling and bounded state perturbations. To establish criteria for robust convergence of the observer, we model the impact of sampling by a reset integrator operator. First, generic conditions for the input-to-state stability of a sampled-data system are presented. Second, it is shown how to derive a tractable numerical criterion for the synthesis of a sampled-data Luenberger observer. Then, new conditions for robustness analysis of a known observation gain are given

Stability and stabilization of sampled-data control for lure systems

Este trabalho apresenta um novo método para a análise de estabilidade e estabilização de sistemas do tipo Lure com controle amostrado, sujeitos a amostragem aperiódica e não linearidades que são limitadas em setor e restritas em derivada, em ambos contextos global e regional. Assume-se que os estados da planta estão disponíveis para medição e que as não linearidades são conhecidas, o que leva a uma formulação mais geral do problema. Os estados são adquiridos por um controlador digital que atualiza a entrada de controle em instantes de tempo discretos e aperiódicos, mantendo-a constante entre dois instantes sucessivos de amostragem. A abordagem apresentada neste trabalho é baseada no uso de uma nova classe de looped-functionals e em uma função do tipo Lure generalizada, que leva a condições de estabilidade e estabilização que são escritas na forma de desigualdades matriciais lineares (LMIs) e quasi-LMIs, respectivamente. Com base nestas condições, problemas de otimização são formulados com o objetivo de computar o intervalo máximo entre amostragens ou os limites máximos do setor para os quais a estabilidade assintótica da origem do sistema de dados amostrados em malha fechada é garantida. No caso em que as condições de setor são válidas apenas localmente, a solução desses problemas também fornece uma estimativa da região de atração para as trajetórias em tempo contínuo do sistema em malha fechada. Como as condições de síntese são quasi-LMIs, um algoritmo de otimização por enxame de partículas é proposto para lidar com as não linearidades envolvidas nos problemas de otimização, que surgem do produto de algumas variáveis de decisão. Exemplos numéricos são apresentados ao longo do trabalho para destacar as potencialidades do método.This work presents a new method for stability analysis and stabilization of sampleddata controlled Lure systems, subject to aperiodic sampling and nonlinearities that are sector bounded and slope restricted, in both global and regional contexts. We assume that the states of the plant are available for measurement and that the nonlinearities are known, which leads to a more general formulation of the problem. The states are acquired by a digital controller which updates the control input at aperiodic discrete-time instants, keeping it constant between successive sampling instants. The approach here presented is based on the use of a new class of looped-functionals and a generalized Luretype function, which leads to stability and stabilization conditions that are written in the form of Linear Matrix Inequalities (LMIs) and quasi-LMIs, respectively. On this basis, optimization problems are formulated aiming to compute the maximal intersampling interval or the maximal sector bounds for which the asymptotic stability of the origin of the sampled-data closed-loop system is guaranteed. In the case where the sector conditions hold only locally, the solution of these problems also provide an estimate of the region of attraction for the continuous-time trajectories of the closed-loop system. As the synthesis conditions are quasi-LMIs, a Particle Swarm Optimization (PSO) algorithm is proposed to deal with the involved nonlinearities in the optimization problems, which arise from the product of some decision variables. Numerical examples are presented throughout the work to highlight the potentialities of the method

Event sampled optimal adaptive regulation of linear and a class of nonlinear systems

In networked control systems (NCS), wherein a communication network is used to close the feedback loop, the transmission of feedback signals and execution of the controller is currently carried out at periodic sampling instants. Thus, this scheme requires a significant computational power and network bandwidth. In contrast, the event-based aperiodic sampling and control, which is introduced recently, appears to relieve the computational burden and high network resource utilization. Therefore, in this dissertation, a suite of novel event sampled adaptive regulation schemes in both discrete and continuous time domain for uncertain linear and nonlinear systems are designed. Event sampled Q-learning and adaptive/neuro dynamic programming (ADP) schemes without value and policy iterations are utilized for the linear and nonlinear systems, respectively, in both the time domains. Neural networks (NN) are employed as approximators for nonlinear systems and, hence, the universal approximation property of NN in the event-sampled framework is introduced. The tuning of the parameters and the NN weights are carried out in an aperiodic manner at the event sampled instants leading to a further saving in computation when compared to traditional NN based control. The adaptive regulator when applied on a linear NCS with time-varying network delays and packet losses shows a 30% and 56% reduction in computation and network bandwidth usage, respectively. In case of nonlinear NCS with event sampled ADP based regulator, a reduction of 27% and 66% is observed when compared to periodic sampled schemes. The sampling and transmission instants are determined through adaptive event sampling conditions derived using Lyapunov technique by viewing the closed-loop event sampled linear and nonlinear systems as switched and/or impulsive dynamical systems. --Abstract, page iii

Dissipativity based stability criterion for aperiodic sampled-data systems subject to time-delay

International audienceThis extended abstract presents a dissipativity-based stability analysis of Linear Time Invariant (LTI) systems subjected to aperiodic sampling and time-varying delay. We provide a novel stability criterion which aids in making the trade-offs between maximum allowable sampling interval and delays while guaranteeing stability. Simulation results have been provided to demonstrate the effectiveness of the proposed criterion

Exponential Synchronization of Nonlinear Oscillators Under Sampled-Data Coupling

International audienceThis paper presents a novel approach towards synchronization analysis of nonlinear oscillatory systems, bidi-rectionally coupled via a networked communication channel. The system under consideration is a two-agent nonlinear system, under the constraint that information is transmitted between the two systems using a sampled-data communication strategy that could be periodic or aperiodic. The networked system dynamics is remodelled as a feedback-interconnection of a continuous-time system, and an operator that accounts for the communication constraints. By studying the properties of this feedback-interconnection in the framework of dissipativity theory, we provide a novel criterion that guarantees exponential synchronization. The provided criterion also aids in deciding the trade-off between a bound on the sampling intervals, the coupling gain, and the desired transient rate of synchronization. Finally, the theoretical results are illustrated using a two-agent Fitzhugh-Nagumo system

Exponential Synchronization of Nonlinear Oscillators Under Sampled-Data Coupling

This paper presents a novel approach towards synchronization analysis of nonlinear oscillatory systems, bidi-rectionally coupled via a networked communication channel. The system under consideration is a two-agent nonlinear system, under the constraint that information is transmitted between the two systems using a sampled-data communication strategy that could be periodic or aperiodic. The networked system dynamics is remodelled as a feedback-interconnection of a continuous-time system, and an operator that accounts for the communication constraints. By studying the properties of this feedback-interconnection in the framework of dissipativity theory, we provide a novel criterion that guarantees exponential synchronization. The provided criterion also aids in deciding the trade-off between a bound on the sampling intervals, the coupling gain, and the desired transient rate of synchronization. Finally, the theoretical results are illustrated using a two-agent Fitzhugh-Nagumo system

Observer analysis and synthesis for Lipschitz nonlinear systems under discrete time-varying measurements

International audienceObserver synthesis for nonlinear Lipschitz systems with time-varying sampling is studied. To establish the exponential convergence of the observer, in this paper, we model the impact of the sampling uncertainty by a reset integrator. First, generic conditions for stability of a sampled data system are recalled. Second it is shown how to derive tractable numerical conditions to analyze the robustness of a continuous-time Luenberger observer when the sampling is discrete and time-varying. Then it is demonstrated that this emulation approach can be passed over allowing for the direct computation of an observer gain. Simulations and comparisons with related articles show the efficiency of the proposed methodology