Event-triggered control with LQ optimality guarantees for saturated linear systems

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.

[1]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[2]  Alexandre Seuret,et al.  Event-triggered sampling algorithms based on a Lyapunov function , 2011, IEEE Conference on Decision and Control and European Control Conference.

[3]  A. Teel.  Semi-global stabilizability of linear null controllable systems with input nonlinearities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[4]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[5]  Wilfrid Perruquetti,et al.  A state dependent sampling for linear state feedback , 2012, Autom..

[6]  Dragan Nesic,et al.  A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models , 2004, IEEE Transactions on Automatic Control.

[7]  Ricardo G. Sanfelice,et al.  Hybrid Dynamical Systems: Modeling, Stability, and Robustness , 2012 .

[8]  Rafal Goebel,et al.  Hybrid Feedback Control and Robust Stabilization of Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[9]  Sophie Tarbouriech,et al.  Guaranteed stability for nonlinear systems by means of a hybrid loop , 2010 .

[10]  W. P. M. H. Heemels,et al.  Output-based event-triggered control with Guaranteed ℒ∞-gain and improved event-triggering , 2010, 49th IEEE Conference on Decision and Control (CDC).

[11]  Eduardo Sontag.  An algebraic approach to bounded controllability of linear systems , 1984 .

[12]  Alexandre Seuret,et al.  Taking into account period variations and actuator saturation in sampled-data systems , 2012, Syst. Control. Lett..

[13]  Sophie Tarbouriech,et al.  Lyapunov-based hybrid loops for stability and performance of continuous-time control systems , 2013, Autom..

[14]  Paulo Tabuada,et al.  Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks , 2007, IEEE Transactions on Automatic Control.

[15]  Karl Henrik Johansson,et al.  Actuator saturation and anti-windup compensation in event-triggered control , 2012, Discrete Event Dynamic Systems.

[16]  Karl Henrik Johansson,et al.  Comparison between sampled-data control, deadband control and model-based event-triggered control , 2012, ADHS.

[17]  Luca Zaccarian,et al.  Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation , 2011 .

[18]  Sophie Tarbouriech,et al.  Stability and Stabilization of Linear Systems with Saturating Actuators , 2011 .

[19]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.