Control Systems with Actuator Saturation.ppt

Outline Control systems with actuator saturation The classical absolute stability Absolute stability within a finite region Conservatism of the local linear sector condition The generalized sector condition Absolute stability – absolutely invariant ellipsoids For a concave/convex function Under the generalized sector condition Convex hull of absolutely invariant ellipsoids A few topics for future research * * Control Systems with Actuator Saturation A Few Recent Results and Future Topics Zongli Lin University of Virginia USA Control Systems with Actuator Saturation u sat(u) A basic control problem: stabilization global stabilization semi-global stabilization regional stabilization local stabilization Questions of interest: stabilizability type of feedback laws robustness Control Systems with Actuator Saturation Global stabilization (A, B ) is asymptotically null controllable with bounded controls (ANCBC) [Sussmann-Sontag-Yang, 90] in general, nonlinear feedback laws are needed [Fuller, 76] nonlinear, but smooth, stabilizers [Sussmann-Sontag-Yang, Teel, Megretski, Lin,…, 90s] Semi-global stabilization (A, B ) is ANCBC [Lin-Saberi, 93] linear feedback laws [Lin-Saberi, Lin] Regional stabilization (for strictly unstable systems) many results, including the recent ones in [Hu-Lin, Birkhauser, 01] Control Systems with Actuator Saturation For strictly unstable systems Null controllable region with bounded controls [Hu-Lin, 01] Semi-global stabilization on the null controllable region by nonlinear feedback laws [Hu-Lin, 01] In general, nonlinear feedback is needed [Hu-Lin, 03] Robustness with respect to actuator nonlinearities Formulation as an absolute stabilization problem The Classical Absolute Stability Consider a system with a nonlinear component