Monitoring strategies in adaptive sliding mode control and event-triggered extremum seeking

Abstract

This thesis proposes monitoring strategies for adaptive sliding mode controllers and event-triggered extremum seeking. The new adaptive sliding mode and unit vector controllers use output feedback for a class of nonlinear systems and can deal with parametric uncertainties and (un)matched disturbances with unknown upper bounds. Finite-time convergence of the tracking error to a predefined neighborhood of the origin of the closed-loop system is proved with guaranteed transient and steady-state performance. The novelty of our result lies on two important adaptation tools: monitoring and barrier functions. Simulation results including the application to Anti-lock Braking System and Overhead-crane to illustrate the advantages of the proposed adaptive control strategies. Finally, based on static maps, this thesis proposes event-triggered schemes for both scalar and multivariable extremum seeking. While the extremum seeking allows the output of a nonlinear map to be held within a vicinity of its extremum, the eventtriggered strategy is responsible to execute the control task aperiodically by using a monitoring mechanism. Static and dynamic triggering condition are developed. Integrating Lyapunov and averaging theories for discontinuous systems, a systematic design procedure and stability analysis are developed. Illustration of the benefits of the new control method are presented using consistent simulation results, which compare the static and the dynamic triggering approaches.Também disponível on-line.