Filtered adaptive constrained sampled‐data control for uncertain multivariable nonlinear systems

Abstract

AbstractA filtered adaptive constrained sampled‐data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low‐pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed‐loop system with the sampled‐data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled‐data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.