Filtering adaptive tracking controller for multivariable nonlinear systems subject to constraints using online optimization method

Abstract

This paper presents a filtering adaptive tracking control architecture for multivariable nonlinear systems subject to constraints by employing an online optimization method. A piecewise constant adaptive law updates the adaptive parameters which represent the uncertainty estimates by solving the error dynamics between the state predictor and the real system with the neglection of unknowns. A filtering control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. In the control scheme, the nonlinear uncertainty compensation component is always active whereas the tracking component is subject to a switching logic. The controller will remain in the tracking mode as long as there exists feasible solution, otherwise this component will be replaced by a new part updated periodically by numerically solving a constrained optimization problem online. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed-loop reference system, which assumes partial cancellation of uncertainties within the bandwidth of the control signal. Compared to the model predictive control (MPC) method and unconstrained controller, the proposed approach is capable of solving the tracking control problems of multivariable nonlinear systems subject to both constraints and uncertainties.