Adaptive Control with Guaranteed Contraction Rate for Systems with Actuator Saturation

The problem of adaptive control of linear discrete-time systems with actuator saturation and unknown parameters is investigated. A novel optimal control method is presented first for linear systems with known parameters and constant actuator saturation by introducing a Lyapunov function and a performance cost function that are both dependent on a contraction rate parameter. Based on the obtained guaranteed contraction-rate control method, an adaptive control algorithm is derived for systems containing unknown system parameters and time-varying actuator saturation. To show that the closed-loop system is stable and that the adaptive control algorithm is convergent, the Lyapunov function is supplemented by an additional part defined by the trace of a quadratic function of the controller gain. The effectiveness and potential of the presented method is demonstrated by a numerical example.