Adaptive Robust Control for Uncertain Systems via Data-Driven Learning

Although solving the robust control problem with offline manner has been studied, it is not easy to solve it using the online method, especially for uncertain systems. In this paper, a novel approach based on an online data-driven learning is suggested to address the robust control problem for uncertain systems. To this end, the robust control problem of uncertain systems is first transformed into an optimal problem of the nominal systems via selecting an appropriate value function that denotes the uncertainties, regulation, and control. Then, a data-driven learning framework is constructed, where Kronecker’s products and vectorization operations are used to reformulate the derived algebraic Riccati equation (ARE). To obtain the solution of this ARE, an adaptive learning law is designed; this helps to retain the convergence of the estimated solutions. The closed-loop system stability and convergence have been proved. Finally, simulations are given to illustrate the effectiveness of the method.

Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.