New approach to non-fragile robust model predictive control for a class of nonlinear systems with constrained inputs

In this paper, the problem of non-fragile robust model predictive control for a class of nonlinear systems under actuator saturation is addressed. The nonlinearities are assumed to satisfy the Lipschitz condition and the uncertainties in controller gain and system parameters are considered as general additive forms. The primary drawback of conventional MPC is the high computational burden required to solve an online optimization problem, which is particularly significant for real-time systems. To remedy this issue, we propose an online optimization problem with smaller-sized LMIs compared to an existing method. Additionally, to avoid online computational burden, an offline optimization problem is presented to minimize the upper bound of an infinite-horizon cost function. In fact, by using the Lyapunov theory and linear matrix inequalities (LMIs), sufficient conditions are obtained to asymptomatically stabilize the closed-loop system and ensure saturation avoidance. The effectiveness and validity of the proposed method are verified by simulation results and comparisons with existing methods.