Tube-Based Robust Model Predictive Control of Nonlinear Systems via Collective Neurodynamic Optimization

This paper presents a collective neurodynamic approach to robust model predictive control (MPC) of discrete-time nonlinear systems affected by bounded uncertainties. The proposed control law is a combination of an MPC within an invariant tube for a nominal system and an ancillary state feedback control. The nominal system is first transformed to a linear parameter-varying (LPV) system, and then its MPC signal is computed by solving a convex optimization problem sequentially in real time using a two-layer recurrent neural network (RNN). The ancillary state feedback control is obtained by means of gain scheduling via robust pole assignment using two RNNs. While the nominal MPC generates an optimal state trajectory in the absence of uncertainties, the ancillary state feedback control confines the actual states within an invariant tube in the presence of uncertainties. Simulation results on stabilization control of three mechatronic systems are provided to substantiate the effectiveness and characteristics of the neurodynamics-based robust MPC approach.