Linear parameter-varying model predictive control for nonlinear systems using general polytopic tubes

Abstract

This paper deals with model predictive control (MPC) for nonlinear systems using linear-parameter varying (LPV) embedding of the nonlinear dynamics (LPVMPC). The proposed LPVMPC can incorporate information of the future evolution of the scheduling parameter over the MPC prediction horizon with uncertainty bounds, which are used to construct anticipated scheduling tubes for robustification. Therefore, this approach is less conservative than the methods that only consider knowledge of the bounds on the scheduling parameter’s rate of variation. The scheduling tubes are employed to synthesize online general polytopic invariant state tubes. The optimization problem of the proposed LPVMPC is a single quadratic program. Recursive feasibility is proven. A numerical example is presented for demonstrating the effectiveness of the proposed LPVMPC algorithm compared to nonlinear MPC and other standard approaches.