Successive Suboptimal Model Predictive Control Using Sequential Convex Programming

This paper proposes a successive suboptimal model predictive control (MPC) framework based on sequential convex programming for general nonlinear systems. The objective is to transform the nonconvex optimization problem within MPC into convex problems while maintaining feasibility. To address the nonlinear model, we introduce adaptive contraction constraints to account for linearization errors, which ensure the satisfaction of constraints for the accurate predicted trajectory. Furthermore, we propose two general methods to convexify nonconvex constraints. Both methods reduce conservatism and achieve weak loss convexification compared to traditional convexification methods. The proposed framework ensures the feasibility of each subproblem while guaranteeing stability. Additionally, it allows for the interruption of the inner loop at any time, generating a feasible predicted trajectory. Furthermore, we discuss the impact of the weak terminal controller, which does not require monotonicity, on closed-loop stability. Simulation results show that the proposed framework can eliminate the risk of infeasibility within an acceptable computational time, and under some mild assumptions, the weak terminal controller can also ensure closed-loop stability.