Analysis of NMPC Algorithm Based on Reduced Precision Solution Criteria

This paper studies the stability of nonlinear model predictive control (NMPC) based on sub-optimal solution obtained under reduced precision solution (RPS) criteria. NMPC needs to solve the optimal control problem (OCP) quickly and the input is injected into the controlled plant in time. Traditional convergence criteria in optimization algorithms usually cost excessive long computation time with little improvement of solution, which results in degradation of control performance eventually. RPS criteria are new convergence criteria for deciding whether the current iterate is good enough and whether the optimization procedure should be terminated. It can terminate the optimization process timely. This work gives the proof of the rps-NMPCs property. Simulations are done to analyze the effect of disturbance, especially when computational delay exists, on the closed-loop system controlled by rps-NMPC, and demonstrate that the algorithm owns good stability when disturbance exists.