Further Results on Performance Limits Analysis of Nonlinear Model Predictive Control Based on Value Iteration

This paper addresses performance limits analysis of MPC by comparing performance of MPC with that of finite or infinite horizon optimal control through value-iteration-based dynamic programming method. For receding horizon optimization problems with arbitrary positive definite terminal cost, three different cases are discussed in detail. Novel convergence properties of value iteration are exploited for each case based on principle of optimality. These properties are then utilized to analyze the stability and further quantify performance limits of the closed-loop MPC systems. Upper and lower bounds of the ratio between the cost of MPC and finite or infinite optimal cost are obtained.