Computational study of the suboptimality of one step ahead optimal control

Abstract

Model predictive control (MPC) is a powerful tool to control discrete-time dynamical systems in a wide range of application areas. However, its application in real-time control is challenging because the computational complexity to solve the associated nonlinear programming (NLP) problem increases with the dimension of the problem and the prediction horizon. Reducing this prediction horizon to only one sampling interval yields the so called one step ahead optimal control (OSAOC). In general, OSAOC is suboptimal with respect to the optimal control calculated over the entire control horizon. This paper shows in an illustrative example that the suboptimality of the OSAOC decreases with the problem dimension while presenting a computational cost that is low and increases sublinearly making OSAOC suitable for application to large scale real-time control problems.