Control strategies with multiple closing instants for linear optimal control problems with disturbances*

Abstract

This paper deals with an optimal control problem for a linear discrete system subject to input and state constraints and unknown bounded disturbances, where the control goal is to minimize a cost function used in linear explicit model predictive control. Since open-loop worst-case solution is conservative or may suffer feasibility problems and dynamic programming solution is computationally demanding, we propose a compromise between those solutions. This compromise is an optimal control strategy that takes into account the state measurements of the system at several future time instants (closing instants). We define control strategies with one and multiple closing instants and propose efficient numerical methods for their construction.