Optimal and receding horizon drift counteraction control: Linear programming approaches

This paper presents new approaches based on linear programming (LP) and mixed-integer linear programming (MILP) to solve the optimal exit-time control problem, that is to maximize the first exit-time of a system from a prescribed set. For linear discrete-time systems with known disturbance inputs, we show that an optimal solution can be obtained by solving an MILP and suboptimal solutions are obtained via LP. For both the MILP and LP, an iterative scheme is introduced that improves robustness and computation time. In addition, feedback control strategies are formulated using model predictive control (MPC) techniques. Two numerical examples of a linearized van der Pol oscillator and of spacecraft attitude control demonstrate the efficiency of the proposed approaches in solving optimal exit-time control problems.