Optimal initial value compensation for fast settling times in mode-switching control systems

This paper presents an approach to state initialization of heterogeneous mode-switching controllers. It is shown how the controller initialization that achieves the minimal settling time for the closed-loop system can be computed via convex optimization. Algorithms are given that minimize the worst-case settling time for all initial values in a polytope or an ellipsoid. The approach can also account for state and control constraints. Special attention is given to systems with bias disturbance and it is shown how the worst-case settling time can be minimized also when the exact value of the bias is not known. Finally, we show how the settling times can be improved further by adding an impulsive control at the switching instant. The impulsive control can be optimized jointly with the initial value compensator to achieve a minimal settling time