A Set of Chance-Constrained Robust Stabilizing PID Controllers

Stabilization of linear SISO systems with random uncertain parameters is considered. A closed-loop system inherits random parameters, and it is stable with some probability. The probabilistic design problem is to tune a controller (e.g., a PID-controller) to stabilize the closed-loop system with high probability. Finding suitable parameters is a probabilistic robust stabilization problem (specifically, a chance-constrained problem). The ultimate goal is to describe the whole set of such controllers instead of individual representative. An algorithm is proposed for finding an inner approximation of the set of chance-constrained stabilizing PID-controllers. The method is based on the robust D-decomposition technique and deterministic error set representation of random uncertainty. A few examples with demonstration of the approach are provided and discussed.