Linear quadratic optimal sampled data control of linear systems with unknown switched modes and stochastic disturbances

It is nontrivial to control a dynamic system that is switched consistently with a completely unknown switched modes. This problem is further complicated if the system is subject to stochastic disturbance. This paper studies the linear quadratic optimal control problem of linear continuous systems with stochastic disturbance and unknown switched process. By integrating one‐step adaptive estimator with optimal control theory, a linear quadratic optimal stabilization controller based on sampled feedback is developed for systems that are continuous in nature yet switched consistently with unknown modes. It is shown that with the proposed control scheme, both parameter estimate error and system stabilization error are ensured to be bounded, and the existence of the upper bound is explicitly confirmed. The results compliment and extend the existing works on digital feedback control of switched linear continuous systems with unknown switched processes and stochastic disturbances