A stochastic approach for fault-tolerant control of linear systems

A special class of stochastic switched dynamical system is used in order to model a possible faulty linear system. In order to address the synthesis of a fault-tolerant controller, with respect to the class of possible faults under consideration (in the aforementioned model), a stochastic quadratic optimal control problem is set up and solved. A novel class of distributed system of Riccati equations is introduced. It serves as a technical tool for solving the optimal control problem via a stochastic completion of squares argument. Existence and uniqueness of solution for that novel class of distributed system of Riccati equations is proved