Indefinite linear quadratic optimal control problem for uncertain random discrete-time systems

We consider an optimal control problem known as indefinite linear quadratic (ILQ) control for discrete-time linear systems that are subject to uncertainty and randomness. By applying chance theory, we propose an uncertain random ILQ optimal control problem in which cost weighting matrices are indefinite. Then we employ the Bellman's principle and design recursive equations (REs) to solve the ILQ problem. Necessary condition for the existence of optimal feedback control and sufficient condition for the well-posedness of ILQ problem are discussed by solving REs. Additionally, an illustrative numerical example is given.