Stochastic Optimal Control Of Systems For Which Control Variation Increases Uncertainty: A Contribution To The Discrete Time Case

This paper applies the CVIU (Control Variation Increases Uncertainty) approach to a discrete time scenario. Important solution characteristics are indicated, which conceptually preserves the findings in the continuous time case presented in [1]. Mainly, the arising of three control regions in the state space and the association of the value function with a discrete Lyapunov and a modified Riccati equation. The former holds within the inaction region, which is near the origin, and the latter holds for regions far from the origin. The SISO case is developed in full and, in conjunction, a comparison with the LQG solution is presented. An evaluation on the system's performance in the context of poorly known systems closes the paper.