A novel cautious controller to uncertain models arising in stochastic control

In this paper we present the Riccati solution of linear quadratic control problems with input and state dependent noise. The proposed solution will be referred to as the cautious Riccati solution. It is suitable for deterministic and stochastic systems characterised by functional uncertainty. Uncertainty of the system equations is quantified using a state and control dependent noise model. The derived optimal control law is shown to be of cautious type controllers. Since the problem considered in this paper is a minimisation problem subject to equality constraints, the derivation of the cautious Riccati solution is based on defining a set of Lagrange multipliers. The cautious Riccati solution is implemented to linear multi dimensional control problem and compared to the certainty equivalent Riccati solution.