Adaptive predictive control policy for nonlinear stochastic systems

The problem of optimal adaptive predictive control for nonlinear stochastic systems is considered. A classification of various suboptimal approaches is given. A new approximation for the probability measure for the extended state of the system is suggested to derive a new suboptimal control law. It is assumed for this approximation that the system operates in closed-loop feedback mode for one part of the extended state vector and in open feedback loop mode for the other part of this vector. The certainty equivalence (CE) assumption is used only for the first part of the extended state vector. An analytical comparison for the suggested control policy shows its superiority in control quality compared with that of the open-loop optimal control policy in the case of an exactly observed first part of the extended state vector. The upper bound of the performance index is determined for this case. The suggested control policy has a simple form for linear systems with unknown parameters. A simulated example is used to demonstrate the potential of the suggested method and its superiority over the usually applied CE policy