Design of adaptive controllers using partial certainty equivalence principle

Optimal stochastic control problem for general non-linear dynamic system with unknown parameters is considered. An approximative assumption, which has been named partial certainty equivalence (PCE) principle, is suggested for design of adaptive controllers of non-linear and linear stochastic systems. For derivation of a suboptimal controller with the PCE principle the certainty equivalence (CE) assumption is used only for the part of the system states and unknown parameters. The PCE control policy has a simple form for linear systems with unknown parameters. It is suggested in the present paper to design adaptive dual control using the PCE assumption and bicriterial optimization to derive the adaptive controller with the optimal persistent excitation. Simulated examples are used to demonstrate the potential of the suggested method and its superiority over the generally used CE-controllers.