Design of improved adaptive controllers using partial certainty equivalence principle

New approximative assumption of the partial certainty equivalence (PCE) has been suggested for adaptive control of nonlinear and linear stochastic systems. For derivation of a suboptimal controller with the PCE 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. At the same time it provides cautious system behaviour and some persistent excitation required. It is suggested in the present paper to design adaptive control using the PCE assumption and bicriterial optimization for providing the optimal persistent excitation. Thus a dual controller will be derived. The synthesis problem is formulated for general nonlinear systems and considered for linear systems in details. The resulting controller demonstrates improved system behaviour and short time of adaptation. A simulated example is used to demonstrate the potential of the suggested method and its superiority over the PCE and the usually applied CE policies