Design of adaptive dual control systems with non-stochastic bounded uncertainty description

Important class of adaptive control systems with non-stochastic description of the uncertainty and disturbances is considered. New approach to the design of the non-stochastic adaptive dual control algorithms is suggested. The elaborated approach is based on the introducing of two new cost functions for optimisation of the control signal and exiting signal added to the control signal. The ellipsoid bounded estimation of the plant parameters is used for the plant parameter estimation and indirect adaptation. This estimation method was also named set-membership estimation. The approach is introduced and described comprehensive using simple controller of self-tuning type. The designed controller, which is used as an example to demonstrate the new suggested method, can be applied to control of nonminimumphase plants. The method can be extended to adaptive controllers of various other types. The violent contrast is attributed to the suggested design method as compared with other dual control approaches for non-stochastic systems with set-membership estimation. The method allows designing of non-stochastic dual adaptive controllers that are very simple computational and consist of the cautious controller with the optimal excitations. Non-stochastic adaptive dual controllers, which are designed using suggested approach, have superiorities over the similar controllers based on the certainty equivalence approach because of the properties of caution and optimal excitation.