Design of a completely model free adaptive control in the presence of parametric, non-parametric uncertainties and random control signal delay

In this paper, an adaptive controller is developed for discrete time linear systems that takes into account parametric uncertainty, internal-external non-parametric random uncertainties, and time varying control signal delay. Additionally, the proposed adaptive control is designed in such a way that it is utterly model free. Even though these properties are studied separately in the literature, they are not taken into account all together in adaptive control literature. The Q-function is used to estimate long-term performance of the proposed adaptive controller. Control policy is generated based on the long-term predicted value, and this policy searches an optimal stabilizing control signal for uncertain and unstable systems. The derived control law does not require an initial stabilizing control assumption as in the ones in the recent literature. Learning error, control signal convergence, minimized Q-function, and instantaneous reward are analyzed to demonstrate the stability and effectiveness of the proposed adaptive controller in a simulation environment. Finally, key insights on parameters convergence of the learning and control signals are provided. •To show that the Hk unknown parameter matrix must be positive definite or h¯k unknown parameter vector must have positive components to minimize the Q-function.•It is stated that the developed AC algorithm in this paper can be extended to Markov jump nonlinear systems.•Some more recent literature related to our work are reviewed and referenced in the paper.