Optimal adaptive guaranteed-cost H-infinity model reference controller design for nonlinear systems

This paper proposes a novel robust adaptive controller for uncertain nonlinear systems subject to external disturbances. The robust part of the controller is designed by coupling the H-infinity and guaranteed-cost control theories. Besides, the adaptive part is developed based on the direct adaptive control strategy. Moreover, the model reference control is included in the proposed control method to achieve good transient response specifications. The control method's optimality is accomplished by performing the design procedure using the Pontryagin Minimum Principle (PMP) approach. In addition, a new optimization method called Black Hole Optimization (BHO) is utilized to improve the optimality of the control method. The Lyapunov stability analysis is implemented to confirm the global asymptotic stability of the closed-loop system. A numerical example is presented as a case study to investigate the proposed controller efficiency. Finally, the results affirm the strength of the proposed controller in compensating the system's nonlinearity and uncertainty under various circumstances, rejecting external disturbances, and achieving perfect asymptotic tracking performance with an adequate control input.