Robust Adaptive Control For A Class Of Nonlinear Systems In Cascade Feedback Form

In light of the complex and highly uncertain nature of dynamical systems requiringcontrols, many reliable system models for high performance engineering applications areunavailable. In the face of such high levels of system uncertainty, robust controllers mayunnecessarily sacrifice system performance whereas adaptive controllers will achieve bet-ter performance, because it can tolerate greater system uncertainty and improve systemperformance to a certain extent. In contrast to fixed-gain robust controllers, which main-tain specified constants within the feedback control law to sustain robust performance,adaptive controllers directly or indirectly adjust feedback gains to maintain closed-loopstability and improve performance in the face of system uncertainties. Specifically, in-direct adaptive controllers utilize parameter update laws to identify unknown system pa-rameters and adjust feedback gains to account for system variation, while direct adaptivecontrollers directly adjust the controller gains in response to plant variations. Thus, thispaper will combine adaptive control and robust control to control the nonlinear systems.The present paper proposes a robust H∞-based adaptive backstepping control schemefor the output stabilization of a special class of nonlinear systems in semi-strict feedbackform. In practical applications, this kind of systems possess the feature that the firstsubsystem is a linear uncertain system which naturally introduces H∞technique to beck-stepping procedure such that their advantages are both retained, i.e., not only the robuststability but also the robust performance can be simultaneously ensured. Afterwards,for each design step, in order to cope with unmodelled nonlinearities and external dis-turbances, virtual control signal is designed as the sum of a compensation term and arobust term, where a projection-type adaptive law is utilized to tackle unknown parame-ters. Within Lyapunov framework, the proposed control scheme is proven to guarantee1) the uniformly ultimate boundedness of the system signals with a small bound that canbe made arbitrarily small by suitably choosing control parameters;2) asymptotic outputstabilization once the uncertain nonlinearities and external disturbances vanish; and3)L2-performance of the closed-loop system.Finally, as an applied study, the problem of vibration suppression for semi-car ac-tive suspension systems is investigated, and the electro-hydraulic systems as actuatorsis taken into account and a nonlinear system cascaded of active suspension system and electro-hydraulic subsystem is finally acquired. The procedure includes two steps: first，applying H∞control to active suspension system to achieve multi-object control.Underthe circumstance of least acceleration of vehicle body of vertical displacement and angleof pitch,suspension system range is constrained during the whole time domain process,relative dynamic tire load, the suspension stroke limitation, actuator saturation. Second,as to electro-hydraulic subsystem, by adaptive control,the paper presents an updated pa-rameter law to estimate the uncertainty, which is efective bulk modulus, design the inputof system to conduct model compensation and adaptive parameter, deal with unsettledmodel and parameter uncertainties. The paper testifies the efectiveness of robust H∞backstepping adaptive control by simulation.