Adaptive–Robust Approach for Time-Delayed Control of a Class of Uncertain EL Systems

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To cope with the over- and under-estimation problems of switching gain in the state-of-the-art adaptive-robust control (ARC) designs, this chapter proposes a new ARC strategy, adaptive-robust time-delayed control (ARTDC), for tracking control problem of a class of uncertain EL systems based on the time-delayed estimation (TDE) technique. ARTDC comprises of three parts: a TDE part, a desired dynamics injection part, and an adaptive-robust part. Specifically, the adaptive-robust part provides robustness against the estimation error stemming from the TDE part without the prerequisites of complete knowledge of system model parameters or uncertainty bound. The main feature of the proposed ARTDC is that, compared to the state-of-the-art, it does not involve any threshold value in its ARC law; thus, it allows the switching gain to increase or decrease whenever the error trajectories move away or move close to the switching surface, respectively. Therefore, compared with the existing ARC schemes, ARTDC is able to alleviate the over- and under-estimation problems of switching gain. The proposed method is experimentally validated in comparison with the conventional methods using ‘PIONEER-3’ wheeled mobile robot.