Global Composite Learning Fixed-Time Control of Robotic Systems With Asymmetric Tracking Error Constraints

Superior parameter convergence is desirable in adaptive robot control as it can enhance the overall stability of the closed-loop system. However, most current studies of adaptive robot control concentrate on parameter convergence in the steady state, parameter convergence speed is rarely investigated. In this article, we propose a novel global composite learning fixed-time control scheme for robotic systems with tracking error constraints requirements. A nonsingular fast integral terminal sliding mode-based composite learning fixed-time controller is designed, which gives the first results that both parameter estimation error and tracking error converge to zero with fast fixed-time speed without singularity. In the composite learning, a modified prediction error is constructed based on online historical data and regressor extension, and both the prediction and tracking error are applied to update parameter estimates such that accurate parameter estimation is obtained under a much weak excitation condition termed interval excitation rather than the typically required stringent persistent excitation condition. Besides, the tracking error constraints are further considered to guarantee prescribed transient behavior for robotic systems. More specifically, by blending a modified error transformation with an asymmetric barrier function, a new tracking error constraints method is proposed to restrict the tracking error within the prescribed asymmetric time-varying boundary. Unlike most existing barrier Lyapunov function-based controls that only achieve semiglobal results, the proposed method not only removes the initial condition-dependent restriction, giving the benefit of global control performance, but also can handle the general case of asymmetric output constraints. Both theoretical analysis and experiments on an industrial manipulator confirm the effectiveness and benefits of the proposed control scheme.