Fixed-Time Composite Learning Control of Robots With Prescribed Time Error Constraints

This article investigates the adaptive composite learning control problem of robots subject to uncertain dynamics and prescribed time error constraints. Existing prescribed time error constraint methods only achieve semiglobal results or guarantee system order-dependent convergence rate. In this article, by integrating a new prescribed time performance function into a tracking error-based barrier function, a novel prescribed time error constraint method is proposed with the following appealing features: 1) the constraint method is global; 2) the tracking error converges to a compact set with a proximate exponential rate, which can be preassigned by the user regardless of system order; 3) both settling time and compact set can be preassigned by the user. To handle the uncertain dynamics caused by inaccurate measurement of parameters, a novel fixed-time composite learning robot control (FTCLRC) method is developed by combining a newly designed nonsingular fixed-time integral terminal sliding mode and the Moore-Penrose pseudoinverse-based composite learning technique. In comparison with existing composite learning robot control methods that can only ensure exponential convergence, or finite-time convergence, which is dependent on the unpredictable excitation strengths and initial system states, the proposed FTCLRC can guarantee that both the tracking error and parameters estimation error converge to zero in fixed-time, under a weak IE without singularity issue. In particular, the convergence time only depends on the user-designed parameters, independent of the system's initial states, and the unpredictable excitation strengths. Experiment results are given to show the superior performance of the proposed control method.