Prescribed-Time Composite Learning Tracking Control for High-Order Fully Actuated Systems With Tracking Error and Output Constraints

Abstract

Existing prescribed-time control methods mostly focus on regulation or tracking control during finite time intervals. In this paper, a novel prescribed-time composite learning tracking control scheme that ensures sustained tracking over an infinite time interval is proposed for uncertain high-order fully actuated (HOFA) systems with both tracking error constraints and output constraints. First, a prediction error reconstruction mechanism is developed by utilizing online historical data and regressor extension. Then, the prediction error and tracking error are employed to construct a novel prescribed-time composite learning adaptation law. Based on the parameter estimation, a prescribed-time composite learning tracking controller is developed for HOFA systems with parametric uncertainties, ensuring that both tracking error and parameter estimation error converge to zero within prescribed time under interval excitation (IE) condition and remain zero thereafter. Furthermore, due to the inherent coupling between the constraints on tracking error and output, existing constrained control methods for HOFA systems can only address one of the two constraint issues. To overcome this limitation, we introduce a novel dual-constraint barrier function (DCBF), allowing users to independently prescribe constraining functions for both desired control performance and safety requirements. The proposed method is validated through simulations and experiments on a robot arm to show its effectiveness. Note to Practitioners—This paper aims to investigate the prescribed-time adaptive tracking control problem for uncertain HOFA systems subject to both tracking error and output constraints, with a particular focus on motion planning for uncertain robotic manipulators to meet prescribed performance requirements and physical limitations. The adopted HOFA framework circumvents the complexity explosion inherent in traditional adaptive backstepping and offers a more streamlined control structure. To achieve decoupling between the tracking error and the output constraints, a novel DCBF is proposed that enables both types of constraints to be satisfied concurrently. Moreover, as robotic systems are typically subject to uncertainties, this paper develops a prescribed-time composite learning tracking control strategy that enables the system to fully compensate for uncertainties within the prescribed time and guarantees effective tracking over an infinite time interval. Simulations and experiments on a Denso robotic arm verify the efficacy of the proposed method.