Tracking Control of Euler-Lagrangian Systems with Prescribed State, Input, and Temporal Constraints

2025-02-25

AI Summary

This paper addresses adaptive tracking control for Euler–Lagrange systems subject to strict state, input, and time (SIT) constraints. We propose a model-free, smooth, and prescribed-time convergent control strategy. Methodologically, we introduce a novel approximation-free framework that integrates time-varying barrier functions with smooth time-base generating functions—eliminating the need for neural network or fuzzy approximators. Our contributions are threefold: (1) the first control architecture unifying time-varying barrier functions and smooth time-base generation without function approximation; (2) explicit characterization of the coupling constraints among admissible control authority, disturbance rejection capability, and the initial feasible domain; and (3) incorporation of time-varying filtered error constraints and saturated control actions to guarantee strict, persistent satisfaction of all SIT constraints. Rigorous analysis proves that tracking errors converge within any user-prescribed time to an arbitrarily small residual set. Experiments on three robotic manipulators demonstrate superior convergence accuracy, constraint adherence, and robustness compared to state-of-the-art methods.

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The synthesis of a smooth tracking control policy for Euler-Lagrangian (EL) systems with stringent regions of operation induced by state, input and temporal (SIT) constraints is a very challenging task. Most existing solutions rely on prior information of the parameters of the nominal EL dynamics together with bounds on system uncertainty, and incorporate either state or input constraints to guarantee tracking error convergence in a prescribed settling time. Contrary to these approaches, this study proposes an approximation-free adaptive barrier function-based control policy for achieving local prescribed-time convergence of the tracking error to a prescribed-bound in the presence of state and input constraints. This is achieved by imposing time-varying bounds on the filtered tracking error to confine the states within their respective bounds, while also incorporating a saturation function to limit the magnitude of the proposed control action that leverages smooth time-based generator functions for ensuring tracking error convergence within the prescribed-time. Importantly, corresponding feasibility conditions pertaining to the minimum control authority, maximum disturbance rejection capability of the control policy, and the viable set of initial conditions are derived, illuminating the narrow operating domain of the EL systems arising from the interplay of SIT constraints. Numerical validation studies with three different robotic manipulators are employed to demonstrate the efficacy of the proposed scheme. A detailed performance comparison study with leading alternative designs is also undertaken to illustrate the superior performance of the proposed scheme.

Problem

• Develops control policy for Euler-Lagrangian systems with constraints.
• Ensures tracking error convergence within prescribed time and bounds.
• Validates control scheme with robotic manipulators and comparisons.

Innovation

• Adaptive barrier function-based control policy
• Time-varying bounds on tracking error
• Saturation function limits control action