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

Abstract

The synthesis of a smooth tracking control for Euler-Lagrangian (EL) systems under stringent state, input, and temporal (SIT) constraints is challenging. In contrast to existing methods that utilize prior knowledge of EL model parameters and uncertainty bounds, this study proposes an approximation-free adaptive barrier function-based control policy to ensure local prescribed time convergence of tracking error under state and input constraints. The proposed approach uses smooth time-based generator functions embedded in the filtered tracking error, which is combined with a saturation function that limits control action and confines states within the prescribed limits by enforcing the time-varying bounds on the filtered tracking error. Importantly, corresponding feasibility conditions are derived pertaining to the minimum control authority, the maximum disturbance rejection capability of the control policy, and the viable set of initial conditions, illuminating the narrow operating domain of EL systems arising from the interplay of SIT constraints. Finally, the efficacy of the proposed approach is demonstrated using experimental and comparison studies.