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

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. In contrast with 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 control policy accomplishes this by utilizing 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 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.