Continuous Control for Fully Damped Mechanical Systems With Input Constraints: Finite-Time and Exponential Tracking

A motion continuous control scheme for fully damped mechanical systems with constrained inputs is proposed. It gives the freedom to choose among finite-time and (local) exponential convergence through a simple design parameter. The control objective is achieved from any initial conditions, for desired trajectories that can be physically tracked avoiding actuator saturation and loss of motion error dissipation, globally induced through the aid of the natural damping terms explicitly considered in the open-loop dynamics. The stability analysis is based on a strict Lyapunov function and is formally developed within an appropriate analytical framework that takes into account the time-varying character naturally adopted by the closed loop. Simulation tests are further included.

I. Introduction

Finite-time control through continuous feedback has been a research topic of increasing interest in the last few years. Such an intriguing topic has attracted attention on its need for a suitable analytical framework around its conceptualization and characterization. In this direction, important contributions have been developed for autonomous systems in the works of Bhat and Bernstein [2], [3], by stating a precise definition of a finite-time stable equilibrium, a Lyapunov-function-based criterion for its determination, and a useful characterization for homogeneous vector fields.