Non-overshooting Fixed Time Control of Free-Flying Space Robotic Manipulators with output constraints: An Inverse Optimal Approach

Abstract

Inverse Optimal Control (IOC) features addressing optimal control problem without the need to solve the complex Hamilton-Jacobi-Bellman (HJB) equation. Although IOC has been extensively studied over the recent years, the state of the art lacks the results of achieving a fixed time non-overshooting response with constrained outputs on IOC schemes. In this paper, an adaptive inverse optimal control scheme is proposed to address the tracking problem of free-flying space robotic manipulators subject to system uncertainties and unknown disturbances, which achieves the practical fixed time non-overshooting response with the constrained tracking errors. More precisely, a novel practical fixed time non-singular virtual controller is designed to define the desired dynamics of tracking errors, which features the non-singular $n^{th}$ derivative where $n$ is any positive integers defined by users. Then, an auxiliary variable is designed to work with the virtual controller to guarantee the absence of overshoot even the system is subject to uncertainties and disturbances. After that, a Fixed Time Disturbance Observer (FTDO) based inverse optimal control scheme is finally constructed to achieve a practical fixed time non-overshooting response with the satisfied output constraints. To the best of author's knowledge, this is the first work of simultaneously achieving non-overshooting response, practical fixed time stability, inverse optimality, and constrained output. The stability of the proposed controller is proven by Lyapunov theory, and the effectiveness is verified by numerical simulations.