Optimal control of nonlinear systems with unsymmetrical input constraints and its applications to the UAV circumnavigation problem

TL;DR

This paper introduces a new optimal control design for nonlinear systems with asymmetrical, state-dependent input constraints, and applies it to UAV circumnavigation, demonstrating improved control performance through simulations.

Contribution

It presents a novel control scheme that handles unsymmetrical input constraints without requiring internal dynamics to be zero at the origin, extending adaptive optimal control methods.

Findings

Successfully stabilizes nonlinear systems with complex input constraints.

Proves stability and optimality of the control policy.

Demonstrates improved UAV circumnavigation control in simulations.

Abstract

In this paper, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of the constructed optimal control policy, we remove the assumption in the current study for the adaptive optimal control, that is, the internal dynamics should hold zero when the state of the system is in the origin. Particularly, nonlinear control systems with partially-unknown dynamics are investigated and the procedure to acquire the corresponding optimal control policy is presented. The stability for the closed-loop dynamics and the optimality of the obtained control policy are both proved. Besides, we apply the proposed control design framework to solve the optimal circumnavigation problem based on the accumulative Fisher information for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our algorithm is compared with that of the existing circumnavigation control policy in a numerical simulation.