The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval(possibly unknown)minimising a cost functional,while satisfying hard...The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval(possibly unknown)minimising a cost functional,while satisfying hard constraints on the input.In this framework,the minimum-time optimal control problem and some related problems are of interest for both theory and applications.For linear systems,the solution of the problem often relies upon the use of bang-bang control signals.For nonlinear systems,the“shape”of the optimal input is in general not known.The control input can be found solving a Hamilton–Jacobi–Bellman(HJB)partial differential equation(PDE):it typically consists of a combination of bang-bang controls and singular arcs.In this paper,a methodology to approximate the solution of the HJB PDE is proposed.This approximation yields a dynamic state feedback law.The theory is illustrated by means of two examples:the minimum-time optimal control problem for an industrial wastewater treatment plant and the Goddard problem,i.e.a maximum-range optimal control problem.展开更多
文摘The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval(possibly unknown)minimising a cost functional,while satisfying hard constraints on the input.In this framework,the minimum-time optimal control problem and some related problems are of interest for both theory and applications.For linear systems,the solution of the problem often relies upon the use of bang-bang control signals.For nonlinear systems,the“shape”of the optimal input is in general not known.The control input can be found solving a Hamilton–Jacobi–Bellman(HJB)partial differential equation(PDE):it typically consists of a combination of bang-bang controls and singular arcs.In this paper,a methodology to approximate the solution of the HJB PDE is proposed.This approximation yields a dynamic state feedback law.The theory is illustrated by means of two examples:the minimum-time optimal control problem for an industrial wastewater treatment plant and the Goddard problem,i.e.a maximum-range optimal control problem.
