Abstract
In this paper we consider a reachability problem for a nonlinear affine-control system with integral constraints, which assumed to be quadratic in the control variables. Under controllability assumptions it was proved [8] that any admissible control, that steers the control system to the boundary of its reachable set, is a local solution to an optimal control problem with an integral cost functional and terminal constraints. This results in the Pontriagyn maximum principle for boundary trajectories. We propose here an numerical algorithm for computing the reachable set boundary based on the maximum principle and provide some numerical examples.
Highlights
We consider here the reachable sets of a nonlinear affine-control system with joint integral constraints on the state and the control
Assuming the controllability property of the linearized system, we proved that any admissible control that steers the control system to the boundary of its reachable set is a local solution to an optimal control problem with an integral cost functional and a terminal constraint
Let us show that any admissible control that steers the control system to the boundary of its reachable set is a local solution to an optimal control problem with an integral cost functional and terminal constraints
Summary
We consider here the reachable sets of a nonlinear affine-control system with joint integral constraints on the state and the control. Assuming the controllability property of the linearized system, we proved that any admissible control that steers the control system to the boundary of its reachable set is a local solution to an optimal control problem with an integral cost functional and a terminal constraint. This leads to the maximum principle for boundary trajectories. The aim of the present paper is to propose a numerical algorithm for computing boundary points of the reachable set This algorithm is based on the solution of equations following from the maximum principle for boundary trajectories
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