Naslov
Mixed Use of Pontryagin’s Principle and the Hamilton-Jacobi-Bellman Equation in Infinite- and Finite-Horizon Constrained Optimal Control

Autori
Weston, Jerome ; Tolić, Domagoj ; Palunko, Ivana

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Skup
International Conference on Intelligent Autonomous Systems (IAS)

Mjesto i datum
Zagreb, Hrvatska, 13.06.2022. - 16.06.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
optimal control ; constrained control ; optimization

Sažetak
This paper proposes a framework for solving a class of nonlinear infinite- and finite-horizon optimal control problems with constraints. Establishment of existence and uniqueness of solutions to the Hamilton-Jacobi-Bellman (HJB) equation plays a crucial role in verifying well- posedness of a given problem and in streamlining numerical solutions. The proposed framework revolves around infinite-horizon Bolza-type cost functions with running costs exponentially decaying in time. We show \Gamma-convergence of solutions with such cost functions to the solutions of initial constrained (in)finite- horizon problems (that is, without running costs exponentially decaying in time). Basically, we demonstrate how to approximate solutions of (in)finite-horizon constrained optimal problems using our framework. Employing a solver based on the Pontryagin’s Principle, we efficiently obtain optimal solutions for finite- and infinite-horizon problems. Efficiency of the proposed framework is demonstrated in simulation by solving a 3D path planing problem with obstacles for a full nonlinear model of an autonomous underwater vehicle (AUV).

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Elektrotehnika, Računarstvo

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