Application of Hamilton–Jacobi–Bellman Equation/Pontryagin’s Principle for Constrained Optimal Control

Jerome Weston, Domagoj Tolić () and Ivana Palunko ()
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Jerome Weston: LARIAT-UNIDU – Laboratory of intelligent and autonomous systems at University of Dubrovnik
Domagoj Tolić: LARIAT-UNIDU – Laboratory of intelligent and autonomous systems at University of Dubrovnik
Ivana Palunko: LARIAT-UNIDU – Laboratory of intelligent and autonomous systems at University of Dubrovnik

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 2, No 1, 437-462

Abstract: Abstract This article applies novel results for infinite- and finite-horizon optimal control problems with nonlinear dynamics and constraints. We use the Valentine transformation to convert a constrained optimal control problem into an unconstrained one and show uniqueness of the value function to the corresponding Hamilton–Jacobi–Bellman (HJB) equation. From there, we show how to approximate the solution of the initial (in)finite-horizon problem with a family of solutions that is $$\varGamma $$ Γ -convergent. Optimal solutions are efficiently obtained via a solver based on Pontryagin’s Principle (PP). The proposed methodology is demonstrated on the path planning problem using the full nonlinear dynamics of an unmanned aerial vehicle (UAV) and autonomous underwater vehicle (AUV) involving state constraints in 3D environments with obstacles.

Keywords: Optimal control; Hamilton–Jacobi–Bellman equation; Pontryagin-based numerical solver; Mobile robots; 49J15; 49L25; 49M05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02364-4

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