Work

Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations

Year: 2025

Type: article

Abstract: This paper applies the Method of Successive Approximations (MSA) based on Pontryagin’s principle to solve optimal control problems with state constraints for semilinear parabolic equations. Error estimates for the first and second derivatives of the function are derived under L∞-bounded conditions. An augmented MSA is developed using the augmented Lagrangian method, and its convergence is proven. The effectiveness of the proposed method is demonstrated through numerical experiments.

Source: Mathematics

DOI: 10.3390/math13071143

Authors: Weilong You, Fu Zhang

Institution: University of Shanghai for Science and Technology

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China