PHYSICS AND MATHEMATICS

Pontryagin's maximum pinciple for a state-constrained optimal control problem governed by a biharmonic equation

D. V. Sugak

Saint-Petersburg State University of Aerospace Instrumentation

Abstract: The article considers the problem of optimal control of biharmonic equation with constraint on the state. The necessary condition of optimality in the form of the Pontryagin's maximum principle was formulated and proved. This result can be useful both for organizing a subsequent computational procedure of successive approximations method, and for qualitative analysis of the problem, perhaps not leading to a final answer, but establishing important components of the solution, meaming an optimal process. It must also be noted that the biharmonic equations describing the features of the optimal control object constantly arise in problems of the mathematical theory of elasticity and related problems of optimization. Phase limitations in setting the optimal control within the problem in question, tend to make it difficult to find a solution.

Keywords: Pontryagin's maximum principle, biharmonic equation, optimum process.

DOI: 10.23670/IRJ.2022.119.5.042