Efficient Global Solutions to Single-Input Optimal Control Problems via Approximation by Sum-of-Squares Polynomials

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Rodrigues, D (Author) Other; Mesbah, A (Author) Other

Journal

Title: IEEE Transactions on Automatic Control

Vol. 67

Pages: 4674-4686

ISSN: 0018-9286

Publisher: IEEE

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 2 Citations

Other information

Authenticus ID: P-00X-68A

DOI: 10.1109/tac.2022.3165481

Abstract (EN): Optimal control problems are prevalent in model-based control, state and parameter estimation, and experimental design for complex dynamical systems. An approach for obtaining solutions to these problems is based on the notion of parsimonious input parameterization and comprises two tasks: the enumeration of arc sequences followed by the computation of optimal values of a small number of decision variables for each sequence. This article proposes an efficient global solution method for single-input optimal control problems for nonlinear dynamical systems with a potentially large number of states or complex dynamics via sum-of-squares polynomials and parallel computing. The method approximates the problem for a given arc sequence as a polynomial optimization problem that can be efficiently solved to global optimality via semidefinite programming. It is established that the difference between the cost obtained by the proposed method and the globally optimal cost of the original problem is bounded and depends on the polynomial approximation error. The method is illustrated by simulation examples of a reaction system and a rocket.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13