Exact Penalizations for Optimal Control Problems

A novel technique to solve optimal control problems with state constraints is proposed. We exploit the theory of exact penalty functions, used in mathematical programming, to construct a systematic procedure to transform two classes of problems with state constraints to equivalent penalized unconstr...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 70; no. 6; pp. 4101 - 4108
Main Authors Grimaldi, Riccardo A., Astolfi, Alessandro
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Constraints
Control systems
Control theory
Infinite horizon
Linear control
Manifolds
Mathematical programming
Matrix decomposition
Nonlinear control
Nonlinear systems
Optimal control
Optimization
optimization algorithms
Penalty function
Programming
Symmetric matrices
Systematics
Vectors
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ISSN0018-9286
1558-2523
DOI10.1109/TAC.2025.3533420

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Summary:A novel technique to solve optimal control problems with state constraints is proposed. We exploit the theory of exact penalty functions, used in mathematical programming, to construct a systematic procedure to transform two classes of problems with state constraints to equivalent penalized unconstrained problems. We focus on a special class of systems with as many states as controls and subject to a set of equality constraints, which reduces the "control authority," both in the case of linear and nonlinear control-affine systems. Two approaches are proposed, and differences, advantages, and drawbacks of such approaches are discussed. Three simple examples illustrate the theory.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2025.3533420