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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| Published in | IEEE transactions on automatic control Vol. 70; no. 6; pp. 4101 - 4108 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.06.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2025.3533420 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Grimaldi, Riccardo A. Astolfi, Alessandro |
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| SubjectTerms | 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 |
| Title | Exact Penalizations for Optimal Control Problems |
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