Exact penalty function approach to constrained optimal control problems

Xing, An-qing; Chen, Z. H.; Wang, C. L.; Yao, Yunpeng

doi:10.1002/oca.4660100207

Cited by 11 publications

(16 citation statements)

References 7 publications

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“…Theorem 4 implies that if w J* we can solve the constrained optimal control problem (1) (4) by solving one single unconstrained problem (5). In general, it is difficult to know the exact value of J.…”

Section: Theoretical Resultsmentioning

confidence: 99%

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The non‐parameter penalty function method in constrained optimal control problems

Xing

1990

International Journal of Stochastic Analysis

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CANADA $4S OAP,This paper is concerned with the generalization, numerical implementation and testing of the non-parameter penalty function algorithm which was initially developed for solving n-dimensional optimization problems.It uses this method to transform a constrained optimal control problem into a sequence of unconstrained optimal control problems. It is shown that the solutions to the original constrained problem. Convergence results are proved both theoretically and numerically.

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Section: Theoretical Resultsmentioning

confidence: 99%

“…It will be shown how a sequence {w of real numbers can be generated automatically by the non-parameter penalty function method. For each w', solve (5) to get a sequence {u(t)} of unconstrained solutions which converges to a solution to the original constrained optimal control problem (1) (4).…”

Section: Introductionmentioning

confidence: 99%

The non‐parameter penalty function method in constrained optimal control problems

Xing

1990

International Journal of Stochastic Analysis

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“…In particular, one can suppose that the integrand is only locally Lipschitz continuous in x and u, and impose the same growth conditions on the Clarke subdifferential (or some other suitable subdifferential), as we did on the derivatives of this functions. Also, it seems worthwhile to analyze connections between necessary/sufficient optimality conditions and the local exactness of penalty functions (cf, the papers of Xing et al, 35,36 and sections 4.6.2 and 4.7.2 in Reference 22).…”

Section: Discussionmentioning

confidence: 99%

Exact penalty functions for optimal control problems II: Exact penalization of terminal and pointwise state constraints

Долгополик

2020

Optim Control Appl Methods

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The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method one can reduce fixed-endpoint problems for linear time-varying systems and linear evolution equations with convex constraints on the control inputs to completely equivalent free-endpoint optimal control problems, if the terminal state belongs to the relative interior of the reachable set. In the nonlinear case, we prove that a local reduction of fixed-endpoint and variable-endpoint problems to equivalent free-endpoint ones is possible under the assumption that the linearized system is completely controllable, and point out some general properties of nonlinear systems under which a global reduction to equivalent free-endpoint problems can be achieved. In the case of problems with pointwise state inequality constraints, we prove that such problems for linear time-varying systems and linear evolution equations with convex state constraints can be reduced to equivalent problems without state constraints, provided one uses the L ∞ penalty term, and Slater's condition holds true, while for nonlinear systems a local reduction is possible, if a natural constraint qualification is satisfied. Finally, we show that the exact L p -penalization of state constraints with finite p is possible for convex problems, if Lagrange multipliers corresponding to the state constraints belong to L p ′ , where p ′ is the conjugate exponent of p, and for general nonlinear problems, if the cost functional does not depend on the control inputs explicitly.

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“…After that, Fletcher 7 introduced the exact penalty function method to find the solution of the continuously differentiable constrained optimization problem. However, many results have been established on exact penalty function method for differentiable and nondifferentiable optimization problems (see, for example, 1,8,9,13,20 ).…”

Section: Introductionmentioning

confidence: 99%

An exact l₁ penalty function method for a multitime control optimization problem with data uncertainty

Jayswal

Preeti

Arana‐Jiménez

2020

Optim Control Appl Methods

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Summary In this article, we study the robust solution set of a multitime first‐order PDE constrained control optimization problem with data uncertainty (MCOPU) and an unconstrained multitime control optimization problem (MCOPU)ρ. We establish the equivalence between a robust optimal solution of (MCOPU) and a robust minimizer of (MCOPU)ρ under the appropriate assumptions. Furthermore, we define the uncertain Lagrange functional for (MCOPU) and show the relationship between the robust solution set of (MCOPU) and (MCOPU)ρ under the convexity hypothesis of uncertain Lagrange functional. Moreover, we present some nontrivial examples to illustrate the established results.

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Exact penalty function approach to constrained optimal control problems

Cited by 11 publications

References 7 publications

The non‐parameter penalty function method in constrained optimal control problems

The non‐parameter penalty function method in constrained optimal control problems

Exact penalty functions for optimal control problems II: Exact penalization of terminal and pointwise state constraints

An exact l₁ penalty function method for a multitime control optimization problem with data uncertainty

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Exact penalty function approach to constrained optimal control problems

Cited by 11 publications

References 7 publications

The non‐parameter penalty function method in constrained optimal control problems

The non‐parameter penalty function method in constrained optimal control problems

Exact penalty functions for optimal control problems II: Exact penalization of terminal and pointwise state constraints

An exact l1 penalty function method for a multitime control optimization problem with data uncertainty

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An exact l₁ penalty function method for a multitime control optimization problem with data uncertainty