Regularization of Pontryagin Maximum Principle in Optimal Control of Distributed Systems

Sumin, M. I.

doi:10.15826/umj.2016.2.008

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…The proof of the necessity of this condition is based on the dual regularization method [2][3][4] that is stable algorithm of constructing a minimizing approximate solutions in Problem (P 0 p,r ). Sketches of the proofs for the theorems in this section (Theorems 1, 2, 3) and some comments may be found in [14,15].…”

Section: Stable Sequential Pontryagin Maximum Principlementioning

confidence: 99%

Stable Sequential Pontryagin Maximum Principle as a Tool for Solving Unstable Optimal Control and Inverse Problems for Distributed Systems

Sumin

2016

IFIP Advances in Information and Communication Technology

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This article is devoted to studying dual regularization method as applied to parametric convex optimal control problem of controlled third boundary-value problem for parabolic equation with boundary control and with equality and inequality pointwise state constraints. These constraints are understood as ones in the Hilbert space L2. A major advantage of the constraints of the original problem which are understood as ones in L2 is that the resulting dual regularization algorithm is stable with respect to errors in the input data and leads to the construction of a minimizing approximate solution in the sense of J. Warga. Simultaneously, this dual algorithm yields the corresponding necessary and sufficient conditions for minimizing sequences, namely, the stable, with respect to perturbation of input data, sequential or, in other words, regularized Lagrange principle in nondifferential form and Pontryagin maximum principle for the original problem. Regardless of the fact that the stability or instability of the original optimal control problem, they stably generate a minimizing approximate solutions for it. For this reason, we can interpret these regularized Lagrange principle and Pontryagin maximum principle as tools for direct solving unstable optimal control problems and reducing to them unstable inverse problems.

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Section: Stable Sequential Pontryagin Maximum Principlementioning

confidence: 99%

Stable Sequential Pontryagin Maximum Principle as a Tool for Solving Unstable Optimal Control and Inverse Problems for Distributed Systems

Sumin

2016

IFIP Advances in Information and Communication Technology

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Regularization of classical optimality conditions in optimization problems of linear distributed Volterra-type systems with pointwise state constraints

Sumin,

Sumin

2024

Russian Universities Reports. Mathematics

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The regularization of classical optimality conditions (COCs) — the Lagrange principle (LP) and the Pontryagin maximum principle (PMP) — in a convex optimal control problem with a strongly convex objective functional and with pointwise state constraints of the equality and inequality type is considered. The control system is defined by a linear functional-operator equation of the second kind of general form in the space L_2^s, the main operator of the righthand side of the equation is assumed to be quasi-nilpotent. Obtaining regularized COCs is based on the dual regularization method. The main purpose of regularized LP and PMP is stable generation of minimizing approximate solutions (MASs) in the sense of J. Warga. Regularized COCs: 1) are formulated as existence theorems of MASs in the original problem with simultaneous constructive representation of these solutions; 2) are expressed in terms of regular classical Lagrange and Hamilton–Pontryagin functions; 3) “overcome” the ill-posedness properties of the COCs and provide regularizing algorithms for solving optimization problems. The article continues a series of works by the authors on the regularization of the COCs for a number of canonical problems of optimal control of linear distributed systems of the Volterra type. As an application of the “abstract results” obtained in the work, the final part considers the regularization of the COCs in a specific optimization problem with pointwise state constraints of the equality and inequality type for a control system with delay.

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Regularization of Pontryagin Maximum Principle in Optimal Control of Distributed Systems

Cited by 2 publications

References 12 publications

Stable Sequential Pontryagin Maximum Principle as a Tool for Solving Unstable Optimal Control and Inverse Problems for Distributed Systems

Stable Sequential Pontryagin Maximum Principle as a Tool for Solving Unstable Optimal Control and Inverse Problems for Distributed Systems

Regularization of classical optimality conditions in optimization problems of linear distributed Volterra-type systems with pointwise state constraints

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