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Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces
This article is a revised version of the lectures given by the author at KROMSH-2019. These lectures are devoted to describing a few different ways...
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Pontryagin Maximum Principle for Fractional Delay Differential Equations and Controlled Weakly Singular Volterra Delay Integral Equations
This article explores two distinct issues. To begin with, we analyze the Pontriagin maximum principle concerning fractional delay differential...
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Modifications of the Pontryagin Conditions in the Problem of Approach of Conflict-Controlled Objects
The authors consider the problem of approach of controlled objects in dynamic game problems and formulate modified sufficient conditions for the game...
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The Pontryagin Maximum Principle Foroptimal Control Problem with an Asymptotic Endpoint Constraint Under Weak Regularity Assumptions
We present a version of the Pontryagin maximum principle for the general infinitehorizon optimal control problem with an additional specific...
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Stable Sequential Pontryagin Maximum Principle in Optimal Control Problems with Phase Restrictions
In this paper, we obtain optimality conditions in an optimal control problem with pointwise phase constraints of the equality and inequality types...
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On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems
AbstractWe consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a...
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The Pontryagin Maximum Principle
This chapter is devoted to a qualitative analysis of some adjoint linear dynamics. We investigate the free endpoint control problem. In this chapter,...
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From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory
Four classical systems, the Kelvin gyrostat, the Maclaurin spheroids, the Brouwer rotating saddle, and the Ziegler pendulum have directly inspired...
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Pontryagin-Type Stochastic Maximum Principle and Beyond
The main purpose of this chapter is to derive first order necessary conditions, i.e., Pontryagin-type maximum principle for optimal controls of...
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Optimal sampled-data controls with running inequality state constraints: Pontryagin maximum principle and bouncing trajectory phenomenon
In the present paper we derive a Pontryagin maximum principle for general nonlinear optimal sampled-data control problems in the presence of running...
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On Representations of Groups and Algebras in Spaces with Indefinite Metric
The paper contains a survey of known results on the structure of J -symmetric operator algebras in Pontryagin and Krein spaces, as well as on...
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Direct Method for Solving Game Problems of Approach of Controlled Objects
The authors analyze the problem of approach of controlled objects in dynamic game problems. The sufficient conditions for the game termination in a...
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Stable Pontryagin–Thom construction for proper maps
We will present proofs for two conjectures stated in Rot (Homotopy classes of proper maps out of vector bundles, 2020. ar**v:1808.08073 ). The first...
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Minimal Passive Realizations of Generalized Schur Functions in Pontryagin Spaces
Passive discrete-time systems in Pontryagin space setting are investigated. In this case the transfer functions of passive systems, or characteristic...
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Optimal Economic Growth Problem
We study the optimal economic growth model based on the controlled Kaldor businesscycle model and formulated as an infinite-horizon optimal control...
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Application of the Maximum Principle to Minimizing Total Production Costs
There are no common methods of the search for optimal solutions to problems of economic dynamics. Application of variational methods is possible for...
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Optimal Control, Contact Dynamics and Herglotz Variational Problem
In this paper, we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin maximum principle. As...
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Spectral Decompositions of Selfadjoint Relations in Pontryagin Spaces and Factorizations of Generalized Nevanlinna Functions
Selfadjoint relations in Pontryagin spaces do not possess a spectral family completely characterizing them in the way that selfadjoint relations in...