scholarly journals Extremal solutions to a class of multivalued integral equations in Banach space

1992 ◽  
Vol 5 (3) ◽  
pp. 205-220 ◽  
Author(s):  
Sergiu Aizicovici ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Control Systems ◽  
Integral Equations ◽  
Important Application ◽  
Extremal Solutions ◽  
Original Equation ◽  
Dimensional Control ◽  
Infinite Dimensional ◽  
Integral Inclusion ◽  
Integral Solutions

We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a “bang-bang” theorem for a class of nonlinear, infinite dimensional control systems.

On exact controllability of linear perturbed boundary systems: a semigroup approach

2020 ◽  
Vol 37 (4) ◽  
pp. 1548-1573
Author(s):  
Marieme Lasri ◽  
Hamid Bounit ◽  
Said Hadd
Keyword(s):  
Control System ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exact Controllability ◽  
Dimensional Control ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Semigroup Approach ◽  
Perturbed Linear Systems

Abstract The purpose of this paper is to investigate the robustness of exact controllability of perturbed linear systems in Banach spaces. Under some conditions, we prove that the exact controllability is preserved if we perturb the generator of an infinite-dimensional control system by appropriate Miyadera–Voigt perturbations. Furthermore, we study the robustness of exact controllability for perturbed boundary control systems. As application, we study the robustness of exact controllability of neutral equations. We mention that our approach is mainly based on the concept of feedback theory of infinite-dimensional linear systems.

Relaxation of infinite dimensional control systems

1989 ◽  
Vol 13 (11) ◽  
pp. 1283-1293 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Control Systems ◽  
Dimensional Control ◽  
Infinite Dimensional

scholarly journals Pareto optimality for nonlinear infinite dimensional control systems

1990 ◽  
Vol 13 (2) ◽  
pp. 233-242
Author(s):  
Evgenios P. Avgerinos ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Control Systems ◽  
Pareto Optimality ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Control Constraints ◽  
Optimal Solutions ◽  
Integral Criterion ◽  
Dimensional Control ◽  
Infinite Dimensional ◽  
State Dependent

In this note we establish the existence of Pareto optimal solutions for nonlinear, infinite dimensional control systems with state dependent control constraints and an integral criterion taking values in a separable, reflexive Banach lattice. An example is also presented in detail. Our result extends earlier ones obtained by Cesari and Suryanarayana.

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