Relaxation and existence of optimal controls for systems governed by evolution inclusions in separable Banach spaces

1990 ◽  
Vol 64 (3) ◽  
pp. 573-594 ◽  
Author(s):  
N. S. Papageorgiou
Keyword(s):  
Banach Spaces ◽  
Optimal Controls ◽  
Evolution Inclusions ◽  
Existence Of Optimal Controls

scholarly journals On the existence of optimal controls in Banach spaces

1983 ◽  
Vol 27 (3) ◽  
pp. 395-401 ◽  
Author(s):  
Mohan Joshi
Keyword(s):  
Optimal Control ◽  
Banach Spaces ◽  
Optimal Controls ◽  
Operator Equations ◽  
Existence Of Optimal Controls ◽  
Hammerstein Operator

We prove the existence of an optimal control in Banach spaces for a system characterized by Hammerstein operator equations.

scholarly journals Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Denghao Pang ◽  
Wei Jiang ◽  
Azmat Ullah Khan Niazi ◽  
Jiale Sheng
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Well Posedness ◽  
Optimal Controls ◽  
Lagrange Problem ◽  
Fractional Differential ◽  
Fractional Evolution Systems ◽  
Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

On the Existence of Optimal Controls

1962 ◽  
Vol 84 (1) ◽  
pp. 13-20 ◽  
Author(s):  
L. Markus ◽  
E. B. Lee
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Control ◽  
Optimal Controls ◽  
Optimum Control ◽  
Existence Of Optimal Controls ◽  
Differential Equation Models ◽  
Controlling Processes

The problem of existence of various types of optimum controls for controlling processes which are described by ordinary differential equation models is considered. The results presented enable one to test if there does exist an optimum control in the class of controls under consideration before proceeding to the construction of an optimal control.

scholarly journals Evolution Inclusions in Banach Spaces under Dissipative Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 750
Author(s):  
Tzanko Donchev ◽  
Shamas Bilal ◽  
Ovidiu Cârjă ◽  
Nasir Javaid ◽  
Alina I. Lazu
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Qualitative Properties ◽  
Evolution Inclusions ◽  
Fully Nonlinear ◽  
Limit Solution ◽  
Nonlinear Differential Inclusions ◽  
Limit Solutions ◽  
Lipschitz Conditions ◽  
Integral Solutions

We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions.

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