scholarly journals Well-posed control problems related to second-order differential inclusions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Doria Affane ◽  
Mustapha Fateh Yarou
Keyword(s):  
Differential Inclusions ◽  
Optimal Control Problems ◽  
Dimensional Space ◽  
Maximal Monotone ◽  
Second Order ◽  
Control Problems ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
Quadratic Optimal Control ◽  
Well Posed

<p style='text-indent:20px;'>The paper deals with quadratic optimal control problems, we study the equivalence between well-posed problems and affinity on the control for a second-order differential inclusions with two-points conditions, governed by a maximal monotone operator in a finite dimensional space.</p>

KOLMOGOROV'S ε-ENTROPY OF ATTRACTORS FOR LATTICE SYSTEMS

2005 ◽  
Vol 15 (07) ◽  
pp. 2295-2301 ◽  
Author(s):  
SHENGFAN ZHOU ◽  
QIULI JIA ◽  
FUQI YIN
Keyword(s):  
Upper Bound ◽  
Dimensional Space ◽  
Global Attractors ◽  
Second Order ◽  
Finite Dimensional Space ◽  
Lattice Systems ◽  
Covering Property ◽  
Finite Dimensional

In this paper, by using the element decomposition and the covering property of a polyhedron by balls of radii ε in the finite dimensional space, we obtain an upper bound of the Kolmogorov's ε-entropy of the global attractors for the first- and second-order lattice systems.

scholarly journals Value Function and Optimal Control of Differential Inclusions

2015 ◽  
Vol 61 (1) ◽  
pp. 181-193 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Unique Solution ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Value Function ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
The Value Function

Abstract Optimal control system described by differential inclusion with continuous and one sided Perron right-hand side in a finite dimensional space is studied in the paper. We prove that the value function is the unique solution of a proximal Hamilton-Jacobi inequalities.

DUAL FORMULATION OF OPTIMAL PROBLEM FOR CONTINUOUS-TIME SYSTEMS

2005 ◽  
Vol 02 (03) ◽  
pp. 251-258
Author(s):  
HANLIN HE ◽  
QIAN WANG ◽  
XIAOXIN LIAO
Keyword(s):  
Objective Function ◽  
Continuous Time ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Error Response ◽  
Infinite Dimensional ◽  
Dual Formulation ◽  
Finite Dimensional ◽  
Continuous Time Systems ◽  
Time Systems

The dual formulation of the maximal-minimal problem for an objective function of the error response to a fixed input in the continuous-time systems is given by a result of Fenchel dual. This formulation probably changes the original problem in the infinite dimensional space into the maximal problem with some restrained conditions in the finite dimensional space, which can be researched by finite dimensional space theory. When the objective function is given by the norm of the error response, the maximum of the error response or minimum of the error response, the dual formulation for the problems of L1-optimal control, the minimum of maximal error response, and the minimal overshoot etc. can be obtained, which gives a method for studying these problems.

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