On the Pontryagin maximum principle for constant-time linear control systems in Banach spaces

1979 ◽  
Vol 27 (2) ◽  
pp. 315-321 ◽  
Author(s):  
I. Singer
Keyword(s):  
Maximum Principle ◽  
Control Systems ◽  
Banach Spaces ◽  
Pontryagin Maximum Principle ◽  
Linear Control ◽  
Constant Time ◽  
Linear Control Systems ◽  
Time Linear ◽  
The Pontryagin Maximum Principle

scholarly journals Toward Applications of Linear Control Systems on the Real World and Theoretical Challenges

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 167
Author(s):  
Víctor Ayala ◽  
María Torreblanca ◽  
William Valdivia
Keyword(s):  
Maximum Principle ◽  
Control Systems ◽  
Lie Group ◽  
Real World ◽  
Pontryagin Maximum Principle ◽  
Optimization Problems ◽  
Linear Control ◽  
Linear Control Systems ◽  
Open Problems ◽  
The Pontryagin Maximum Principle

Many significant real world challenges arise as optimization problems on different classes of control systems. In particular, ordinary differential equations with symmetries. The purpose of this review article is twofold. First, we give the information we have about the class of Linear Control Systems ΣG on a low dimension matrix Lie group G. Second, we invite the Mathematical community to consider possible applications through the Pontryagin Maximum Principle for ΣG. In addition, we challenge some theoretical open problems. The class ΣG is a perfect generalization of the classical Linear Control System on the Abelian group Rn. Let G be a Lie group of dimension two or three. Related to ΣG, this review describes the actual results about controllability, the time-optimal Hamiltonian equations and, the Pontryagin Maximum Principle. We show how to build ΣG, through several examples on low dimensional matrix groups.

Stability Analysis of Finite-Level Quantized Discrete-Time Linear Control Systems

2010 ◽  
Vol 16 (3) ◽  
pp. 258-271 ◽  
Author(s):  
Carlos E. de Souza ◽  
Daniel F. Coutinho ◽  
Minyue Fu
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Discrete Time ◽  
Linear Control ◽  
Linear Control Systems ◽  
Time Linear

scholarly journals On exponential dichotomy in Banach spaces

1981 ◽  
Vol 23 (2) ◽  
pp. 293-306 ◽  
Author(s):  
Mihail Megan ◽  
Petre Preda
Keyword(s):  
Banach Space ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Linear Control ◽  
Linear Control Systems

In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems. The obtained results are generalizations of well-known results of W.A. Coppel, J.L. Massera and J.J. Schäffer, K.J. Palmer.

scholarly journals Measurable multifunctions and their applications to convex integral functionals

1989 ◽  
Vol 12 (1) ◽  
pp. 175-191 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Control Systems ◽  
Banach Spaces ◽  
Time Dependent ◽  
Linear Control ◽  
Linear Control Systems ◽  
Integral Functionals ◽  
Control Constraints ◽  
Infinite Dimensional ◽  
Measurable Multifunctions

The purpose of this paper is to establish some new properties of set valued measurable functions and of their sets of Integrable selectors and to use them to study convex integral functionals defined on Lebesgue-Bochner spaces. In this process we also obtain a characterization of separable dual Banach spaces using multifunctions and we present some generalizations of the classical “bang-bang” principle to infinite dimensional linear control systems with time dependent control constraints.

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