Optimal Control Theory for Infinite Dimensional Systems

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Springer Science & Business Media, 6 dic. 2012 - 450 páginas
Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.
 

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Índice

Control Problems in Infinite Dimensions
1
Mathematical Preliminaries
24
Existence Theory of Optimal Controls
81
Necessary Conditions for Optimal Controls
130
3 Other Preliminary Results
137
4 Proof of the Maximum Principle
150
5 Applications
159
Remarks
165
Remarks
220
2 Properties of the Value Functions
227
3 Viscosity Solutions
239
Relation to Maximum Principle and Optimal Synthesis
256
6 Infinite Horizon Problems
264
Remarks
272
Optimal Switching and Impulse Controls
319
Linear Quadratic Optimal Control Problems
361

2 Variation along Feasible Pairs
175
4 Variational Inequalities
183
Quasilinear Equations
191

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