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Birkhäuser - Birkhäuser Mathematics | The Robust Maximum Principle - Theory and Applications

The Robust Maximum Principle

Theory and Applications

Boltyanski, Vladimir G., Poznyak, Alexander

2012, XXII, 432p. 36 illus..

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  • Class-tested in mathematical institutions throughout the world
  • Includes a stand-alone review of classical optimal control theory
  • Presents a new version of the maximum principle for the construction of optimal control strategies for the class of uncertain systems given by a system of ordinary differential equations with unknown parameters from a given set that corresponds to different scenarios of possible dynamics
  • Real-world applications to areas such as production planning and reinsurance-dividend management
  • Applications of obtained results from dynamic programming derivations to multi-model sliding mode control and multi-model differential games

Both refining and extending previous publications by the authors, the material in this monograph has been class-tested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT)—a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time—the authors use new methods to set out a version of OCT’s more refined ‘maximum principle’ designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Referred to as a ‘min-max’ problem, this type of difficulty occurs frequently when dealing with finite uncertain sets.

The text begins with a standalone section that reviews classical optimal control theory, covering the principal topics of the maximum principle and dynamic programming and considering the important sub-problems of linear quadratic optimal control and time optimization. Moving on to examine the tent method in detail, the book then presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems. The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games.

Key features and topics include:

* A version of the tent method in Banach spaces

* How to apply the tent method to a generalization of the Kuhn-Tucker Theorem as well as the Lagrange Principle for infinite-dimensional spaces

* A detailed consideration of the min-max linear quadratic (LQ) control problem

* The application of obtained results from dynamic programming derivations to multi-model sliding mode control and multi-model differential games

* Two examples, dealing with production planning and reinsurance-dividend management, that illustrate the use of the robust maximum principle in stochastic systems

Using powerful new tools in optimal control theory, The Robust Maximum Principle explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.

Content Level » Research

Keywords » Banach spaces - Feynman–Kac formula - Kuhn–Tucker Theorem - Lagrange principle - Riccati differential equation - deterministic systems - dynamic programming methods - linear quadratic control - maximum robust principle - min-max problem - optimal control theory - robust maximum principle - stochastic systems - tent method - viscosity solutions

Related subjects » Birkhäuser Engineering - Birkhäuser Mathematics

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