The Robust Maximum Principle: Theory and Applications

The text begins with a standalone section that reviews classical optimal control theory, covering its principle 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:

* An examination of Crandall & Lions’ ‘viscosity solutions’ for non-smooth situations in optimal control

* 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.