The Robust Maximum Principle

Covering key areas of optimal control theory, this book uses new methods to set out a version of OCT's more refined 'maximum principle' aimed at solving the problem of constructing optimal control strategies for uncertain systems with some unknown parameters.

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 timethe 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. Known 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. 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.

Using powerful new tools in optimal control theory, this book 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.

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 Includes supplementary material: sn.pub/extras

Contenu
Preface.- Introduction.- I Topics of Classical Optimal Control.- 1 Maximum Principle.- 2 Dynamic Programming.- 3 Linear Quadratic Optimal Control.- 4 Time-Optimization Problem.- II Tent Method.- 5 Tent Method in Finite Dimensional Spaces.- 6 Extrenal Problems in Banach Space.- III Robust Maximum Principle for Deterministic Systems.- 7 Finite Collection of Dynamic Systems.- 8 Multi-Model Bolza and LQ-Problem.- 9 Linear Multi-Model Time-Optimization.- 10 A Measured Space as Uncertainty Set.- 11 Dynamic Programming for Robust Optimization.- 12 Min-Max Sliding Mode Control.- 13 Multimodel Differential Games.- IV Robust Maximum Principle for Stochastic Systems.- 14 Multi-Plant Robust Control.- 15 LQ-Stochastic Multi-Model Control.- 16 A Compact as Uncertainty Set.- References.- Index.