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. 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.
Table of Content
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.
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