Invariance entropy for deterministic control systems : an introduction / Christoph Kawan

This book provides an introduction to the theory of invariance entropy, a subject closely related to the control task of making a subset invariant in the state space of a control system. The concept of invariance entropy was first described by Colonius and is developed in some generality by his student in this book. Although the basic concept applies to both continuous and discrete systems, the focus here is on continuous systems given by differential equations.

The motivation for the theory of invariance entropy derives from communication constraints in digitally networked control systems. Classical assumptions in control theory include instantaneous communication without loss and with arbitrary precision and are unrealistic for practical systems. A natural question that arises is about the smallest possible information rate necessary for a given control system given realistic communication assumptions. Consideration of this problem led first to the notion of topological feedback entropy, and then to the author’s current work.

The book begins with basic control-theoretic notions, and then moves quickly to a discussion of invariance entropy for topological time-invariant systems, their basic properties, and some nontrivial examples. The next two chapters treat the linear and nonlinear theory, respectively. Following that the theory is embellished for sets with additional controllability properties.

The final two chapters take up more specialized topics: the achievement of tighter lower bounds for invariance entropy, and examples of application of the theory to particular classes of systems. (Zentralblatt)