Bücher der Reihe SpringerBriefs in Control, Automation and Robotics

Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems.

This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk¿s retraction theory and the index-theoretic methodology of Krasnosel¿skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or relatedfields.

This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or 'boxes'.

This brief describes the basics of Riemannian optimization¿optimization on Riemannian manifolds¿introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields.To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numericallinear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.

Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived.

This brief introduces people with a basic background in probability theory to various problems in cancer biology that are amenable to analysis using methods of probability theory and statistics.

The subject of this brief is the application of linear parameter-varying (LPV) control to a class of dynamic systems to provide a systematic synthesis of gain-scheduling controllers with guaranteed stability and performance.

This Springer brief discusses the use of control engineering methods to plan a cancer therapy which tends to reduce tumour size in patients, striking a balance that minimizes the toxic effects of the treatment.

This Springer brief provides the necessary foundations to understand differential privacy and describes practical algorithms enforcing this concept for the publication of real-time statistics based on sensitive data.

This brief broadens readers' understanding of stochastic control by highlighting recent advances in the design of optimal control for Markov jump linear systems (MJLS).

This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered.

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators.

Iterative learning control (ILC) has its origins in the control of processes that perform a task repetitively with a view to improving accuracy from trial to trial by using information from previous executions of the task.

This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary.

This brief introduces game- and decision-theoretical techniques for the analysis and design of resilient interdependent networks. It unites game and decision theory with network science to lay a system-theoretical foundation for understanding the resiliency of interdependent and heterogeneous network systems.The authors pay particular attention to critical infrastructure systems, such as electric power, water, transportation, and communications. They discuss how infrastructure networks are becoming increasingly interconnected as the integration of Internet of Things devices, and how a single-point failure in one network can propagate to other infrastructures, creating an enormous social and economic impact. The specific topics in the book include:· static and dynamic meta-network resilience game analysis and design;· optimal control of interdependent epidemics spreading over complex networks; and· applications to secure and resilient design of critical infrastructures.These topics are supported by up-to-date summaries of the authors' recent research findings. The authors then discuss the future challenges and directions in the analysis and design of interdependent networks and explain the role of multi-disciplinary research has in computer science, engineering, public policy, and social sciences fields of study.The brief introduces new application areas in mathematics, economics, and system and control theory, and will be of interest to researchers and practitioners looking for new approaches to assess and mitigate risks in their systems and enhance their network resilience. A Game- and Decision-Theoretic Approach to Resilient Interdependent Network Analysis and Design also has self-contained chapters, which allows for multiple levels of reading by anyone with an interest in game and decision theory and network science.

Electronic codes are supplied to allow reproduction of text examples

Passivity-based Model Predictive Control for Mobile Vehicle Navigation represents a complete theoretical approach to the adoption of passivity-based model predictive control (MPC) for autonomous vehicle navigation in both indoor and outdoor environments.

Experimental results confirm the effectiveness of the control algorithm in regulating the mean-value rail pressure independently from engine working conditions (engine speed and time of injection) with limited design effort.

In this book, the authors propose efficient characterizations of the non-convex regions that appear in many control problems, such as those involving collision/obstacle avoidance and, in a broader sense, in the description of feasible sets for optimization-based control design involving contradictory objectives.

This brief introduces wireless communications ideas and techniques into the study of networked control systems.