Uncertain Order

For all its elaborate theories and models, economics always reduces to comparisons. Should we build A rather than B? Will I be better off if I eat D rather than C? How much will it cost me to produce F instead of E? At root, the ultimate goal of economics is simple: assessing the alternatives and finding the best possible outcome. This basic mathematical concept underlies all introductions to the field of economics, yet as advanced students progress through the discipline, they often lose track of this foundational idea when presented with real-world complications and uncertainty. In Competitive Agents in Certain and Uncertain Markets, Robert G. Chambers develops an integrated analytic framework for treating consumer, producer, and market equilibrium analyses as special cases of a generic optimization problem. He builds on lessons learned by all beginning students of economics to show how basic concepts can still be applied even in complex and highly uncertain conditions. Drawing from optimization theory, Chambers demonstrates how the same unified mathematical framework applies to both stochastic and non-stochastic decision settings. The book borrows from both convex and variational analysis and gives special emphasis to differentiability, conjugacy theory, and Fenchel's Duality Theorem. Throughout, Chambers includes practical examples, problems, and exercises to make abstract material accessible. Bringing together essential theoretical tools for understanding decision-making under uncertainty, Competitive Agents in Certain and Uncertain Markets provides a unified framework for analyzing a broad range of microeconomic decisions. This book will be an invaluable resource for advanced graduate students and scholars of microeconomic theory.

Multi-agent systems are special networked systems full of research interest and practical sense, which are abundant in real life, ranging from mobile robot networks, intelligent transportation management, to multiple spacecraft, surveillance and monitoring. Consensus control is one of the most typical and hot research issues for multi-agent systems. Distributed Adaptive Consensus Control of Uncertain Multi-agent Systems provides innovative technologies to design and analyze distributed adaptive consensus for multi-agent systems with model uncertainties. Based on the basic graph theory and adaptive backstepping control, this monograph: · Describes the state of the art on distributed adaptive control, finite-time consensus control and event-triggered consensus control · Studies distributed adaptive consensus under directed communication graph condition: the methods with linearly parametric reference, hierarchical decomposition, and design of auxiliary filers · Explores adaptive finite-time consensus for uncertain nonlinear systems · Considers distributed adaptive consensus with event-triggered communication via state feedback and output feedback · Investigates distributed adaptive formation control of nonholonomic mobile robots with experimental verification · Provides distributed adaptive attitude synchronization control schemes for multiple spacecraft with event-triggered communication Distributed Adaptive Consensus Control of Uncertain Multi-agent Systems can help engineering students and professionals to efficiently learn distributed adaptive control design tool for handling uncertain multi-agent systems with directed communication graph, guaranteeing finite-time convergence and saving communication resources.

Uncertain Decisions: Bridging Theory and Experiments presents advanced directions of thinking on decision theory - in particular the more recent contributions on non-expected utility theory, fuzzy decision theory and case-based theory. This work also provides theoretical insights on measures of risk aversion and on new problems for general equilibrium analysis. It analyzes how the thinking that underlies the theories described above spills over into real decisions, and how the thinking that underlies these real decisions can explain the discrepancies between theoretical approaches and actual behavior. This work elaborates on how the most recent laboratory experiments have become an important source both for evaluating the leading theory of choice and decision, and for contributing to the formation of new models regarding the subject.

Providing readers with a detailed examination of resilient controls in risk-averse decision, this monograph is aimed toward researchers and graduate students in applied mathematics and electrical engineering with a systems-theoretic concentration. This work contains a timely and responsive evaluation of reforms on the use of asymmetry or skewness pertaining to the restrictive family of quadratic costs that have been appeared in various scholarly forums. Additionally, the book includes a discussion of the current and ongoing efforts in the usage of risk, dynamic game decision optimization and disturbance mitigation techniques with output feedback measurements tailored toward the worst-case scenarios. This work encompasses some of the current changes across uncertainty quantification, stochastic control communities, and the creative efforts that are being made to increase the understanding of resilient controls. Specific considerations are made in this book for the application of decision theory to resilient controls of the linear-quadratic class of stochastic dynamical systems. Each of these topics are examined explicitly in several chapters. This monograph also puts forward initiatives to reform both control decisions with risk consequences and correct-by-design paradigms for performance reliability associated with the class of stochastic linear dynamical systems with integral quadratic costs and subject to network delays, control and communication constraints.

Explore the applications of range analysis to power systems under conditions of uncertainty In Interval Methods for Uncertain Power System Analysis, accomplished engineer Dr. Alfredo Vaccaro delivers a comprehensive discussion of the mathematical foundations of range analysis and its application to solving traditional power system operation problems in the presence of strong and correlated uncertainties. The book explores highly relevant topics in the area, from interval methods for uncertainty representation and management to a variety of application examples. The author offers readers the latest methodological breakthroughs and roadmaps to implementing the mathematics discussed within, as well as best practices commonly employed across the industry. Interval Methods for Uncertain Power System Analysis includes examinations of linear and non-linear equations, as well as: A thorough introduction to reliable computing, including discussions of interval arithmetic and interval-based operators Comprehensive explorations of uncertain power flow analysis, including discussions of problem formulation and sources of uncertainty in power flow analysis In-depth examinations of uncertain optimal power flow analysis Fulsome discussions of uncertain small signal stability analysis, including treatments of how to compute eigenvalues of uncertain matrices Perfect for engineers working in power flow and optimal power flow analyses, optimization theory, and computer aided simulation, Interval Methods for Uncertain Power System Analysis will also earn a place in the libraries of researchers and graduate students studying decision making under uncertainty in power systems operation.

INHALT LANG: Introduction: Introductory Survey; Vector Norm. Matrix Norm. Matrix Measure; Functional Analysis, Function Norms and Control Signals.- Differential Sensitivity. Small-Scale Perturbation: Kronecker Calculus in Control Theory; Analysis Using Matrices and Control Theory; Eigenvalue and Eigenvector Differential Sensitivity; Transition Matrix Differential Sensitivity; Characteristic Polynomial Differential Sensitivity; Optimal Control and Performance Sensitivity; Desensitizing Control.- Robustness in the Time Domain: General Stability Bounds in Perturbed Systems; Robust Dynamic Interval Systems; Lyapunov-Based Methods for Perturbed Continuous-Time Systems; Lyapunov-Based Methods for Perturbed Discrete-Time Systems; Robust Pole Assignment; Models for Optimal and Interconnected Systems; Robust State Feedback Using Ellipsoid Sets; Robustness of Observers and Kalman-Bucy Filters; Initial Condition Perturbation, Overshoot and Robustness; Lnp-Stability and Robust Nonlinear Control.- Robustness in the Frequency Domain: Uncertain Polynomials. Interval Polynomials; Eigenvalues and Singular Values of Complex Matrices; Resolvent Matrix and Stability Radius; Robustness Via Singular-Value Analysis; Generalized Nyquist Stability of Perturbed Systems; Block-Structured Uncertainty and Structured Singular Value; Performance Robustness; Robust Controllers Via Spectral Radius Technique.- Coprime Factorization and Minimax Frequency Optimization: Robustness Based on the Internal Model Principle; Parametrization and Factorization of Systems; Hardy Space Robust Design.- Robustness Via Approximative Models: Robust Hyperplane Design in Variable Structure Control; SIngular Perturbaitons. Unmodelled High-Frequendy Dynamics; Control Using Aggregation Models; Optimum Control of Approximate and Nonlinear Systems; System Analysis via Orthogonal Functions; System Analysis Via Pulse Functions and Piecewise Linear Functions; Orthogonal Decomposition Applications.

With the increasing of the complexity of a system, there is a variety of indeterminacy in the practical applications of graph theory. We focus on uncertain random graph, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. In this paper, the chance theory is applied to construct the cycle index of an uncertain random graph. Then a method to calculate the cycle index of an uncertain random graph is presented. We also discuss some properties of the cycle index.

Uncertain computation is a system of computation and reasoning in which the objects of computation are not values of variables but restrictions on values of variables. This compendium includes uncertain computation examples based on interval arithmetic, probabilistic arithmetic, fuzzy arithmetic, Z-number arithmetic, and arithmetic with geometric primitives. The principal problem with the existing decision theories is that they do not have capabilities to deal with such environment. Up to now, no books where decision theories based on all generalizations level of information are considered. Thus, this self-containing volume intends to overcome this gap between real-world settings' decisions and their formal analysis. Contents: Decision EnvironmentAnalysis of the Existing Decision TheoriesInterval ComputationProbabilistic ArithmeticFuzzy Type-1 and Fuzzy Type-2 ComputationsComputation with Z-NumbersComputation with U-NumbersFuzzy Geometry Based ComputationsInterval Granular-Based Decision MakingDecision Making in Fuzzy EnvironmentThe Z-Restriction Centered Decision TheorySimulation and Applications Readership: Researchers, academics, professionals and graduate students in fuzzy logic, decision sciences and mathematical economics. Keywords: Uncertain Computation;Decision Making;Interval Arithmetic;Fuzzy Arithmetic;Z-Number;Combined State;Fuzzy EconomicsReview:0