Andrey V. Savkin

Bio: Andrey V. Savkin is an academic researcher from University of New South Wales. The author has contributed to research in topics: Mobile robot & Robot. The author has an hindex of 63, co-authored 607 publications receiving 14262 citations. Previous affiliations of Andrey V. Savkin include Umeå University & Australian Defence Force Academy.

Robust control design using H-∞ methods

Abstract: 1. Introduction.- 1.1 The concept of an uncertain system.- 1.2 Overview of the book.- 2. Uncertain systems.- 2.1 Introduction.- 2.2 Uncertain systems with norm-bounded uncertainty.- 2.2.1 Special case: sector-bounded nonlinearities.- 2.3 Uncertain systems with integral quadratic constraints.- 2.3.1 Integral quadratic constraints.- 2.3.2 Integral quadratic constraints with weighting coefficients.- 2.3.3 Integral uncertainty constraints for nonlinear uncertain systems.- 2.3.4 Averaged integral uncertainty constraints.- 2.4 Stochastic uncertain systems.- 2.4.1 Stochastic uncertain systems with multiplicative noise.- 2.4.2 Stochastic uncertain systems with additive noise: Finitehorizon relative entropy constraints.- 2.4.3 Stochastic uncertain systems with additive noise: Infinite-horizon relative entropy constraints.- 3. H? control and related preliminary results.- 3.1 Riccati equations.- 3.2 H? control.- 3.2.1 The standard H? control problem.- 3.2.2 H? control with transients.- 3.2.3 H? control of time-varying systems.- 3.3 Risk-sensitive control.- 3.3.1 Exponential-of-integral cost analysis.- 3.3.2 Finite-horizon risk-sensitive control.- 3.3.3 Infinite-horizon risk-sensitive control.- 3.4 Quadratic stability.- 3.5 A connection between H? control and the absolute stabilizability of uncertain systems.- 3.5.1 Definitions.- 3.5.2 The equivalence between absolute stabilization and H? control.- 4. The S-procedure.- 4.1 Introduction.- 4.2 An S-procedure result for a quadratic functional and one quadratic constraint.- 4.2.1 Proof of Theorem 4.2.1.- 4.3 An S-procedure result for a quadratic functional and k quadratic constraints.- 4.4 An S-procedure result for nonlinear functionals.- 4.5 An S-procedure result for averaged sequences.- 4.6 An S-procedure result for probability measures with constrained relative entropies.- 5. Guaranteed cost control of time-invariant uncertain systems.- 5.1 Introduction.- 5.2 Optimal guaranteed cost control for uncertain linear systems with norm-bounded uncertainty.- 5.2.1 Quadratic guaranteed cost control.- 5.2.2 Optimal controller design.- 5.2.3 Illustrative example.- 5.3 State-feedback minimax optimal control of uncertain systems with structured uncertainty.- 5.3.1 Definitions.- 5.3.2 Construction of a guaranteed cost controller.- 5.3.3 Illustrative example.- 5.4 Output-feedback minimax optimal control of uncertain systems with unstructured uncertainty.- 5.4.1 Definitions.- 5.4.2 A necessary and sufficient condition for guaranteed cost stabilizability.- 5.4.3 Optimizing the guaranteed cost bound.- 5.4.4 Illustrative example.- 5.5 Guaranteed cost control via a Lyapunov function of the Lur'e-Postnikov form.- 5.5.1 Problem formulation.- 5.5.2 Controller synthesis via a Lyapunov function of the Lur'e-Postnikov form.- 5.5.3 Illustrative Example.- 5.6 Conclusions.- 6. Finite-horizon guaranteed cost control.- 6.1 Introduction.- 6.2 The uncertainty averaging approach to state-feedback minimax optimal control.- 6.2.1 Problem Statement.- 6.2.2 A necessary and sufficient condition for the existence of a state-feedback guaranteed cost controller.- 6.3 The uncertainty averaging approach to output-feedback optimal guaranteed cost control.- 6.3.1 Problem statement.- 6.3.2 A necessary and sufficient condition for the existence of a guaranteed cost controller.- 6.4 Robust control with a terminal state constraint.- 6.4.1 Problem Statement.- 6.4.2 A criterion for robust controllability with respect to a terminal state constraint.- 6.4.3 Illustrative example.- 6.5 Robust control with rejection of harmonic disturbances.- 6.5.1 Problem Statement.- 6.5.2 Design of a robust controller with harmonic disturbance rejection.- 6.6 Conclusions.- 7. Absolute stability, absolute stabilization and structured dissipativity.- 7.1 Introduction.- 7.2 Robust stabilization with a Lyapunov function of the Lur'e-Postnikov form.- 7.2.1 Problem statement.- 7.2.2 Design of a robustly stabilizing controller.- 7.3 Structured dissipativity and absolute stability for nonlinear uncertain systems.- 7.3.1 Preliminary remarks.- 7.3.2 Definitions.- 7.3.3 A connection between dissipativity and structured dissipativity.- 7.3.4 Absolute stability for nonlinear uncertain systems.- 7.4 Conclusions.- 8. Robust control of stochastic uncertain systems.- 8.1 Introduction.- 8.2 H? control of stochastic systems with multiplicative noise.- 8.2.1 A stochastic differential game.- 8.2.2 Stochastic H? control with complete state measurements.- 8.2.3 Illustrative example.- 8.3 Absolute stabilization and minimax optimal control of stochastic uncertain systems with multiplicative noise.- 8.3.1 The stochastic guaranteed cost control problem.- 8.3.2 Stochastic absolute stabilization.- 8.3.3 State-feedback minimax optimal control.- 8.4 Output-feedback finite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.4.1 Definitions.- 8.4.2 Finite-horizon minimax optimal control with stochastic uncertainty constraints.- 8.4.3 Design of a finite-horizon minimax optimal controller.- 8.5 Output-feedback infinite-horizon minimax optimal control of stochastic uncertain systems with additive noise.- 8.5.1 Definitions.- 8.5.2 Absolute stability and absolute stabilizability.- 8.5.3 A connection between risk-sensitive optimal control and minimax optimal control.- 8.5.4 Design of the infinite-horizon minimax optimal controller.- 8.5.5 Connection to H? control.- 8.5.6 Illustrative example.- 8.6 Conclusions.- 9. Nonlinear versus linear control.- 9.1 Introduction.- 9.2 Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty.- 9.2.1 Problem statement.- 9.2.2 Output-feedback nonlinear versus linear control.- 9.2.3 State-feedback nonlinear versus linear control.- 9.3 Decentralized robust state-feedback H? control for uncertain large-scale systems.- 9.3.1 Preliminary remarks.- 9.3.2 Uncertain large-scale systems.- 9.3.3 Decentralized controller design.- 9.4 Nonlinear versus linear control in the robust stabilizability of linear uncertain systems via a fixed-order output-feedback controller.- 9.4.1 Definitions.- 9.4.2 Design of a fixed-order output-feedback controller.- 9.5 Simultaneous H? control of a finite collection of linear plants with a single nonlinear digital controller.- 9.5.1 Problem statement.- 9.5.2 The design of a digital output-feedback controller.- 9.6 Conclusions.- 10. Missile autopilot design via minimax optimal control of stochastic uncertain systems.- 10.1 Introduction.- 10.2 Missile autopilot model.- 10.2.1 Uncertain system model.- 10.3 Robust controller design.- 10.3.1 State-feedback controller design.- 10.3.2 Output-feedback controller design.- 10.4 Conclusions.- 11. Robust control of acoustic noise in a duct via minimax optimal LQG control.- 11.1 Introduction.- 11.2 Experimental setup and modeling.- 11.2.1 Experimental setup.- 11.2.2 System identification and nominal modelling.- 11.2.3 Uncertainty modelling.- 11.3 Controller design.- 11.4 Experimental results.- 11.5 Conclusions.- A. Basic duality relationships for relative entropy.- B. Metrically transitive transformations.- References.

Robust Kalman Filtering for Signals and Systems with Large Uncertainties

Abstract: From the Publisher: The purpose of this new book is to present recent developments in the theory of robust-state estimation for the case in which a process model contains significant uncertainties and nonlinearities. In particular, the book looks at the various ways in which the standard Kalman Filter can be modified to make it robust against large parameter uncertainties.. "The book is an essential text/reference for graduates, researchers, and professionals in electrical, mechanical, and control engineering, applied mathematics, and computer engineering. All scientists and engineers engaged in robust control and filtering theory research will find the book a useful resource.

Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey

Abstract: We review a range of techniques related to navigation of unmanned vehicles through unknown environments with obstacles, especially those that rigorously ensure collision avoidance (given certain assumptions about the system). This topic continues to be an active area of research, and we highlight some directions in which available approaches may be improved. The paper discusses models of the sensors and vehicle kinematics, assumptions about the environment, and performance criteria. Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are all reviewed. In preference to global approaches based on full knowledge of the environment, particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.

Estimation and Control over Communication Networks

Abstract: Preface Introduction Topological Entropy, Observability, Robustness, Stabilizability, and Optimal Control Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels Detectability and Output Feedback Stabilizability of Nonlinear Systems via Limited Capacity Communication Channels Robust Set-Valued State Estimation via Limited Capacity Communication Channels An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noiseless Plants via Noisy Discrete Channels An Analog of Shannon Information Theory: State Estimation and Stabilization of Linear Noisy Plants via Noisy Discrete Channels An Analog of Shannon Information Theory: Stable in Probability Control and State Estimation of Linear Noisy Plants via Noisy Discrete Channels Decentralized Stabilization of Linear Systems via Limited Capacity Communication Networks H-infinity State Estimation via Communication Channels Kalman State Estimation and Optimal Control Based on Asynchronously and Irregularly Delayed Measurements Optimal Computer Control via Asynchronous Communication Channels Linear-Quadratic Gaussian Optimal Control via Limited Capacity Communication Channels Kalman State Estimation in Networked Systems with Asynchronous Communication Channels and Switched Sensors Robust Kalman State Estimation with Switched Sensors Appendix A: Proof of Proposition 7.6.13 Appendix B: Some Properties of Square Ensembles of Matrices Appendix C: Discrete Kalman Filter and Linear-Quadratic Gaussian Optimal Control Problem Appendix D: Some Properties of the Joint Entropy of a Random Vector and Discrete Quantity References Index

Coordinated collective motion of Groups of autonomous mobile robots: analysis of Vicsek's model

Abstract: This note gives a qualitative analysis of the dynamics of a system consisting of several mobile robots coordinating their motion using simple local nearest neighbor rules. We show that under some assumptions the headings of all robots will be eventually constant.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Linear Matrix Inequalities in System and Control Theory

Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

Consensus and Cooperation in Networked Multi-Agent Systems

Abstract: This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

A Survey of Recent Results in Networked Control Systems

Abstract: Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

Abstract: From the Publisher: The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.