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.

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Linear Matrix Inequalities in System and Control Theory

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

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Consensus and Cooperation in Networked Multi-Agent Systems

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.

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Factor graphs and the sum-product algorithm

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

The Karhunen-Loeve expansion of a random process is used to derive the impulse response of the optimal realizable linear estimator for the process. The expansion is truncated to yield an approximate state-variable model of the process in terms of the first N eigenvalues and eigenfunctions. The Kalman-Bucy filter for this model provides an approximate realizable linear estimator which approaches the optimal one as N \rightarrow \infty . A bound on the truncation error is obtained.

On the approximation of optimal realizable linear filters using a Karhunen-Loeve expansion (Corresp.)

This paper considers the problem of passing from a linear time-invariant high order controller designed for a linear time-invariant plant (of presumably high order) to a low order approximation of the controller. The approximation problem is often best posed as a frequency weighted L ? approximation problem. Many different controller representations are possible, giving different performance of the various reduction algorithms.

Controller Reduction: Concepts and Approaches

Consider a rational discrete-time transfer function H(z) with the property that the associated causal impulse response h(k) is nonnegative for all k. A positive realization is a quadruple A, b, c, d such that 

$$ H\left( z \right) = d + c{\left( {zI - A} \right)^{ - 1}}b $$

and all entries of A, b, c, d are nonnegative.

Positive system realizations

This paper studies the information propagation process in a 1D mobile ad-hoc network formed by vehicles traveling on a highway. We consider that vehicles can be divided into traffic streams; vehicles in the same traffic stream have the same speed distribution, while the speed distributions of vehicles in different traffic streams are different. Analytical formulas are derived for the fundamental properties of the information propagation process as well as the information propagation speed. Using the formulas, one can straightforwardly study the impact on the information propagation speed of various parameters such as radio range, vehicular traffic density, vehicular speed distribution and the time variation of vehicular speed.

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On the information propagation process in multi-lane vehicular ad-hoc networks

In this letter, we study the evolutionary dynamics of two different types of communities in an evolving environment. We model the dynamics using an evolutionary differential game consisting of two sub-games: 1) a game between two different communities and 2) a game between communities and the environment. Our interest is to clarify when the two communities and environment can coexist dynamically under the feedback from the changing environment. Mathematically speaking, we show that for specific game payoffs, the corresponding 3-D replicator dynamics induced by the evolutionary game have an infinite number of periodic orbits.

https://pure.rug.nl/ws/files/64111853/2018_IEEE_CSL_co_evolution.pdf

Brian D. O. Anderson

Papers

On the approximation of optimal realizable linear filters using a Karhunen-Loeve expansion (Corresp.)

Controller Reduction: Concepts and Approaches

Positive system realizations

On the information propagation process in multi-lane vehicular ad-hoc networks

Evolutionary Dynamics of Two Communities Under Environmental Feedback