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

The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems

YALMIP : a toolbox for modeling and optimization in MATLAB

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

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Higher-order sliding modes, differentiation and output-feedback control

The notion of an integral manifold M is used to obtain an exact separation of the parameter update equation from the state equations in continuous adaptive schemes. The update equation on M is then analyzed by averaging and the results used to interpret and justify several previous approaches.

Integral manifold approach to slow adaptation

The authors study the tracking and disturbance rejection problem of a class of time-invariant nonlinear systems which are linear equivalent to controllable linear systems By using a nonlinear feedback control and a slowly varying integral control, the closed-loop system asymptotically tracks a reference input and rejects disturbances which are both unknown and slowly varying The integral manifold concept is used to design a nonlinear controller >

Tracking and disturbance rejection in nonlinear systems: the integral manifold approach

Foreword.- Preface.- List of Contributors.- Part I: State Estimation and Identification.- Circle-criterion observers and their feedback applications: an overview.- Unknown input observers and residual generators for linear time delay systems.- Set membership identification: the H-infinity case.- Algebraic methods for nonlinear systems: parameter identification and state estimation.- Recent techniques for the identification of piecewise affine and hybrid systems.- Part II: Control and System Theory.- Dual matrix inequalities in stability and performance analysis of linear differential/difference inclusions.- Oscillators as systems and synchrony as a design principle.- Nonlinear anti-windup for exponentially unstable linear plants.- Constrained pole assignment control.- An overview of finite-time stability.- Finite-time control of linear systems: a survey.- Part III: Robotics.- An application of iterative identification and control in the robotics field.- Friction identification and model-based digital control of a direct-drive manipulator.- A singular perturbation approach to control of flexible arms in compliant motion.- Fault tolerant tracking of a robot manipulator: an internal model based approach.- Set membership localization and map building for mobile robots.- Visual servoing with central catadioptric camera.- Motion control and coordination in mechanical and robotic systems.- Coordination of robot teams: a decentralized approach.- Part IV: Control of Electromechanical Systems.- Transient stabilization of multimachine power systems.- Robust controllers for large-scale interconnected systems: applications to web processing machines.- Control strategy using vision for the stabilization of an experimental PVTOL aircraft setup.- Neural network model reference adaptive control of marine vehicles.- Part V: ManufacturingSystems.- Projection and aggregation in maxplus algebra.- A switched system model for the optimal control of two symmetric competing queues with finite capacity.- Cooperative inventory control.- Part VI: Networked Control Systems.- Communication logic design and analysis for networked control systems.- Networked decentralized control of multirate sampled-data systems.- Finite-time stability for nonlinear networked control systems.- Index

Current trends in nonlinear systems and control : in honor of Petar Kokotović and Turi Nicosia

The problem of controlling dynamic systems where the position of the operating point in the state space is unknown is addressed An adaptive control scheme in which the uncertain parameter is the operating point is proposed The usually applied solution to this problem is a particular case, with limited applicability, of the proposed scheme With the proposed scheme the exponential stability of the unknown operating point is obtained under very general conditions Illustrative examples are also presented

On the control of dynamic systems with unknown operating point

We present a new design procedure for the nonlinear system transformable into the output-feedback canonical form. The key ingredient is an observer-based parameter identifier which substitutes the tuning function as a tool for avoiding overparametrization.

http://ieeexplore.ieee.org/iel5/4792781/4792782/04793412.pdf

Petar V. Kokotovic

Papers

Integral manifold approach to slow adaptation

Tracking and disturbance rejection in nonlinear systems: the integral manifold approach

Current trends in nonlinear systems and control : in honor of Petar Kokotović and Turi Nicosia

On the control of dynamic systems with unknown operating point

Adaptive Nonlinear Output-Feedback Control with an Observer-Based Identifier