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

http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

http://web.aeromech.usyd.edu.au/AMME4500/mpc_survey.pdf

A survey of industrial model predictive control technology

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

Predictive constrained control of time-varying and/or uncertain linear systems has been effected through the use of ellipsoidal invariant sets (Kothare et al., 1996). Linear matrix inequalities (LMIs) have been used to design a state-dependent state-feedback law that maintains the state vector inside invariant feasible sets. For the purposes of prediction however, at each time instant, the state feedback law is assumed constant. In addition, due to the large number of LMIs involved, online computation becomes intractable for anything other than small dimensional systems. Here we propose an approach that deploys a fixed state-feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state-feedback law. The problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online. Over and above the very significant reduction in computational cost, the extra degrees of freedom allow for better performance and wider applicability.

Efficient robust predictive control

A numerically robust state-space approach to stable-predictive control strategies

For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplicative and stochastic model uncertainty. The book provides: extensive use of illustrative examples; sample problems; and discussion of novel control applications such as resource allocation for sustainable development and turbine-blade control for maximized power capture with simultaneously reduced risk of turbulence-induced damage. Graduate students pursuing courses in model predictive control or more generally in advanced or process control and senior undergraduates in need of a specialized treatment will find Model Predictive Control an invaluable guide to the state of the art in this important subject. For the instructor it provides an authoritative resource for the construction of courses

Model Predictive Control: Classical, Robust and Stochastic

Stochastic model predictive control (MPC) strategies can provide guarantees of stability and constraint satisfaction, but their online computation can be formidable. This difficulty is avoided in the current technical note through the use of tubes of fixed cross section and variable scaling. A model describing the evolution of predicted tube scalings facilitates the computation of stochastic tubes; furthermore this procedure can be performed offline. The resulting MPC scheme has a low online computational load even for long prediction horizons, thus allowing for performance improvements. The efficacy of the approach is illustrated by numerical examples.

Stochastic Tubes in Model Predictive Control With Probabilistic Constraints

* Part I * Chapter 1: Review of nonlinear model predictive control applications * Chapter 2: Nonlinear model predictive control: issues and applications * Part II * Chapter 3: Model predictive control: output feedback and tracking of nonlinear systems * Chapter 4: Model predictive control of nonlinear parameter varying systems via receding horizon control Lyapunov functions * Chapter 5: Nonlinear model-algorithmic control for multivariable nonminimum-phase processes * Part III * Chapter 6: Open-loop and closed-loop optimality in interpolation MPC * Chapter 7: Closed-loop predictions in model based predictive control linear and nonlinear systems * Chapter 8: Computationally efficient non linear predictive control algorithm for control of constrained nonlinear systems * Part IV * Chapter 9: Long-prediction-horizon nonlinear model predictive control * Chapter 10: Nonlinear control of industrial processes * Chapter 11: Nonlinear model based predictive control using multiple local models * Chapter 12: Neural network control of a gasoline engine with rapid sampling

Basil Kouvaritakis

Papers

Efficient robust predictive control

A numerically robust state-space approach to stable-predictive control strategies

Model Predictive Control: Classical, Robust and Stochastic

Stochastic Tubes in Model Predictive Control With Probabilistic Constraints

Nonlinear predictive control : theory and practice