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

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

Vol. 9 Issue 1 pp. 000‐000 There is a growing need for integrating environmentally sound choices into supply-chain management research and practice. Perusal of the literature shows that a broad frame of reference for green supply-chain management (GrSCM) is not adequately developed. Regulatory bodies that formulate regulations to meet societal and ecological concerns to facilitate growth of business and economy also suffer from its absence. A succinct classification to help academicians, researchers and practitioners in understanding integrated GrSCM from a wider perspective is needed. Further, sufficient literature is available to warrant such classification. This paper takes an integrated and fresh look into the area of GrSCM. The literature on GrSCM is covered exhaustively from its conceptualization, primarily taking a ‘reverse logistics angle’. Using the rich body of available literature, including earlier reviews that had relatively limited perspectives, the literature on GrSCM is classified on the basis of the problem context in supply chain’s major influential areas. It is also classified on the basis of methodology and approach adopted. Various mathematical tools/techniques used in literature vis-a-vis the contexts of GrSCM are mapped. A timeline indicating relevant papers is also provided as a ready reference. Finally, the findings and interpretations are summarized, and the main research issues and opportunities are highlighted.

Green supply‐chain management: A state‐of‐the‐art literature review

The continuous- and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H∞-suboptimal controllers, including reduced-order controllers.

The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions.

Thanks to such connections, the LMI-based characterization of H∞ controllers opens new perspectives for the refinement of H∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.

A linear matrix inequality approach to H∞ control

This paper presents an overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers. The design objectives can be a mix of H/sub /spl infin// performance, H/sub 2/ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. In addition, these objectives can be specified on different channels of the closed-loop system. When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example.

/pdf/multiobjective-output-feedback-control-via-lmi-optimization-8cihrh828q.pdf

Multiobjective output-feedback control via LMI optimization

LPV control and full block multipliers

• Facts from convex analysis. LMI’s: history, algorithms and software. • The role of LMI’s in dissipativity Stability and nominal performance. Analysis results. • From analysis to synthesis. State-feedback, estimation and output-feedback synthesis. • From nominal to robust stability, robust performance and robust synthesis. • IQC’s and multipliers. Relations to classical tests and to μ-theory. • Mixed control problems and parameter-varying systems and control design.

http://www.eeci-institute.eu/pdf/M012/lec1.pdf

Linear Matrix Inequalities in Control

Part I: Introduction to Modeling and Control of LPV Systems.- An Overview of LPV Systems.- Prediction Error Identification of LPV Systems: Present and Beyond.- Part II: Theoretical Advancements on LPV Control and Estimation.- Parametric Gain-scheduling Control via LPV-stable Realization.- Explicit Controller Parameterizations for Linear Parameter Varying Affine Systems using Linear Matrix Inequalities.- A Parameter-dependent Lyapunov Approach for the Control of Nonstationary LPV Systems.- Generalized Asymptotic Regulation for LPV Systems with Additional Performance Objectives.- Robust Stabilization and Disturbance Attenuation of Switched Linear Parameter Varying Systems in Discrete Time.- Gain-scheduled Output Feedback Controllers with Good Implementability and Robustness.- Decentralized Model Predictive Control of Time-varying Splitting Parallel Systems.- Robust Estimation with Partial Gain-scheduling through Convex Optimization.- Delay-dependent Output Feedback Control of Time-delay LPV Systems.- Part III: Recent Applications of LPV Methods in Control of Complex Systems.- Structured Linear Parameter Varying Control of Wind Turbines.- Attitude Regulation for Spacecraft with Magnetic Actuators: an LPV Approach.- Modeling and Control of LPV Systems: A Vibroacoustic Application.- LPV Modeling and Control of Semi-active Dampers in Automotive Systems.- LPV H[yen] Control for Flexible Hypersonic Vehicles.- Identification of Low-complexity LPV Input-output Models for Control of a Turbocharged Combustion Engines.- Constrained Freeway Traffic Control via Linear Parameter Varying Paradigms.- Linear Parameter Varying Control for the X-53 Active Aeroelastic Wing.- Design of Integrated Vehicle Chassis Control Based on LPV Methods.

Control of linear parameter varying systems with applications

We consider robust semi-definite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description. On the basis of matrix sum-of-squares decompositions, we suggest a systematic procedure to construct a family of linear matrix inequality relaxations for computing upper bounds on the optimal value of the corresponding robust counterpart. With a novel matrix-version of Putinar's sum-of-squares representation for positive polynomials on compact semi-algebraic sets, we prove asymptotic exactness of the relaxation family under a suitable constraint qualification. If the uncertainty region is a compact polytope, we provide a new duality proof for the validity of Putinar's constraint qualification with an a priori degree bound on the polynomial certificates. Finally, we point out the consequences of our results for constructing relaxations based on the so-called full-block S-procedure, which allows to apply recently developed tests in order to computationally verify the exactness of possibly small-sized relaxations.

Carsten W. Scherer

Papers

Multiobjective output-feedback control via LMI optimization

LPV control and full block multipliers

Linear Matrix Inequalities in Control

Control of linear parameter varying systems with applications

Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs