Robust control synthesis through optimization

The problem addressed in this course concerns the synthesis of robust multivariable filters. Two families of filters are considered: robust multivariable correctors and robust state estimators. In this context, the approaches studied are based on the notions of Hinfini norm, convex optimization and matrix linear inequalities.

The problem of synthesizing robust correctors is defined as the problem of synthesizing a control law that simultaneously stabilizes a family of systems, possibly nonlinear and of infinite dimension. This family of systems is represented by a family of models consisting of a nominal model and models for endogenous (model uncertainties) and exogenous (input disturbances, measurement noise, etc.) disturbances.
In the problem of synthesizing robust estimators, the aim is to reconstruct a linear combination of the state from the available signals, such that the estimation error is robust to endogenous and exogenous disturbances.
In both problems, the notion of robustness is considered in the sense of the Hinfini norm.

State representation - Continuous control law synthesis (frequency and modal approaches)

The course content is as follows:
* Introduction and motivation: Presentation of objectives and review of existing approaches (LQ / LQG commands / Kalman filters / eigenstructure placement ...etc....)
* Fundamental tools: Singular values, RHinfinite space and induced L2 norm and Hinfini
* Representation of model uncertainties: LFT (Linear Fractional Transformation) formalism
* The Hinfini problem in multivariable control: Mixed sensitivity approach, small gain theorem, solving the problem using convex optimization techniques and the LMI formalism, post-analysis of robust performance using the structured singular value.
* The robust estimation problem in a Hinfini context: Formulation of the problem as a fictitious control law synthesis problem, Fundamental Difference, Resolution and post-analysis of performance.
* Design office: Application of the Hinfini method to the control problem of a DC motor and to the problem of reconstructing the state of an uncertain academic system (mass-spring-damper system).

1] "Hinfini control and micro-analysis: tools for robustness", G. Duc and S. Font, Hermes Science Publications, France. Font, Hermes Science Publications, France, 1999.
[2] "FEEDBACK CONTROL THEORY", J.C. Doyle, B.A. Francis and A.R. Tannenbaum. Macmillan Publishing Company, USA, 1992.
[3] "A Practical Approach to Robustness Analysis with Aeronautical Applications" G. Ferreres, Kluwer Academic/Plenum Publishers, USA.