Nonlinear systems and quadratic controls

MODULE INCLUDED IN "Modeling and Control in State Space". 

This course complements modules AU 201 (Linear Control and Linearizing Approaches) and AU 209 (Nonlinear Systems 1). It enables students to master the representation of the evolution of nonlinear systems in the phase plane, and to study their stability using the Lyapunov method. In a second step, the Lyapunov equation is used in Gramian calculations to establish an equilibrium state realization and linear quadratic control (LQR). The course is illustrated with numerous examples enabling the tools studied to be applied.
The outline of the course given by André Benine Neto (Univ. de Bordeaux/IMS) is as follows:

- Nature of singular points and tangent linearization
- Lyapunov method
- Commandability and observability Gramian
- Equilibrium realization
- Linear quadratic control (LQR)

Linear systems and linear system control. Control of discrete-time linear systems (AU 201). Frequency analysis of non-linear systems (AU 209).

Automatic