Observation of non-linear dynamic systems

This Module will start by reviewing the basics of observer synthesis for linear dynamical systems. Then, based on examples from physics, we will introduce the various notions (geometric and analytical) of the observability of nonlinear systems. After a classification of SNs, a panel of nonlinear observers will be treated and proofs of convergences established. Implementation on a closed-loop simulation case will enable us to deal with the separation principle.

1. Introduction (4 hrs)

• Reminder of linearity and non-linearity; Behavior of nonlinear systems: Autonomous and non-autonomous systems, same class on nonlinear systems (Physical examples)
• Different notions of observability (distinguishability, global observability, local observability), Analytic conditions of observability, notion of persistence of input (examples)

2. Observe design:

• Observer formulated as mean square estimation, Kalman observer for LTV systems (proof of asymptotic convergence)
• Extended KF for nonlinear systems in a deterministic framework
• Uniform observability and observer design: canonical form and high gain observer design
• Adaptive observers
• Sliding mode observers

3. Close the loop: notion of separation principle ?
4. Simulation on Matlab