Nonlinear Estimation and Control

In this talk we present a novel quasi-infinite horizon nonlinear model predictive control scheme for stable and unstable constrained plants for which we can proof asymptotic stability. Unlike for other known nonlinear model predictive control schemes, for which stability can also be proven, only a finite prediction and finite control horizon have to be considered. The objective function includes a terminal state penalty term and a terminal inequality state constraint where the terminal state penalty is chosen as the positive definite solution an appropriate Lyapunov equation. Like other known stability results for nonlinear predictive control schemes, the given stability conditions are only sufficient and unfortunately rather conservative. The approach will be illustrated with several process control examples.

Nonlinear worst-case output feedback design: an illustrative example
A. Rapaport (Imperial College, London).

A simple pursuit in the plane, whose solution is already known under perfect information, is investigated under the framework of an incomplete information structure where the Certainty Equivalence Principle cannot be applied. The nonlinear theory, proposed by Bernhard for partial information differential games, is stretched here for free end-time problems.

Nonlinear Dynamics and Control of a Fixed Bed Reactor
Bodil Recke and Sten Bay Joergensen (Department of Chemical Engineering, Technical University of Denmark, Lyngby).

This presentation will describe the dynamic behaviour which arise when recycle is applied to a fixed bed reactor. The types of recycle which are investigated are: recycle of mass (unconverted reactant), recycle of energy (heat exchange between cold inlet and hot outlet gas), or a combination of the two. The results are the multiple steady states can occur, when energy recycle is applied. Furthermore periodic solutions can exist with all the types of recycle. The dynamic behaviour is described in form of bifurcation diagrams. Control aspects are brefly described.

Simple global nonlinear observers for polymerization reactors
D. Guillaume, P. Rouchon, J. Rudolph (Ecole des Mines de Paris, Centre Automatique et Systèmes).

Using temperature and density measures, we propose nonlinear global exponential observers for the three compositions (monomer, initiator and solvent) in the reactor. Such observers are based on the structure of the system and thus can be used for a large class of polymerization reactors, such as the ones considered by Gauthier and coworkers in a recent paper.

Local "tracking observer" for flat chemical reactors
J. Rudolph, M. Fliess (CAS and ISR, University of Stuttgart and Laboratoire des signaux et systemes, CNRS, Supelec).

Flatness allows to change the operating regime along trajectories chosen off-line. Linearization along such known trajectories allows to freely assign locally exponentially stable observer error dynamics by using a "gain scheduling" like technique.

Robustness of MPC-Based Schemes for Constrained Control of Nonlinear Systems
V. Nevistic, M. Morari (Automatic Control Laboratory, ETH Zurich).

An efficient method for the robustness analysis of model predictive control (MPC) based techniques for constrained nonlinear control is proposed. Performance properties of nonlinear MPC (NLMPC) and MPC with feedback linearization (FL) are measured in terms of an induced norm. dynamical optimization problem with a newly developed power algorithm. The efficiency of the proposed method is demonstrated on two test plants, where the robustness properties of MPC+FL and NLMPC are compared.