Eric Busvelle

Brief paper: An adaptive high-gain observer for nonlinear systems

In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously (1) extended Kalman filters good noise filtering properties, and (2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations. The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example.

Observation and identification tools for non-linear systems: application to a fluid catalytic cracker

In this paper we recall general methodologies we developed for observation and identification in non-linear systems theory, and we show how they can be applied to real practical problems. In a previous paper, we introduced a filter which is intermediate between the extended Kalman filter in its standard version and its high-gain version, and we applied it to certain observation problems. But we were missing some important cases. Here, we show how to treat these cases. We also apply the same technique in the context of our identifiability theory. As non-academic illustrations, we treat a problem of observation and a problem of identification, for a fluid catalytic cracker (FCC). This FCC unit is one of the most crucial from an economic point of view for the petroleum industry.

Adaptive-gain observers and applications

We distinguish two kinds of observers for nonlinear systems which are used by scientists and engineers: empirical observers and converging observers.

New Results on Identifiability of Nonlinear Systems

Abstract In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability. In a previous paper (Busvelle and Gauthier, 2003), we have established that • If the number of observations is three or more, then, systems are generically identifiable. • If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results in the first case.

Using an Adaptive High-Gain Extended Kalman Filter With a Car Efficiency Model

The authors apply the Adaptive High-Gain Extended Kalman Filter (AEKF) to the problem of estimating engine efficiency with data gathered from normal driving. The AEKF is an extension of the traditional Kalman Filter that allows the filter to be reactive to perturbations without sacrificing noise filtering. An observability normal form of the engine efficiency model is developed for the AEKF. The continuous-discrete AEKF is presented along with strategies for dealing with asynchronous data. Empiric test results are presented and contrasted with EKF-derived results.Copyright

On the stability of a differential Riccati equation for continuous-discrete observers

ABSTRACT This article deals with the stability properties of a continuous-discrete Riccati differential equation. The main motivation comes from the theory of Kalman filters for continuous-time nonlinear systems with sampled measurements, where this type of equation often arises. Stability is to be understood in the following sense: under appropriate hypotheses, the solution matrix is always symmetric positive definite and bounded from above and below. No uniformity is expected from the sampling procedure, only an upper bound on the elapsed time between consecutive samples is needed. The exposition consists of two parts. First, the stability properties are proven and second, by means of three examples, it is shown how the articles main result applies.

GEOMETRIC OPTIMAL CONTROL OF THE ATMOSPHERIC ARC FOR A SPACE SHUTTLE

We give preliminary remarks concerning the optimal control of the atmospheric arc for a space shuttle (earth re-entry or Mars sample return project). The system governing the trajectories is 6–dimensional, the control is the bank angle, the cost–integrand is the thermal flux and we have state constraints on the thermal flux and the normal acceleration. Our study is geometric and founded on the analysis of the solutions of a minimum principle and direct evaluation of the small–time reachable set for the problem taking into account the state constraints.