Nicolas Boizot

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.

Motion Planning for Kinematic Systems

In this paper, we present a general theory of motion planning for kinematic systems. In particular, the theory deals with ε-approximations of non-admissible paths by admissible ones in a certain optimal sense. The need for such an approximation arises for instance in the case of highly congested configuration spaces. This theory has been developed by one of the authors in a previous series of papers. It is based upon concepts from subriemannian geometry. Here, we summarize the results of the theory, and we improve on, by developing in details an intricate case: the ball with a trailer, which corresponds to a distribution with flag of type 2, 3, 5, 6.

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.

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

High-gain extended Kalman filter for continuous-discrete systems with asynchronous measurements

ABSTRACT This paper investigates an adaptation of the high-gain Kalman filter for nonlinear continuous-discrete system with multirate sampled outputs under an observability normal form. The contribution of this article is twofold. First, we prove the global exponential convergence of this observer through the existence of bounds for the Riccati matrix. Second, we show that, under certain conditions on the sampling procedure, the observers asynchronous continuous-discrete Riccati equation is stable and also, that its solution is bounded from above and below. An example, inspired by mobile robotics, with three outputs available is given for illustration purposes.