Michel Fliess

A Lie-Backlund approach to equivalence and flatness of nonlinear systems

A new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives. This is a Lie-Backlund isomorphism. The authors prove that, although the state dimension is not preserved, the number of input channels is kept fixed. They also prove that a Lie-Backlund isomorphism can be realized by an endogenous feedback. The differentially flat nonlinear systems introduced by the authors (1992) via differential algebraic techniques, are generalized and the new notion of orbitally flat systems is defined. They correspond to systems which are equivalent to a trivial one, with time preservation or not. The endogenous linearizing feedback is explicitly computed in the case of the VTOL aircraft to track given reference trajectories with stability.

Real-time estimation for switched linear systems

We extend previous works on real-time estimation, via algebraic techniques, to the recovering of the switching signal and of the state for switching linear systems. We characterize also singular inputs for which the switched systems become undistinguishable. Several convincing numerical experiments are illustrating our techniques which are easily implementable.

Multivariable decoupled longitudinal and lateral vehicle control: A model-free design

The newly introduced model-free control is applied to a multivariable decoupled longitudinal and lateral vehicle control. It combines two outputs (lateral and longitudinal motions) via two inputs (braking/traction wheel torques and steering angle). It yields driving maneuvers requiring a control coordination of steering angle, braking and traction torques, in order to ensure an accurate tracking in straight or curved trajectories. It is also robust with respect to modeling errors and parametric uncertainties, even during critical driving situations, where such a control is required. Convincing computer simulations are displayed with noisy real data from a laboratory vehicle, which were used as reference trajectories and acquired under high lateral accelerations.

Active magnetic bearing: A new step for model-free control

The newly introduced model-free control is applied to the stabilization of an active magnetic bearing, which is a most important industrial device. Experimental results are compared to those obtained via other control techniques, showing at least on-par performance with this very straightforward approach, which is moreover quite easy to implement.

Stability margins and model-free control: A first look

We show that the open-loop transfer functions and the stability margins may be defined within the recent model-free control setting. Several convincing computer experiments are presented including one which studies the robustness with respect to delays.

Robust grey-box closed-loop stop-and-go control

This paper presents a robust stop-and-go control law, especially well adapted to car following scenarios in urban environments. Since many vehicle/road interaction factors (road slope, rolling resistance, aerodynamic forces) are very poorly known and measurements are quite noisy, a robust strategy is proposed within an algebraic framework. On the one hand, noisy signals will be processed in order to obtain accurate derivatives, and thereafter, variable estimates. On the other hand, a grey-box closed-loop control will be implemented to compensate all kind of unmodeled dynamics or parameter uncertainties.

A new computational approach for the demodulation of CPM signal

We present a straightforward algebraic setting for the demodulation of continuous phase modulated signals over an additive noise channel. We are exploiting the form of the continuous-time signal and the developments rely on classical deterministic numerical analysis. No assumption is required for the statistical properties of the signals and noises. The information-bearing symbol data are identified on-line, directly from the continuous time signal, without any sampling process. The approach is very simple to implement. It is robust with respect to additive noise disturbance. Simulation results are presented.