Thierry Floquet

Finite-Time Observers: Application to Secure Communication

In this paper, control theory is used to formalize finite-time chaos synchronization as a nonlinear finite-time observer design issue. This paper introduces a finite-time observer for nonlinear systems that can be put into a linear canonical form up to an output injection. The finite-time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the problem of secure data transmission based on the finite-time chaos synchronization and the two-channel transmission method.

A novel higher order sliding mode control scheme

A higher order sliding mode control algorithm is proposed for a class of uncertain multi-input multi-output nonlinear systems. This problem can be viewed as the flnite time stabilization of a higher order input-output dynamic system with bounded uncertainties. The developed control scheme is based on geometric homogeneity and sliding mode control. The proposed procedure provides explicit conditions on the controller parameters and guarantees robustness against uncertainties. An illustrative example of a hovercraft vessel control demonstrates the advantages of the strategy.

Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

This article highlights the interest of step-by-step higher order sliding mode observers for Multi-Input Multi-Output (MIMO) nonlinear systems with unknown inputs. A structural matching condition, commenting on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.

Brief Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems

This paper deals with nonholonomic perturbed systems. Necessary and sufficient geometric conditions on the perturbation vector field are given in order to put the system into a perturbed one-chained form. Two different sliding mode control strategies are then designed to robustly stabilize, under some conditions, this chained system: one providing a practical stabilization, the other performing a finite time convergence. As a way of illustration, simulations on the example of the unicycle-type mobile robot are presented.

On the robust fault detection via a sliding mode disturbance observer

This paper deals with robust fault detection for non-linear systems. This problem is usually solved by designing an observable subsystem which is only affected by the fault and not by the control and disturbance inputs. However, such a subsystem may not exist so that the so-called fundamental problem of residual generation (FPRG) is not solvable. The aim of the present paper is to design a fault detection filter when the conditions for the existence of a solution to the non-linear FPRG are not satisfied. Our approach is made in a geometric context. Under some decoupling assumptions, the design of sliding mode observers allows us to reconstruct the disturbance inputs and then to generate an effective residual. An illustrative example is given throughout the paper.

State and unknown input estimation for linear discrete-time systems

In this paper, a state and unknown input delayed estimator is designed for discrete-time linear systems even if some well-known matching condition does not hold. This result is obtained using a constructive algorithm that analyzes the state observability and the left invertibility of the systems with unknown inputs and that provides a suitable canonical transformation for the design of the estimator.

A Third-Order Sliding-Mode Controller for a Stepper Motor

This paper deals with the robust control problem of a stepper motor subject to parameter uncertainties and load torque perturbation. The developed algorithm is based on third-order sliding-mode control such that a desired angular motor position is accurately tracked. The proposed scheme requires the measurement or the estimation of the motor speed and acceleration for feedback. To avoid the use of tachometers and accelerometers which add cost and energy consumption, a robust second-order sliding-mode observer is presented. Experimental results illustrate the performance and the advantages of the proposed controller.

An algebraic framework for the design of nonlinear observers with unknown inputs

The observability properties of nonlinear systems with unknown inputs are characterized via differentially algebraic techniques. State variables and unknown inputs are estimated thanks to a new algebraic numerical differentiator. It is shown through an academic example and a concrete case-study that the proposed scheme can be applied to systems that fail to fulfill some usual structural assumptions.

Robust finite time observer design for multicellular converters

In this article, a nonlinear finite time observer is designed for multicellular converters. The aim is to estimate the capacitor voltages by taking into account the hybrid behaviour of the converter. This article extends the validity of the strong Lyapunov function, proposed in Moreno and Osorio (Moreno, J., and Osorio, M. (2008), ‘A Lyapunov Approach to Second Order Sliding Mode Controllers and Observers’, in Proceedings of the IEEE Conference on Decision and Control, New Orleans, USA, pp. 2856–2861), in order to deeply study the reaching time estimation and robustness of the homogeneous finite time observer given in Perruquetti et al. (Perruquetti, W., Floquet, T., and Moulay, E. (2008), ‘Finite Time Observers: Application to Secure Communication’, IEEE Transactions on Automatic Control, 53, 356–360). The proposed approach enables the stabilisation of the observation errors in spite of the presence of perturbations and uncertainties. Some simulations and comparisons with the super-twisting sliding mode observer highlight the efficiency of the proposed strategy.

Motion planning for cooperative unicycle-type mobile robots with limited sensing ranges: A distributed receding horizon approach

This paper presents a decentralized motion planner for a team of nonholonomic mobile robots subject to constraints imposed by sensors and the communication network. The motion planning scheme consists of decentralized receding horizon planners that reside on each vehicle to achieve coordination among flocking agents. The advantage of the proposed algorithm is that each vehicle only requires local knowledge of its neighboring vehicles. The main requirement for designing an optimal conflict-free trajectory in a decentralized way is that each robot does not deviate too far from its presumed trajectory designed without taking the coupling constraints into account. A comparative study between the proposed algorithm and other existing algorithms is provided in order to show the advantages, especially in terms of computing time. Finally, experiments are performed on a team of three mobile robots to demonstrate the validity of the proposed approach.