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.

This paper considers the control of a group of autonomous mobile robots. A coordinated control scheme based on a leader-follower approach is developed to achieve formation maneuvers. First and second order sliding-mode controllers are proposed for asymptotically stabilizing the vehicles to a time-varying desired formation. The latter controller, based on the relative motion states, eliminates the need for measurement or estimation of the leader velocity. It enables formation stabilization using a vision system carried by the followers and ensures the collision avoidance from the initial time instance. Experimental investigation has been conducted using a test bench made of three nonholonomic mobile robots in order to demonstrate the effectiveness of the proposed strategy.

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.

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.