Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications

It is due to the modularity of the analysis that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on ``adding integrators''. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when decoupled, the subsystems constituting the cascade are uniformly globally asymptotically stable (UGAS). Hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable (USPAS). This situation is often encountered in control practice, e.g., in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, etc. This paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition, the cascade of two USPAS systems remains USPAS. An analogous result can be derived for USAS systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that links the parameter-dependency of the lower and upper bounds on the Lyapunov function, stronger condition of uniform boundedness of solutions, modification and simplification of the proofs accordingl

Global stabilization of linear systems with bounds on the feedback and its successive derivatives

We address the global stabilization of linear time-invariant (LTI) systems when the magnitude of the control input and its successive time derivatives, up to an order $p\in\mathbb N$, are bounded by prescribed values. We propose a static state feedback that solves this problem for any admissible LTI systems, namely for stabilizable systems whose internal dynamics has no eigenvalue with positive real part. This generalizes previous work done for single-input chains of integrators and rotating dynamics

Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives

In this paper, we address the global stabilization of chains of integrators by means of a bounded static feedback law whose p first time derivatives are bounded. Our construction is based on the technique of nested saturations introduced by Teel. We show that the control amplitude and the maximum value of its p first derivatives can be imposed below any prescribed values. Our results are illustrated by the stabilization of the third order integrator on the feedback and its first two derivatives

Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases

Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\mu,T$ such that, for every $t\geq 0$, $\int_t^{t+T}\alpha(s)ds\geq \mu$. In particular, when $\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback $u=Kx$, with $K$ only depending on $(A,B)$ and possibly on $\mu,T$, which globally asymptotically stabilizes the system? We give a positive answer to this question for two cases: when $A$ is neutrally stable and when the system is the double integrator

Quantised control of nonlinear systems: analysis of robustness to parameter uncertainty, measurement errors, and exogenous disturbances

International audienceWe propose a variant of the recently introduced strategy for stabilisation with limited information by D. Liberzon and J.P. Hespanha and analyse its robustness properties. We show that, if the nominal plant can be made input-to-state stable with respect to measurement errors, parameter uncertainty and exogenous disturbances, then this robustness is preserved with this quantised feedback. More precisely, if a sufficient bandwidth is available on the communication network, then the resulting closed loop is shown to be semiglobally input-to-state practically stable

Workshop on "Robotic assembly of 3D MEMS".

Proceedings of a workshop proposed in IEEE IROS'2007.The increase of MEMS' functionalities often requires the integration of various technologies used for mechanical, optical and electronic subsystems in order to achieve a unique system. These different technologies have usually process incompatibilities and the whole microsystem can not be obtained monolithically and then requires microassembly steps. Microassembly of MEMS based on micrometric components is one of the most promising approaches to achieve high-performance MEMS. Moreover, microassembly also permits to develop suitable MEMS packaging as well as 3D components although microfabrication technologies are usually able to create 2D and "2.5D" components. The study of microassembly methods is consequently a high stake for MEMS technologies growth. Two approaches are currently developped for microassembly: self-assembly and robotic microassembly. In the first one, the assembly is highly parallel but the efficiency and the flexibility still stay low. The robotic approach has the potential to reach precise and reliable assembly with high flexibility. The proposed workshop focuses on this second approach and will take a bearing of the corresponding microrobotic issues. Beyond the microfabrication technologies, performing MEMS microassembly requires, micromanipulation strategies, microworld dynamics and attachment technologies. The design and the fabrication of the microrobot end-effectors as well as the assembled micro-parts require the use of microfabrication technologies. Moreover new micromanipulation strategies are necessary to handle and position micro-parts with sufficiently high accuracy during assembly. The dynamic behaviour of micrometric objects has also to be studied and controlled. Finally, after positioning the micro-part, attachment technologies are necessary

On the robustness analysis of triangular nonlinear systems: iISS and practical stability

International audienceThis note synthesizes recent results obtained by the authors on the stability and robustness analysis of cascaded systems. It focuses on two properties of interest when dealing with perturbed systems, namely integral input-to-state stability and practical stability. We present sufficient conditions for which each of these notions is preserved under cascade interconnection. The obtained conditions are of a structural nature, which makes their use particularly easy in practice

Micromanipulation and Micro-Assembly Systems.

International audienceThe needs to manipulate micrometer sized objects keeps growing and concerns numerous and various fields like microsystems (MEMS1 and MOEMS2), micromechanics, optics, biology or pharmacy. The specificities of size, material, geometry and consistency of manipulated micro-objects, their surrounding, the kind of task to perform and the free size are all the more specific parameters that strongly influence the design and working of micromanipulation and micro-assembly systems. These systems are widely developing because they correspond both to industrial needs and really challenging scientific problematics. For these reasons, the present paper aimed at dealing with a review that mainly focuses on systems recently developed to assemble small series of microcomponents. The paper especially points out different solutions of carriers structures, gripping principles, sensors, other peri-microrobotic systems and control systems presenting the main solution and justifying their use and interest