poster presentation

ER - TY - CONF T1 - Constructive robustness analysis of a limited-information feedback approach for nonlinear systems T2 - Proc. IEEE International Conference on Decision and Control Y1 - 2009 A1 - A. Franci A1 - A. Chaillet KW - Embedded Control KW - Robotics AB -We analyze the robustness properties of a recently introduced strategy for stabilization with limited information. We show that if the nominal closed-loop system can be made Input-to-State Stable (ISS) with respect to measurement errors, parameter uncertainty and exogenous disturbances then this robustness is preserved when only limited information is available on the plant. More precisely, if a sufficiently bandwidth is available on the communication network, then the resulting closed-loop is semiglobally practically ISS.

JF - Proc. IEEE International Conference on Decision and Control CY - Shangai, China ER - TY - CONF T1 - Delay compensation in packet-switching networked controlled systems T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2008 A1 - A. Chaillet A1 - A. Bicchi KW - Embedded Control KW - Robotics JF - Proc. IEEE Int. Conf. on Decision and Control ER - TY - JOUR T1 - Uniform Semiglobal Practical Asymptotic Stability for Non-autonomous Cascaded Systems and Applications JF - Automatica Y1 - 2008 A1 - A. Chaillet A1 - A. Lor KW - Robotics AB -It is due to the modularity they provide 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 \emph{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, ıt e.g.}, in control of physical systems with external perturbations, measurement noise, unmodelled dynamics, ıt etc}. After giving a rigorous framework for the analysis of such stability properties, this paper generalizes previous results for cascades by establishing that, under a uniform boundedness condition on its solutions, the cascade of two USPAS systems remains USPAS. An analogous result is derived for uniformly semiglobally asymptotically stable (USAS) systems in cascade. Furthermore, we show the utility of our results in the PID control of mechanical systems affected by unknown non-dissipative forces and considering the dynamics of the DC motors.

VL - 44 IS - 2 ER - TY - ABST T1 - Towards uniform linear time-invariant stabilization of systems with persistency of excitation Y1 - 2007 A1 - A. Chaillet A1 - Y. Chitour A1 - A. Lor A1 - M. Sigalotti KW - Robotics AB -Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizableand $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting. 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, only depending on $(A,B)$ and the parameters of the persistent excitation, which globally exponentially 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.

JF - Submitted to CDC 2007 CY - New Orleans, USA ER - TY - ABST T1 - Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases Y1 - 2007 A1 - A. Chaillet A1 - Y. Chitour A1 - A. Lor A1 - M. Sigalotti KW - Robotics AB -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. 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, only depending on $(A,B)$ and the parameters of the persistent excitation, 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.

JF - Submitted to Mathematics of Control, Signals and Systems ER - TY - CONF T1 - Adaptive output feedback control of spacecraft relative translation T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2006 A1 - R. Kristiansen A1 - A. Lor A1 - A. Chaillet A1 - P. J. Nicklasson KW - Robotics AB -We address the problem of tracking relative translation in a leader-follower spacecraft formation using feedback from relative position only and under parameter uncertainty (spacecraft mass) and uncertainty in the leader variables (true anomaly rate and rate of change). We only assume boundedness of orbital perturbations and the leader control force but with unknown bounds. Under these conditions we propose a controller that renders the closed-loop system, uniformly semiglobally practically asymptotically stable. In particular, the domain of attraction can be made arbitrarily large by picking convenient gains, and the state errors in the closed-loop system are proved to converge from any initial condition within the domain of attraction to a ball in close vicinity of the origin in a stable way; moreover, this ball can be diminished arbitrarily by increasing the gains in the control law. Simulation results of a leader-follower spacecraft formation using the proposed controller are presented.

JF - Proc. IEEE Int. Conf. on Decision and Control CY - San Diego, USA ER - TY - CONF T1 - Cascaded lemma for set-stable systems T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2006 A1 - J. Tsonnas A1 - A. Chaillet A1 - E. Panteley A1 - T. A. Johansen KW - Robotics AB -A previous result about uniform global asymptotic stability (UGAS) of the equilibrium of a cascaded time-varying systems, is here also shown to hold for closed (not necessarily compact) sets composed by set-stable subsystems of a cascade. In view of this result an optimal control allocation approach is discussed.

JF - Proc. IEEE Int. Conf. on Decision and Control CY - San Diego, USA ER - TY - CONF T1 - A converse Lyapunov theorem for semiglobal practical asymptotic stability and application to cascades-based control T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2006 A1 - A. Chaillet A1 - A. Lor KW - Robotics AB -We present a converse Lyapunov result for nonlinear time-varying systems that are uniformly semiglobally asymptotically stable. This stability property pertains to the case when the size of initial conditions may be arbitrarily enlarged and the solutions of the system converge, in a stable way, to a closed ball that may be arbitrarily diminished by tuning a design parameter of the system (typically but not exclusively, a control gain). This result is notably useful in cascaded-based control when uniform practical asymptotic stability is established without a Lyapunov function, , ıt e.g.} via averaging. We provide a concrete example by solving the stabilization problem of a hovercraft.

JF - Proc. IEEE Int. Conf. on Decision and Control CY - San Diego, USA ER - TY - CONF T1 - Estim T2 - CIFA 2006 Y1 - 2006 A1 - A. Chaillet AB - Pour les systèmes non-linéaires, il est connu que la propriété de stabilité asymptotique est conservée par la structure de cascade. Le pr JF - CIFA 2006 CY - Bordeaux, France N1 - In French ER - TY - CONF T1 - Integral Input to State Stability for cascaded systems T2 - MTNS 2006 Y1 - 2006 A1 - A. Chaillet A1 - D. Angeli KW - Robotics AB -The Integral Input to State Stability (iISS) property is studied is the context of nonlinear time-invariant systems in cascade. A sufficient condition is given, in terms of the storage function of each subsystem, to ensure that the cascade composed of an iISS system driven by a Globally Asymptotically Stable (GAS) one remains GAS. Some sufficient conditions for the preservation of the iISS property under a cascade interconnection are also presented.

JF - MTNS 2006 CY - Kyoto, Japan ER - TY - JOUR T1 - Necessary and sufficient conditions for uniform semiglobal practical asymptotic stability: Application to cascaded systems JF - Automatica Y1 - 2006 A1 - A. Chaillet A1 - A. Lor KW - Robotics AB -It is well established that for a cascade of two uniformly globally asymptotically stable (UGAS) systems, the origin remains UGAS provided that the solutions of the cascade are uniformly globally bounded. While this result has met considerable popularity in specific applications it remains restrictive since, in practice, it is often the case that the decoupled subsystems are only uniformly \emph{semiglobally} \emph{practically} asymptotically stable (USPAS). Recently, we established that the cascade of USPAS systems is USPAS under a local boundedness assumption and the hypothesis that one knows a Lyapunov function for the driven subsystem. The contribution of this paper is twofold: 1) we establish USPAS of cascaded systems without the requirement of a Lyapunov function and 2) we present a converse theorem for USPAS. While other converse theorems in the literature cover the case of USPAS ours has the advantage of providing a bound on the gradient of the Lyapunov function, which is fundamental to establish theorems for cascades.

VL - 42 ER - TY - CHAP T1 - Output feedback control of relative translation in a leader-follower spacecraft formation Y1 - 2006 A1 - R. Kristiansen A1 - A. Lor A1 - A. Chaillet A1 - P. J. Nicklasson KW - Robotics AB -We present a solution to the problem of tracking relative translation in a leader-follower spacecraft formation using feedback from relative position only. Three controller configurations are presented which enables the follower spacecraft to track a desired reference trajectory relative to the leader. The controller design is performed for different levels of knowledge about the leader spacecraft and its orbit. The first controller assumes perfect knowledge of the leader and its orbital parameters, and renders the equilibrium points of the closed-loop system uniformly globally asymptotically stable (UGAS). The second controller uses the framework of the first to render the closed-loop system uniformly globally practically asymptotically stable (UGPAS), with knowledge of bounds on some orbital parameters, only. That is, the state errors in the closed-loop system are proved to converge from any initial conditions to a ball in close vicinity of the origin in a stable way, and this ball can be diminished arbitrarily by increasing the gains in the control law. The third controller, based on the design of the second, utilizes adaptation to estimate the bounds that were previously assumed to be known. The resulting closed-loop system is proved to be uniformly semiglobally practically asymptotically stable (USPAS). The last two controllers assume boundedness only of orbital perturbations and the leader control force. Simulation results of a leader-follower spacecraft formation using the proposed controllers are presented.

T3 - Lecture Notes in Control and Information Sciences PB - Springer Verlag CY - Tromsoe, Norway ER - TY - CONF T1 - Robustness of PID controlled manipulators with respect to external disturbances T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2006 A1 - A. Chaillet A1 - A. Lor A1 - R. Kelly KW - Robotics AB -We present a robustness analysis for PID-controlled robot manipulators. For robot manipulators under the influence of external disturbances we provide a proof, and a tuning procedure, to establish uniform semiglobal practical asymptotic stability. In particular, in contrasts to other works on robust stability of PIDs, we do not use La Salle's principle but provide a strict Lyapunov function. The perturbations that we consider include discontinuous functions of the state, such as Coulomb friction. As corollaries of our main results, one may conclude the same stability property for the case of motion control using linear PID.

JF - Proc. IEEE Int. Conf. on Decision and Control CY - San Diego, USA ER - TY - THES T1 - On stability and robustness of nonlinear systems – Applications to cascaded systems Y1 - 2006 A1 - A. Chaillet KW - Robotics PB - Universit CY - Orsay, France N1 -Obtained Cum Laude. Jury: J.M. Coron, T.I. Fossen (reviewer), A. Lor

ER - TY - CONF T1 - Stability of sets for nonlinear systems in cascade T2 - MTNS 2006 Y1 - 2006 A1 - A. Chaillet A1 - E. Panteley KW - Robotics AB -The stability of (not necessarily compact) sets for nonlinear systems in cascade is addressed. It is proved that if two sets are globally asymptotically stable (GAS) for the subsystems taken separately then their cross-product is GAS for the corresponding cascade, provided that the solutions of the latter are globally bounded. In the case of a suitable growth rate of the interconnection in the state of the driven subsystem, we show that this latter requirement can be relaxed to just forward completeness of the cascade. Our results extend similar results on the stability analysis of cascaded systems and find applications in partial stability analysis and adaptive control.

JF - MTNS 2006 CY - Kyoto, Japan ER - TY - CHAP T1 - Tools for semiglobal practical stability analysis of cascaded systems and applications Y1 - 2006 A1 - A. Chaillet KW - Robotics AB -We present sufficient conditions for semiglobal and/or practical stability in terms of Lyapunov-like functions. Based on this, we provide a result for the stability analysis of cascaded systems. A converse result is also presented for a particular class of uniformly semiglobally practically asymptotically stable systems. We briefly show the usefulness of these results through various applications in the control of mechanical systems.

T3 - International Scientific and Technical Encyclopedia CY - Paris, France ER - TY - JOUR T1 - Uniform global practical asymptotic stability for non-autonomous cascaded systems JF - European Journal of Control Y1 - 2006 A1 - A. Chaillet A1 - A. Lor KW - Robotics AB -This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalise previous theorems that establish the uniform global asymptotic stability of cascades.

VL - 12 ER - TY - CONF T1 - Uniform Global Practical Stability for non-autonomous cascaded systems T2 - MTNS 2006 Y1 - 2006 A1 - A. Chaillet A1 - A. Lor KW - Robotics AB -This paper aims to give sufficient conditions for a cascade composed of nonlinear time-varying systems that are uniformly globally practically asymptotically stable (UGPAS) to be UGPAS. These conditions are expressed as relations between the Lyapunov function of the driven subsystem and the interconnection term. Our results generalize previous theorems that establish the uniform global asymptotic stability of cascades.

JF - MTNS 2006 CY - Kyoto, Japan ER - TY - CHAP T1 - A virtual vehicle approach to underway replenishment Y1 - 2006 A1 - E. Kyrkjebo A1 - E. Panteley A1 - A. Chaillet A1 - K. Pettersen KW - Robotics AB -The problem of coordinated control of a leader-follower system is solved using a virtual vehicle approach to alleviate information requirements on the leader. The virtual vehicle stabilizes to a shifted reference position/heading defined by the leader, and provides a reference velocity for the synchronization control law of the follower. Only position/heading measurements are available from the leader, and the closed-loop errors are shown to be uniformly globally practically asymptotically stable.

T3 - Lecture Notes in Control and Information Sciences PB - Springer Verlag CY - Tromsoe, Norway ER - TY - ABST T1 - Integral Input to State Stable systems in cascade Y1 - 2005 A1 - A. Chaillet A1 - D. Angeli KW - Robotics AB -The Integral Input to State Stability (iISS) property is studied is the context of nonlinear time-invariant systems in cascade. A sufficient condition is given, in terms of the storage function of each subsystem, to ensure that the cascade composed of an iISS system driven by a Globally Asymptotically Stable (GAS) one remains GAS. Some sufficient conditions for the preservation of the iISS property under a cascade interconnection are also presented.

JF - Submitted to Systems and Control Letters ER - TY - CONF T1 - Output feedback control via adaptive observers with persistency of excitation T2 - Proc. 16th. IFAC World Congress Y1 - 2005 A1 - De Leon Morales, J. A1 - A. Chaillet A1 - A. Lor A1 - G. Besancon KW - Robotics AB -We address the problem of adaptive observer design for nonlinear time-varying systems which can be transformed in the so-called output feedback form (linear in the unmeasured variables). The observer design follows up previous work on adaptive observers for linear systems and has the form of the classical Luenberger observers for linear systems except that the observer gain is time-varying. A specific form of persistency of excitation is imposed to guarantee the convergence of the (state and parameter) estimation errors. As for the output feedback loop, we proceed using a cascade approach, i.e., we impose the appropriate conditions so that the closed loop system has a cascaded structure. Uniform global asymptotic stability may then be concluded based on cascaded systems theory.

JF - Proc. 16th. IFAC World Congress CY - Praha, Tcheck Republic ER - TY - CONF T1 - On the PE stabilization of time-varying systems: open questions and preliminary answers T2 - Proc. IEEE Int. Conf. on Decision and Control Y1 - 2005 A1 - A. Lor A1 - A. Chaillet A1 - G. Besancon A1 - Y. Chitour KW - Robotics AB -We address the following fundamental question: given a double integrator and a linear control that stabilizes it exponentially, is it possible to use the {\em same} control input in the case that the control input is multiplied by a time-varying term? Such question has many interesting motivations and generalizations: 1) we can pose the same problem for an input gain that depends on the state and time hence, a specific persistency of excitation property for nonlinear systems must be imposed; 2) the stabilization –with the same method– of chains of integrators of higher order than two is fundamentally more complex and has applications in the stabilization of driftless systems; 3) the popular backstepping method stabilization method for systems with non-invertible input terms. The purpose of this note is two-fold: we present some open questions that we believe are significant in time-varying stabilization and present some preliminary answers for simple, yet challenging case-studies.

JF - Proc. IEEE Int. Conf. on Decision and Control CY - Sevilla, Spain ER - TY - CONF T1 - Uniform Semiglobal Practical Asymptotic Stability for nonlinear time-varying systems in cascade T2 - Proc. 16th. IFAC World Congress Y1 - 2005 A1 - A. Chaillet A1 - A. Lor KW - Robotics JF - Proc. 16th. IFAC World Congress CY - Praha, Tcheck Republic ER -