Control of the chaotic Duffing equation with uncertainty in all parameters

In this work, we deal with the open problem of controlling the periodically forced Duffing equation with uncertainty in all parameters. To date, several control schemes have been proposed to adapt for the linearly appearing unknown parameters but no solution exists for the case when the frequency of the periodic forcing is also unknown. We prove for the state feedback control case, global, asymptotic convergence for constant and time-varying references. We extend these results to the position feedback case and prove global ultimate boundednes

Robust output stabilization: improving performance via supervisory control

We analyze robust stability, in an input-output sense, of switched stable systems. The primary goal (and contribution) of this paper is to design switching strategies to guarantee that input-output stable systems remain so under switching. We propose two types of {\em supervisors}: dwell-time and hysteresis based. While our results are stated as tools of analysis they serve a clear purpose in design: to improve performance. In that respect, we illustrate the utility of our findings by concisely addressing a problem of observer design for Lur'e-type systems; in particular, we design a hybrid observer that ensures ``fast'' convergence with ``low'' overshoots. As a second application of our main results we use hybrid control in the context of synchronization of chaotic oscillators with the goal of reducing control effort; an originality of the hybrid control in this context with respect to other contributions in the area is that it exploits the structure and chaotic behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA

Linear robust output−feedback control for permanent−magnet synchronous motors with unknown load

International audienceWe solve the problem of set-point (respectively, tracking) control of a permanent-magnet synchronous motor via linear time-invariant (respectively, time varying) control. Our control approach is based on the physical properties of the machine: inherent stability and robustness to external disturbances. Our analysis is carried out under mild conditions, using cascaded systems theory. For all cases: constant operating point, trajectory tracking, and with known and unknown load, we show uniform global asymptotic stability of the closed-loop system with a linear controller that uses only velocity measurements. Furthermore, we explore natural extensions of our results to improve robustness with respect to external disturbances and parametric uncertainties

Control of the new 4th order hyper-chaotic system with one input

We solve the problem of chaos suppression of Lu's hyper-chaotic system via feedback control. We use only one control input and moreover the controller is a simple proportional feedback and uses the measurement of only one variable. We show that this simple control law suffices to stabilize the hyper-chaotic system to the zero equilibrium globally and asymptotically. We present stability proofs based on Lyapunov's direct method and integration of solutions. As a corollary of our main result we draw the conclusion that the system is globally stabilizable by simply varying one parameter, when possible. Simulation experiments that show the effectiveness of our method are also presented

Robust formation-tracking control of mobile robots in a spanning-tree topology

International audienceWe solve the formation-tracking control problem for mobile robots via linear control, under the assumption that each agent communicates only with one "leader" robot and with one follower. As in the classical tracking control problem for nonholonomic systems, the swarm is driven by a fictitious robot which moves about freely and which is leader to one robot only. For a spanning-tree topology we show that persistency of excitation on the velocity of the virtual leader is sufficient and necessary to achieve consensus tracking. Furthermore, we establish uniform global exponential stability for the error system which implies robustness with respect to additive bounded disturbances. From a graph viewpoint, our main result corroborates that the existence of a spanning tree is necessary and sufficient for consensus as opposed to the usual but restrictive assumption of all-to-all undirected communication

Adaptive unknonwn-input observers-based synchronization of chaotic circuits for secure telecommunication

International audienceWe propose a robust adaptive chaotic synchronization method based on unknown-input observers for master-slave syn- chronization of chaotic systems, with application to secured com- munication. The slave system is modelled by an unknown input observer in which, the unknown input is the transmitted informa- tion. As in the general observer-based synchronization paradigm, the information is recovered if the master and slave systems ro- bustly synchronize. In the context of unknown-input observers, this is tantamount to estimating the master's states and the unknown inputs. The set-up also considers the presence of perturbations in the chaotic transmitter dynamics and in the output equations (the transmitted signal). That is, the estimator (slave system) must syn- chronize albeit noisy measurements and reject the effect of pertur- bations on the transmitter dynamics. We provide necessary and sufficient conditions for synchronization to take place. To highlight our contribution, we also present some simulation results with the purpose of comparing the proposed method to classical adaptive observer-based synchronization (without disturbance rejection). It is shown that additive noise is perfectly canceled and the encoded message is well recovered despite the perturbations

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

A simple one-to-one communication algorithm for formation-tracking control of mobile robots

International audienceWe solve the formation-tracking control problem for mobile robots via linear control. As in the classical tracking control problem for two nonholonomic systems, the swarm is driven by a fictitious robot which moves about freely. Only one "leader" robot communicates with the reference vehicle and in turn, acts as a leader to a second robot hence forming a fixed spanning tree. We show that a simple condition on the reference angular velocity (persistency of excitation) suffices to achieve consensus tracking