80 research outputs found
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
Uniting observers
International audienceWe propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviours for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: one, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behaviour. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented
Quasi-optimal robust stabilization of control systems
In this paper, we investigate the problem of semi-global minimal time robust
stabilization of analytic control systems with controls entering linearly, by
means of a hybrid state feedback law. It is shown that, in the absence of
minimal time singular trajectories, the solutions of the closed-loop system
converge to the origin in quasi minimal time (for a given bound on the
controller) with a robustness property with respect to small measurement noise,
external disturbances and actuator noise
Robust stabilization of chained systems via hybrid control
Published versio
Uniting Nesterov and Heavy Ball Methods for Uniform Global Asymptotic Stability of the Set of Minimizers
We propose a hybrid control algorithm that guarantees fast convergence and
uniform global asymptotic stability of the unique minimizer of a smooth, convex
objective function. The algorithm, developed using hybrid system tools, employs
a uniting control strategy, in which Nesterov's accelerated gradient descent is
used "globally" and the heavy ball method is used "locally," relative to the
minimizer. Without knowledge of its location, the proposed hybrid control
strategy switches between these accelerated methods to ensure convergence to
the minimizer without oscillations, with a (hybrid) convergence rate that
preserves the convergence rates of the individual optimization algorithms. We
analyze key properties of the resulting closed-loop system including existence
of solutions, uniform global asymptotic stability, and convergence rate.
Additionally, stability properties of Nesterov's method are analyzed, and
extensions on convergence rate results in the existing literature are
presented. Numerical results validate the findings and demonstrate the
robustness of the uniting algorithm.Comment: The technical report accompanying "Uniting Nesterov and Heavy Ball
Methods for Uniform Global Asymptotic Stability of the Set of Minimizers",
submitted to Automatica, 2022. Revisions made according to first round
reviewer feedbac
Output-Feedback Shared-Control for Fully Actuated Linear Mechanical Systems
This paper presents an output feedback shared-control algorithm for fully-actuated, linear, mechanical systems. The feasible configurations of the system are described by a group of linear inequalities which characterize a convex admissible set. The properties of the shared-control algorithm are established with a Lyapunov-like analysis. Simple numerical examples demonstrate the effectiveness of the strategy
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