42,027 research outputs found
Incremental generalized homogeneity, observer design and semiglobal stabilization
The notion of incremental generalized homogeneity is introduced, giving new results on semiglobal stabilization by output
feedback and observer design and putting into a unifying framework the stabilization design for triangular (feedback/
feedforward) and homogeneous systems. A state feedback controller and an asymptotic state observer are designed separately by
dominating the generalized homogeneity degree of the nonlinearities with the degree of the linear approximation of the system
and an output feedback controller is obtained according to a certainty-equivalence principle
Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers
Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers
Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves
In this paper, we shall prove a Carleman estimate for the so-called Zaremba
problem. Using some techniques of interpolation and spectral estimates, we
deduce a result of stabilization for the wave equation by means of a linear
Neumann feedback on the boundary. This extends previous results from the
literature: indeed, our logarithmic decay result is obtained while the part
where the feedback is applied contacts the boundary zone driven by an
homogeneous Dirichlet condition. We also derive a controllability result for
the heat equation with the Zaremba boundary condition.Comment: 37 pages, 3 figures. Final version to be published in Amer. J. Mat
Stabilization via generalized homogeneous approximations
We introduce a notion of generalized homogeneous approximation at the origin and at infinity which extends the classical notions and captures a large class of nonlinear systems, including (lower and upper) triangular systems. Exploiting this extension and although this extension does not preserve the basic properties of the classical notion, we give basic results concerning stabilization and robustness of nonlinear systems, by designing a homogeneous (in the generalized sense) feedback controller which globally asymptotically stabilizes a chain of power integrators and makes it the dominant part at infinity and at the origin (in the generalized sense) of the dynamics. Stability against nonlinear perturbation follows from domination arguments
Homogeneity in the bi-limit as a tool for observer and feedback design
International audienceWe introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system
Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right
This paper is devoted to the study of the rapid exponential stabilization
problem for a controlled Korteweg-de Vries equation on a bounded interval with
homogeneous Dirichlet boundary conditions and Neumann boundary control at the
right endpoint of the interval. For every noncritical length, we build a
feedback control law to force the solution of the closed-loop system to decay
exponentially to zero with arbitrarily prescribed decay rates, provided that
the initial datum is small enough. Our approach relies on the construction of a
suitable integral transform.Comment: 45 page
Homogeneous Approximation, Recursive Observer Design, and Output Feedback
We introduce two new tools that can be useful in nonlinear observer and
output feedback design. The first one is a simple extension of the notion of
homogeneous approximation to make it valid both at the origin and at infinity
(homogeneity in the bi-limit). Exploiting this extension, we give several
results concerning stability and robustness for a homogeneous in the bi-limit
vector field. The second tool is a new recursive observer design procedure for
a chain of integrator. Combining these two tools, we propose a new global
asymptotic stabilization result by output feedback for feedback and feedforward
systems
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