43,150 research outputs found
Error-constrained filtering for a class of nonlinear time-varying delay systems with non-gaussian noises
Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected].
By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the quadratic error-constrained filtering problem is formulated and investigated for discrete time-varying nonlinear systems with state delays and non-Gaussian noises. Both the Lipschitz-like and ellipsoid-bounded nonlinearities are considered. The non-Gaussian noises are assumed to be unknown, bounded, and confined to specified ellipsoidal sets. The aim of the addressed filtering problem is to develop a recursive algorithm based on the semi-definite programme method such that, for the admissible time-delays, nonlinear parameters and external bounded noise disturbances, the quadratic estimation error is not more than a certain optimized upper bound at every time step. The filter parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the
U.K., the National Natural Science Foundation of China under Grant 61028008
and Grant 61074016, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany.
Recommended by Associate Editor E. Fabre
Robust Stability Analysis of Nonlinear Hybrid Systems
We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems
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
Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities
We study pattern formation associated with the polarization degree of freedom
of the electric field amplitude in a mean field model describing a nonlinear
Kerr medium close to a two-photon resonance, placed inside a ring cavity with
flat mirrors and driven by a coherent -polarized plane-wave field. In
the self-focusing case, for negative detunings the pattern arises naturally
from a codimension two bifurcation. For a critical value of the field intensity
there are two wave numbers that become unstable simultaneously, corresponding
to two Turing-like instabilities. Considered alone, one of the instabilities
would originate a linearly polarized hexagonal pattern whereas the other
instability is of pure vectorial origin and would give rise to an elliptically
polarized stripe pattern. We show that the competition between the two
wavenumbers can originate different structures, being the detuning a natural
selection parameter.Comment: 21 pages, 6 figures. http://www.imedea.uib.es/PhysDep
Analysis of switched and hybrid systems - beyond piecewise quadratic methods
This paper presents a method for stability analysis of switched and hybrid systems using polynomial and piecewise polynomial Lyapunov functions. Computation of such functions can be performed using convex optimization, based on the sum of squares decomposition of multivariate polynomials. The analysis yields several improvements over previous methods and opens up new possibilities, including the possibility of treating nonlinear vector fields and/or switching surfaces and parametric robustness analysis in a unified way
Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing
We study the excitation of spatial patterns by resonant, multi-frequency
forcing in systems undergoing a Hopf bifurcation to spatially homogeneous
oscillations. Using weakly nonlinear analysis we show that for small amplitudes
only stripe or hexagon patterns are linearly stable, whereas square patterns
and patterns involving more than three modes are unstable. In the case of
hexagon patterns up- and down-hexagons can be simultaneously stable. The
third-order, weakly nonlinear analysis predicts stable square patterns and
super-hexagons for larger amplitudes. Direct simulations show, however, that in
this regime the third-order weakly nonlinear analysis is insufficient, and
these patterns are, in fact unstable
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