Stable invariant manifolds with application to control problems

Balanced realizations near stable invariant manifolds

It is shown that the notion of balancing a state space realization about a stable, isolated equilibrium point can be generalized to systems possessing only a stable invariant regular submanifold of arbitrary dimension, for example, a stable limit cycle.

Laguerre approximation of stable manifolds with application to connecting orbits

We present an algorithm, based on approximation by Laguerre polynomials, for computing a point on the stable manifold of a stationary solution of an autonomous system. A superconvergence phenomenon means that the accuracy of our results is much higher than the usual spectral accuracy. Both the theory and the implementation of the method are considered. Finally, as an application of the algorith...

Resilient Parameter-Invariant Control With Application to Vehicle Cruise Control

This work addresses the general problem of resilient control of unknown stochastic linear time-invariant (LTI) systems in the presence of sensor attacks. Motivated by a vehicle cruise control application, this work considers a first order system with multiple measurements, of which a bounded subset may be corrupted. A frequency-domain-designed resilient parameter-invariant controller is introdu...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Analyticity of Stable Invariant Manifolds for Ginzburg-landau Equation

This paper is devoted to prove analyticity of stable invariant manifold in a neighbourhood of an unstable steady-state solution for GinzburgLandau equation defined in a bounded domain of dimension not more than three. This investigation is made for possible applications in stabilization theory for semilinear parabolic equation. Introduction In this paper we prove analyticity of stable invariant...