For single-input multi-output C^infty-systems, we state conditions under which observability for every C^infty-input implies observability for every almost everywhere continuous, bounded input (for every L^infty$-input in the control-affine case). A normal system is then defined as a system whose only bad inputs are smooth on some nonempty open set. When the state space is compact, normality turns out to be generic and enables us to extend some results of genericity of observability to nonsmooth inputs.
M.A. Hammami. On the Stability of Nonlinear Control Systems with Uncertainty. J. Dynam. Control Systems 7 (2001), no. 2, 171--179.
In this paper, we study the stability problem of nonlinear dynamical control systems. We consider continuous-time dynamical systems whose nominal part is stable and whose perturbed part (uncertainties) is norm-bounded by a positive function. Under some conditions on the perturbation, by using Lyapunov techniques, we show that the system can be uniformly asymptotically stable by a continuous controller.
Zhonghai Ding. Optimal Boundary Controls of Linear Elastostatics on Lipschitz Domains with Point Observations. J. Dynam. Control Systems 7 (2001), no. 2, 181--207.
In this paper, we study optimal boundary control problems of the linear elastostatic equations on Lipschitz domains with point observations on boundary. By using the elastostatic potentials, existence and uniqueness of solutions to the optimal control problems with or without constraints on controls are investigated, and explicit characterization formulas of optimal controls are derived. A regularity property of the single layer elastostatic potential on Lipschitz domains is also established.
Ugo Boscain and Benedetto Piccoli. Extremal Synthesis for Generic Planar Systems. J. Dynam. Control Systems 7 (2001), no. 2, 209--258.
For a generic single-input planar control system we analyze the structure of the set of extremals for the time-optimal problem. Generically all extremals are finite concatenations of regular arcs that are bang or correspond to a smooth feedback. Moreover, the support of extremals is a Whitney stratified set. We collect these information in the definition of extremal synthesis. In the cotangent bundle, we give a topological classification of the singularities of the extremal synthesis and study the projections of the support of extremals (regarded as a two-dimensional object, after normalization) from (R^2 \times S^1) to the plane. With respect to the Whitney classical singularities here we deal with a stratified set with ``edges'' and ``corners,'' and along with cusps and folds, we find other stable singularities.
A.A. Arzhanov. Small Oscillations of Viscous Capillary Fluid: The WKB Approximation. J. Dynam. Control Systems 7 (2001), no. 2, 259--275.
For the Helmholtz equation with a spectral parameter in the boundary condition, series of quasmodes (i.e., asymptotic eigenvalues and eigenfunctions) are constructed in assumption that spectral parameter is large enough. Making use of certain integral relations and identities, the imaginary parts of the quasi-eigenvalues are shown to decrease faster than any power of the spectral parameter when the latter tends to infinity.
M. Lemasurier. Singularities of Second-Order Implicit Differential Equations: A Geometrical Approach. J. Dynam. Control Systems 7 (2001), no. 2, 277--298.
A second-order implicit differential equation
R(x, y, dy/dx, d^2y/dx^2)=0
is an equation for which the second derivative
cannot be written as a single-valued function of x, y,
and the first derivative dy/dx=p.
Such an equation defines a direction field in the space of 1-jets
(x,y,p), but the existence and uniqueness of a direction at a
point may not hold. Singularities can arise in a number of ways,
and we examine the equation and its solution
curves near the simplest of these singularities.
|
|
|
|
of manuscripts |
|
|