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Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phase-space geometry after conjugation...
In the paper, a possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proven that under specific conditions there is at least one trajectory of generalized semiflow, which lies inside an arbitrary covering of the solution set. The trajectory mutually connects each subset of the covering. A connection with symbolic dynamical systems is mentioned and a possible numerical method of analysis of dynamical behavior is outlined....
The paper presents a new approach to fuzzy classification in the case of missing data. Rough-fuzzy sets are incorporated into logical type neuro-fuzzy structures and a rough-neuro-fuzzy classifier is derived. Theorems which allow determining the structure of the rough-neuro-fuzzy classifier are given. Several experiments illustrating the performance of the roughneuro-fuzzy classifier working in the case of missing features are described.
Linear, continuous dynamical systems with multiple delays in control are studied. Their relative and absolute controllability with constrained control is discussed. Definitions of various types of constrained relative and absolute controllability for linear systems with delays in control are introduced. Criteria of relative and absolute controllability with constrained control are established. Constraints on control values are considered. Mutual implications between constrained relative controllability...
One establishes some convexity criteria for sets in . They will be applied in a further Note to treat the existence of solutions to minimum time problems for certain Lagrangian systems referred to two coordinates, one of which is used as a control. These problems regard the swing or the ski.
This Note is the Part II of a previous Note with the same title. One refers to holonomic systems with two degrees of freedom, where the part can schemetize a swing or a pair of skis and schemetizes whom uses . The behaviour of is characterized by a coordinate used as a control. Frictions and air resistance are neglected. One considers on minimum time problems and one is interested in the existence of solutions. To this aim one determines a certain structural condition which implies...
See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case , and satisfy conditions (11.7) when is a polynomial in , conditions (C)-i.e. (11.8) and (11.7) with -are proved to be necessary for treating satisfactorily 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....
In [1] I and II various equivalence theorems are proved; e.g. an ODE with a scalar control is linear w.r.t. iff its solution with given initial conditions (chosen arbitrarily) is continuous w.r.t. in a certain sense, or iff
This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability...
In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...
In this paper, we consider general nonlinear systems with observations,
containing a (single) unknown function φ. We study the possibility to
learn about this unknown function via the observations: if it is possible to
determine the [values of the] unknown function from any experiment [on the set
of states visited during the experiment], and for any arbitrary input
function, on any time interval, we say that the system is “identifiable”.
For systems without controls, we give a more or less complete...
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