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576
In this Note, applying our recent Theorem 3.1 of [7], we prove that suitable perturbations of a completely controllable linear control system, do not affect the controllability of the system.
This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters and . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order and . Using a discrete...
This paper studies the
exact controllability of a finite dimensional system obtained by
discretizing in space and time the linear 1-D wave system with a
boundary control at one extreme. It is known that usual schemes
obtained with finite difference or finite element methods are not
uniformly controllable with respect to the discretization
parameters h and Δt. We introduce an implicit finite
difference scheme which differs from the usual centered one by
additional terms of order h2 and Δt2. Using...
We consider real analytic finite-dimensional control problems with a scalar input that enters linearly in the evolution equations. We prove that, whenever it is possible to steer a state x to another state y by means of a measurable control, then it is possible to steer x to y by means of a control that has an extra regularity property, namely, that of being analytic on an open dense subset of its interval of definition. Since open dense sets can have very small measure, this is a very weak property....
Contrary to state space systems, there are different notions of controllability for linear time invariant descriptor systems due to the non smooth inputs and inconsistent initial conditions. A comprehensive study of different notions of controllability for linear descriptor systems is performed. Also, it is proved that reachable controllability for general linear time invariant descriptor system is equivalent to the controllability of some matrix pair under an assumption milder than impulse controllability....
The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,...
Geometric control theory and Riemannian techniques are used to describe
the reachable set at time t of left invariant single-input control systems
on semi-simple compact Lie groups and to
estimate the minimal time needed to reach any point from identity.
This method provides an effective way to give an upper and a lower bound
for the minimal time needed to transfer a controlled quantum system
with a drift from a given initial position to a given final position.
The bounds include diameters...
This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium for Markov chains games. For solving the cooperative -leaders and -followers Markov game we consider the minimization of the norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong Stackelberg/Nash...
The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples....
Le but de cet article est de montrer l’état de l’art dans l’analyse des systèmes distribués lorsque l’on examine certains concepts à partir de considérations régionales. Autrement dit, à partir de la donnée d’un système dynamique défini sur un domaine , on ne s’intéresse à sa contrôlabilité, à son observabilité, à sa stabilité, ... que sur une région privilégiée , . Partant de concepts classiques, on développe leur adaptation au cas régional. On développe ensuite des concepts régionaux propres...
Le but de cet article est de montrer l'état de l'art dans l'analyse des systèmes
distribués lorsque l'on examine certains concepts à partir de considérations régionales.
Autrement dit, à partir de la donnée d'un système dynamique défini sur un domaine
Ω, on ne
s'intéresse à sa contrôlabilité, à son observabilité, à sa stabilité, ... que sur une région
privilégiée ω, .
Partant de concepts classiques, on développe leur adaptation au cas
régional. On développe ensuite des concepts régionaux...
The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
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