Sufficient condition of affine system controllability

a sufficient condition for null controllability of nonlinear control systems

classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

A High Order Sufficient Condition for Local Controllability

A necessary and sufficient condition for the controllability of linear systems in Hilbert spaces and applications

As we have announced in the title of this work, we show that a broad class of linear evolution equations are exactly controllable. This class is represented by the following infinite dimensional linear control system: ż = Az + Bu(t), t > 0, z ∈ Z, u(t) ∈ U where Z, U are Hilbert spaces, the control function u belong to L2(0, t1; U), t1 > 0, B ∈ L(U,Z), A generates a strongly continuous semigrou...

A Sufficient and Controllability Necessary Condition for the of Linear Hybrid Systems

AbsirmAn algebraic approach for the controllability analy sir of a class of h) brid control syslems rallcd cootrolled awltching linear h)hrid r y a e m r is proposcd. A rufficicnl and neccrrar, condition is obtained bared on the algebraic manipulalion 01 related system matriccs. This consequence is directly oriented Io numerical romputnlion of Ibe controllability. Beside that, the existing resu...

A Sufficient Condition for Hyperinvariance

A linear transformation on a finite-dimensional complex linear space has the property that all of its invariant subspaces are hyperinvariant if and only if its lattice of invariant subspaces is distributive [1]. It is shown that an operator on a complex Hilbert space has this property if its lattice of invariant subspaces satisfies a certain distributivity condition. 1. Preliminaries. Throughou...