The systems-theoretic concept of controllability is elaborated for quantum-mechanical systems, sufficient conditions being sought under which the state vector ψ can be guided in time to a chosen point in the Hilbert space ℋ of the system. The Schrödinger equation for a quantum object influenced by adjustable external fields provides a state-evolution equation which is linear in ψ and linear in the external controls (thus a bilinear control system). For such systems the existence of a dense analytic domain 𝒟ω in the sense of Nelson, together with the assumption that the Lie algebra associated with the system dynamics gives rise to a tangent space of constant finite dimension, permits the adaptation of the geometric approach developed for finite-dimensional bilinear and nonlinear control systems. Conditions are derived for global controllability on the intersection of 𝒟ω with a suitably defined finite-dimensional submanifold of the unit sphere Sℋ in ℋ. Several soluble examples are presented to illuminate the general theoretical results.

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When a two-qubit system is initially maximally-entangled, two independent decoherence channels, one per qubit, would greatly reduce the entanglement of the two-qubit system when it reaches its stationary state. We propose a method on how to minimize such a loss of entanglement in open quantum systems. We find that the quantum entanglement of general two-qubit systems with controllable parameters can be protected by tuning both the single-qubit parameters and the twoqubit coupling strengths. Indeed, the maximum fidelity Fmax between the stationary entangled state, ρ∞, and the maximally-entangled state, ρm, can be about 2/3 ≈ max{tr(ρ∞ρm)} = Fmax, corresponding to a maximum stationary concurrence, Cmax, of about 1/3 ≈ C(ρ∞) = Cmax. This is significant because the quantum entanglement of the two-qubit system can be protected, even for a long time. We apply our proposal to several types of two-qubit superconducting circuits, and show how the entanglement of these two-qubit circuits can be optimized by varying experimentallycontrollable parameters.

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This paper is devoted to the problem of controlling a robot manipulator for a class of constrained motions. The task under consideration is to control the manipulator, such that the end-effector follows a path on an unknown surface, with the aid of a single camera assumed to be uncalibrated with respect to the robot coordinates. To accomplish a task of this kind, we propose a new control strategy based on multisensor fusion. We assume that three different sensors-that is, encoders mounted at each joint of the robot with six degrees of freedom, a force-torque sensor mounted at the wrist of the manipulator, and a visual sensor with a single camera fixed to the ceiling of the workcell-are available. Also, we assume that the contact point between the tool grasped by the end-effector and the surface is frictionless. To describe the proposed algorithm that we have implemented, first we decouple the vector space of control variables into two subspaces. We use one for controlling the magnitude of the contact force on the surface and the other for controlling the constrained motion on the surface. This way, the control synthesis problem is decoupled and we are able to develop a new scheme that utilizes sensor fusion to handle uncalibrated parameters in the workcell, wherein the surface on which the task is to be performed is assumed to be visible, but has an a priori unknown position.

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minors of R ; A [ [ R ; p t ] is the Mcl\Iillan degree of the pole pn of R and IVote Added in Proof: Recent work shows that condition (9) rea [ R ] = ~~= l A I R ; p k ] [24]. quires that the return difference I + F&(s) not have a zero of Corollary 1: Let (?be defined by (3) and let L Y~ be defined by Fact 3. transmission at, P, = 1 7 % ' ' . J 1271. Under these conditions, for any k E { 1, 2,. . .,l] for which Re P k > 0, REFEREXCES det X k ( p s ) # 0 if and only if where in the triangular Hankel matrix, t.he Rka's are the coefficient matrices of R k defined by (4). Proof: From (17) and (19)-(20),m ) l ; hence and for any integer Bk > -,t lim (spk)'*det [I + F&(s)] = 0. Hence, by Lemma 2, (9) is true if and only if Q[det [ I f Fk] : p k ] = 7s. Let [ A , B, C , 01 be any minimal realization of the strictly proper element R of CnXn(s) defined by (15); then, because of the coprime factorization (16), det D ( s ) = c det (SI --4) [lti], [20]. S o a d e t (SI - 0). 1 : is still valid for poles on the boundary (i.e., Re pk = 0) whenever Gp(s) is meromorphic in a neighborhood of such p s . This will always be the case for differential delay systems.