This paper considers the stabilization and H1 control of the Hamiltonian control systems with dissipation. Certain

In this paper, we first express a multimachine power system as a Hamiltonian control system with dissipation. Then, using the Hamiltonian function method a decentralized excitation control scheme, as a static measurable feedback, is proposed to stabilize the multimachine power system. Then, it is shown that the control scheme with properly chosen parameters is also an H ∞ control, which solves the problem of disturbance attenuation simultaneously. Finally, the design technique is demonstrated by a three-machine power system.

This note deals with chained form systems with strongly nonlinear unmodeled dynamics and external disturbances. The objective is to design a robust nonlinear state feedback law such that the closed-loop system is globally Kexponentially stable. We propose a novel switching control strategy involving the use of input/state scaling and integrator backstepping. The new features of our controllers include the ability to achieve Lyapunov stability, exponential convergence, and robustness to a set of uncertain drift terms.

We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters, such as the temperature and the ratio r between ω0, the characteristic frequency of the quantum system of interest, and ωc, the cut-off frequency of the Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-Markovian entanglement concurrence {\cal C}_{\rho}(t) at temperature kBT = 0 is different from the kBT > 0 case. We find that 'entanglement sudden death' (ESD) depends on the initial state when kBT = 0, otherwise the concurrence always disappears at a finite time when kBT > 0, which means that the ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence {\cal C}_{\rho}(t) oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.

We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρΦAB(0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N, amount of initial entanglement α and the purity r. For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ0t and one of the parameters N, α and r.

We investigate the optimal control problem for non-Markovian open, dissipative quantum system.

A direct method of constructing a decentralized saturated controller is very important in the controller design of multimachine power systems. Among the existing designs the author first constructed a state feedback, then saturated the controller. However, the author could not prove that this saturated controller was valid. In this paper a multi-machine power system as a Hamiltonian control system with dissipation is first represented. Then using a Hamiltonian function a decentralized saturated excitation control scheme, which is a static measurable feedback, is proposed. Last, the design is discussed in detail on a three-machine power system. Simulations show that the saturated, simple control law works well.

This paper deals with chained form systems with strongly nonlinear disturbances and drift terms. The objective is to design robust nonlinear output feedback laws such that the closed-loop systems are globally exponentially stable. The systematic strategy combines the input-state-scaling technique with the so-called backstepping procedure.

This paper deals with global output regulation with nonlinear exosystems for a class of uncertain nonlinear output feedback systems. The circle criterion is exploited for the internal model design to accommodate the nonlinearities in the exosystems, and the explicit conditions are given for the exosystems such that the proposed internal model design can be applied. The uncertainties of the output feedback systems are in the form of unknown constant parameters, and adaptive control techniques are used to ensure the global stability of the proposed control design for output regulation.

This paper deals with chained form systems with strongly nonlinear disturbances and drift terms. The objective is to design robust nonlinear output feedback laws such that the closed-loop systems are globally exponentially stable. The systematic strategy combines the input-state-scaling technique with the so-called backstepping procedure. A dynamic output feedback controller for general case of uncertain chained system is developed with a filter of observer gain. Furthermore, two special cases are considered which do not use the observer gain filter. In particular, a switching control strategy is employed to get around the smooth stabilization issue (difficulty) associated with nonholonomic systems when the initial state of system is known.

A qubit which is prepared in one of two non-orthogonal states and subjected to bit-flipping noise is considered. The objective is to use measurement and feedback control to correct the state of the qubit. Three classical schemes using projective measurements, i.e. discrimination and re-preparation, do nothing and random preparation, have been discussed, and are not optimal with respect to a performance which is quantified by the average fidelity of the corrected state compared to the initial state. In addition, one quantum scheme using a non-projective measurement with an optimum measurement strength achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. The performance of a quantum control scheme outperforms the classical schemes. Furthermore, no universal corrected scheme is discussed.

This paper deals with asymptotic rejection of disturbances generated from non-linear exosystems for uncertain nonlinear systems in an extended output feedback form, which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements. A new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance. Adaptive control techniques are then used to deal with the uncertainty in the system. The proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown nonlinear disturbance and the boundedness of all the variables.

We propose a control approach to transfer the population between selected quantum states in the non-Markovian open quantum system. This transfers, assisted by single qubit phase shift operations can generate universal logic gates for quantum computing. We find that the occupation probability behaves differently for different environmental conditions, such as the temperature and the ratio between the frequency of the quantum system of interest, and the cut-off frequency of Ohmic reservoir. We provide an active control over non-Markovian open quantum system for the quantum state engineering.

We investigate the optimal dynamical decoupling sequence for a qubit coupled to an ohmic environment.

Quantum correlations (QC) are generally considered to be the crucial resource for quantum information processing, however, in practice, the inevitable interaction of the quantum systems with the environment can cause decoherence and thus destroy the QC. In this paper, by comparatively studying the model of a two-qubit system in a common environment with and without dynamical control, we show that dynamical control can be exploited to protect QC from being completely destroyed for a long time. For certain product states, the dynamical control can even be used to generate the QC.