Stochastic affine quadratic regulator with applications to tracking control of quantum systems

This paper deals with the regulator theory of stochastic affine systems. Applying a tensor formal power series method, stochastic bilinear quadratic regulator is solved numerically. An example about tracking control of quantum systems is given to show the usefulness of the developed theory.     

Generation and protection of steady-state quantum correlations due to quantum channels with memory

We have proposed a scheme of the generation and preservation of two-qubit steady-state quantum correlations through quantum channels where successive uses of the channels are correlated. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels, have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of quantum correlations has been discussed in detail. The results show that steady-state entanglement between two initial qubits whose initial states are prepared in a specific family states without entanglement subject to amplitude damping channel with memory can be generated. The entanglement creation is related to the memory coefficient of channel \(\mu \). The stronger the memory coefficient of channel \( \mu \) is, the more the entanglement creation is, and the earlier the separable state becomes the entangled state. Besides, we compare the dynamics of entanglement with that of quantum discord when a two-qubit system is initially prepared in an entangled state. We show that entanglement dynamics suddenly disappears, while quantum discord dynamics displays only in the asymptotic limit. Furthermore, two-qubit quantum correlations can be preserved at a long time in the limit of \(\mu \rightarrow 1\).     

A design scheme for incomplete state or output feedback with applications to boiler and power system control

The problem of designing a linear feedback when all state variables are not available is discussed. The design scheme is based on computation of a complete state feedback and a reduction to a specified structure. The reduction is made by approximation of the eigenspace corresponding to a set of dominant eigenvalues. The method consists of successive choices of weightings on this space. The method is applied to the control of a boiler and a three-machine power system. In the power system case the complete state feedback can be replaced by local output feedback without significant decrease in performance.The examples indicate that the proposed method is a realistic design method for multivariable systems.     

Fuzzy control stabilization with applications to motorcycle control

This study develops fuzzy control that is designed with sliding modes to achieve stability of the fuzzy controller. Fuzzy control is formulated in the form of variable structure system (VSS) control. In contrast to previous works in which Lyapunov functions are used to examine the stability, the current study investigates the stability of fuzzy control from the viewpoints of differential geometric methods and the sliding mode theory. Best values for parameters in fuzzy control rules are determined with the aid of sliding modes. In order to improve control performance, a tuning algorithm is executed to adjust parameters for dealing with uncertainties and disturbances. Both computer simulations and experiments with regard to an inverted pendulum hinged to a rotating disk are carried out to validate the proposed method. This apparatus can to some extent represent cornering motion of a motorcycle on which a rider leans to maintain stability. Effects of rider's leaning angle on both stability and handling control are examined according to Bode plots.     

An efficient single output fuzzy control algorithm for adaptive applications

A new single output fuzzy control algorithm which is simple and efficient is developed in the paper. Assuming standard type membership functions, a fuzzy set is characterized in this approach by that element in the fuzzy set with maximal membership. Fuzzy rules are then represented by a set of numbers. The algorithm uses a matrix representation of the rules in which the input part of the rule is used as an index, and the indexed element is the corresponding output. This is shown to allow for easy expansion of the output universe. Modification and introduction of new rules are further shown to be very simple and as a salient feature the efficiency of the algorithm is found to increase, when the number of rules increases. This new algorithm is therefore particularly useful and efficient when combined with a rule adaption mechanism. Because of simplicity and efficiency, this algorithm is very suitable for implementation even on small micro processor systems, making adaptive fuzzy control feasible for industrial applications, where a fast and nonlinear control is required.     

Algorithm to control linear plants with measurable quantized output

Consideration was given to the control of linear plants under external perturbations and measurement of the quantized plant output. The “consecutive compensator” method was used to design the controller. The obtained algorithm tracks the quantized plant output with respect to the reference signal with precision depending on the quantization step. The simulations illustrate the efficiency of the proposed scheme.     

Optimal control on Lie groups with applications to attitude control

In this paper we solve a class of optimal control problems on Lie groups in the sense that we derive differential equations which the optimal controls must satisfy. These results are applied to the attitude control of a spacecraft modeled as a rigid body. Specifically, we derive control laws (both in open-loop and closed-loop form) to maneuver the spacecraft between two given rotational states in finite time. The laws are such that a cost functional measuring the over-all angular velocity during the spacecraft’s motion is minimized. They do not require recourse to numerical methods and hence can be easily implemented in an on-board attitude control system. After dealing with a three-axis controlled spacecraft we also discuss the case that only torques about two principal axes of an axisymmetric spacecraft can be exerted.     

Dynamics of quantum entanglement in quantum channels

Based on the von Neumann entropy, we give a computational formalism of the quantum entanglement dynamics in quantum channels, which can be applied to a general finite systems coupled with their environments in quantum channels. The quantum entanglement is invariant in the decoupled local unitary quantum channel, but it is variant in the non-local coupled unitary quantum channel. The numerical investigation for two examples, two-qubit and two-qutrit models, indicates that the quantum entanglement evolution in the quantum non-local coupling channel oscillates with the coupling strength and time, and depends on the quantum entanglement of the initial state. It implies that quantum information loses or gains when the state of systems evolves in the quantum non-local coupling channel.     

Hadamard quantum broadcast channels

We consider three different communication tasks for quantum broadcast channels, and we determine the capacity region of a Hadamard broadcast channel for these various tasks. We define a Hadamard broadcast channel to be such that the channel from the sender to one of the receivers is entanglement-breaking and the channel from the sender to the other receiver is complementary to this one. As such, this channel is a quantum generalization of a degraded broadcast channel, which is well known in classical information theory. The first communication task we consider is classical communication to both receivers, the second is quantum communication to the stronger receiver and classical communication to other, and the third is entanglement-assisted classical communication to the stronger receiver and unassisted classical communication to the other. The structure of a Hadamard broadcast channel plays a critical role in our analysis: The channel to the weaker receiver can be simulated by performing a measurement channel on the stronger receiver’s system, followed by a preparation channel. As such, we can incorporate the classical output of the measurement channel as an auxiliary variable and solve all three of the above capacities for Hadamard broadcast channels, in this way avoiding known difficulties associated with quantum auxiliary variables.     

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

1IntroductionBifurcation control has attracted great attention in thepast two decades[1].The study of bifurcation control atpresent mostly concerns bifurcation stabilization,delay ofthe onset of aninherent bifurcation,changingthe parametervalue of an existing bifurcation point,and so on[1~4].Fromthe stability point of view,a bifurcation point of anonlinear systemis very disadvantageous.Asystemthat hasa bifurcation point may have more than one equilibriumpoint in a neighborhood of the bifurcati…     

Classical capacities of quantum channels with environment assistance

A quantum channel physically is a unitary interaction between an information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [1], we consider a benevolent third party, i.e., a helper, controlling the environment state, and show how the helper’s presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, in two variants: one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.     

Networked iterative learning control design for discrete-time systems with stochastic communication delay in input and output channels

This paper develops two kinds of derivative-type networked iterative learning control (NILC) schemes for repetitive discrete-time systems with stochastic communication delay occurred in input and output channels and modelled as 0-1 Bernoulli-type stochastic variable. In the two schemes, the delayed signal of the current control input is replaced by the synchronous input utilised at the previous iteration, whilst for the delayed signal of the system output the one scheme substitutes it by the synchronous predetermined desired trajectory and the other takes it by the synchronous output at the previous operation, respectively. In virtue of the mathematical expectation, the tracking performance is analysed which exhibits that for both the linear time-invariant and nonlinear affine systems the two kinds of NILCs are convergent under the assumptions that the probabilities of communication delays are adequately constrained and the product of the input–output coupling matrices is full-column rank. Last, two illustrative examples are presented to demonstrate the effectiveness and validity of the proposed NILC schemes.     

Periodic optimization with applications to solar energy control

It is reasonable to assume in many temperature control applications, that disturbance signals, i.e. solar insolation, ambient temperature, etc. are periodic with 24 hour period and that these periodic disturbances persist over a sufficiently long time interval to allow the system response to settle into a steady-state periodic mode. In this study a linear model is assumed for the system being controlled. The steady-state average of an integral quadratic measure is selected as a performance index. Disturbance signals are assumed to be representable by Fourier series expansions. The periodic optimal control input, which minimizes the given performance index, is then computed in terms of its Fourier coefficient. The optimal control-input coefficients are obtained explicitly in terms of disturbance-input coefficients.     

Quantum coherence of two-qubit over quantum channels with memory

Using the axiomatic definition of the quantum coherence measure, such as the \(l_{1}\) norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffected by the phase damping as well as depolarizing channels. Besides, we also investigate the cohering and decohering power of quantum channels with memory.     

Nonlinear iterative learning control with applications to lithographic machinery

An experimental demonstration is given of (nonlinear) iterative learning control applied to a reticle stage of a lithographic wafer scanner. To limit the presence of noise in the learned forces, a nonlinear amplitude-dependent learning gain is proposed. With this gain, high-amplitude signal contents is separated from low-amplitude noise, the former being compensated by the learning algorithm. Contrary to the underlying linear design, the continuously varying trade-off between high-gain convergence rates and low-gain noise transmission demonstrates a significant improvement of the nonlinear design in achieving performance.     

Neuro-sliding mode control with its applications to seesaw systems

This paper proposes an approach of cooperative control that is based on the concept of combining neural networks and the methodology of sliding mode control (SMC). The main purpose is to eliminate the chattering phenomenon. Next, the system performance can be improved by using the method of SMC. In the present approach, two parallel Neural Networks are utilized to realize a neuro-sliding mode control (NSMC), where the equivalent control and the corrective control are the outputs of neural network 1 and neural network 2, respectively. Based on expressions of the SMC, the weight adaptations of neural network can be determined. Furthermore, the gradient descent method is used to minimize the control force so that the chattering phenomenon can be eliminated. Finally, experimental results are given to show the effectiveness and feasibility of the approach.     

Qualitative robust fuzzy control with applications to 1992 ACCbenchmark

Robust control has long been the purview of quantitative linear control techniques, while qualitative symbolic control has been deemed more suitable to obtaining complex control objectives that require only low-output precision. The intelligent techniques of fuzzy control have, however, shown promise in obtaining results comparable to those obtained from H_∞ and H₂ robust control techniques. Often though, these fuzzy control techniques ignore the original intent of fuzzy logic: implementation of symbolic linguistic control laws based on qualitative models of the plant and control behaviors. We show that robust control objectives, even for simple plants, can be achieved by first developing qualitative behaviors that stabilize the plant and then superimposing tracking behaviors that achieve control objectives. Specifically, by superimposing qualitative stability and tracking behaviors, we can achieve robustness and tracking stability comparable to the best published linear compensators for the 1992 ACC robust control benchmark     

Parametric output feedback control with response insensitivity

A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.