Shuang Cong

PID-Like Neural Network Nonlinear Adaptive Control for Uncertain Multivariable Motion Control Systems

A mix locally recurrent neural network was used to create a proportional-integral-derivative (PID)-like neural network nonlinear adaptive controller for uncertain multivariable single-input/multi-output system. It is composed of a neural network with no more than three neural nodes in hidden layer, and there are included an activation feedback and an output feedback, respectively, in a hidden layer. Such a special structure makes the exterior feature of the neural network controller able to become a P, PI, PD, or PID controller as needed. The closed-loop error between directly measured output and expected value of the system is chosen to be the input of the controller. Only a group of initial weights values, which can run the controlled closed-loop system stably, are required to be determined. The proposed controller can update weights of the neural network online according to errors caused by uncertain factors of system such as modeling error and external disturbance, based on stable learning rate. The resilient back-propagation algorithm with sign instead of the gradient is used to update the network weights. The basic ideas, techniques, and system stability proof were presented in detail. Finally, actual experiments both of single and double inverted pendulums were implemented, and the comparison of effectiveness between the proposed controller and the linear optimal regulator were given.

Lyapunov control methods of closed quantum systems

According to special geometric or physical meanings, the paper summarizes three Lyapunov functions in controlling closed quantum systems and their controller designing processes. Specially, for the average value-based method, the paper gives the generalized condition of the largest invariant set in the original reference and develops the construction method of the imaginary mechanical quantity; for the error-based method, this paper gives its strict mathematical proof train of thought on the asymptotic stability and the corresponding physical meaning. Also, we study the relations among the three Lyapunov functions and give a unified form of these Lyapunov functions. Finally, we compare the control effects of three Lyapunov methods by doing some simulation experiments.

Active Joint Synchronization Control for a 2-DOF Redundantly Actuated Parallel Manipulator

This brief applies the synchronization to solve control problem of redundantly actuated parallel manipulators. With the synchronization method, a new controller termed active joint-synchronization (AJ-S) controller is developed for a 2-degree-of-freedom (DOF) redundantly actuated parallel manipulator. The dynamic model of the parallel manipulator is formulated in the active joint space, in which the internal force is calculated by the projection method and the friction is depicted with the Coulomb + viscous friction model. By defining the tracking error, synchronization error, coupled error, and the referenced trajectory vector of the active joints, the AJ-S controller based on the dynamic model is designed. And the AJ-S controller is proven to guarantee asymptotic convergence to zero of both tracking and synchronization errors by the Barbalats lemma. The AJ-S controller is implemented in the trajectory tracking experiments of an actual 2-DOF redundantly actuated parallel manipulator, and the superiority of the AJ-S controller over the well-known tracking controller is studied.

Population Control of Equilibrium States of Quantum Systems via Lyapunov Method

Abstract This paper studies the population control problem associated with the equilibrium states of mixed-state quantum systems by using a Lyapunov function with degrees of freedom. The control laws are designed by ensuring the monotonicity of the Lyapunov function; main results on the largest invariant set in the sense of LaSalle are given; and the strict expression of any state in the largest invariant set is normally deduced in the framework of Bloch vectors. By analyzing the obtained largest invariant set and the Lyapunov function itself, this paper also discusses the determination problem of the degrees of freedom. Numerical simulation experiments on a three-level system show the validity of research results.

Population control of quantum states based on invariant subsets under a diagonal Lyapunov function

This paper deduces and analyzes the invariant set in quantum Lyapunov control, explores the principles for constructing and adjusting diagonal elements of a diagonal Lyapunov function, and achieves the convergence to any goal state in some invariant subset of closed loop systems by using dynamical system theory and energy-level connectivity graph. Research results show that if a goal state is an eigenstate of the inner Hamiltonian, then it is very easy to achieve convergence to the goal state with a high probability; and if a goal state is a superposition state in some invariant subset, then it is possible to achieve satisfactory control when the diagonal elements are properly constructed.

A reconstruction algorithm for compressive quantum tomography using various measurement sets

Compressed sensing (CS) has been verified that it offers a significant performance improvement for large quantum systems comparing with the conventional quantum tomography approaches, because it reduces the number of measurements from O(d2) to O(rd log(d)) in particular for quantum states that are fairly pure. Yet few algorithms have been proposed for quantum state tomography using CS specifically, let alone basis analysis for various measurement sets in quantum CS. To fill this gap, in this paper an efficient and robust state reconstruction algorithm based on compressive sensing is developed. By leveraging the fixed point equation approach to avoid the matrix inverse operation, we propose a fixed-point alternating direction method algorithm for compressive quantum state estimation that can handle both normal errors and large outliers in the optimization process. In addition, properties of five practical measurement bases (including the Pauli basis) are analyzed in terms of their coherences and reconstruction performances, which provides theoretical instructions for the selection of measurement settings in the quantum state estimation. The numerical experiments show that the proposed algorithm has much less calculating time, higher reconstruction accuracy and is more robust to outlier noises than many existing state reconstruction algorithms.

Modelling and performance analysis of networked control systems under different driven modes

In remote Networked Control Systems (NCSs), the system setup depends on the driven mode for each network node, such as time-driven or event-driven. In this paper, based on the NCS with a special kind of network delay, the general formulae of system models are deduced for different cases, in which the sensor adopts the time-driven mode, with the controller and the actuator using either the time-driven or the event-driven mode. The effects of different driven modes for network nodes on the system performance are studied and compared. The issue about how to select suitable driven modes for nodes is discussed with regard to different system requirements and delay ranges. The theoretical results are further illustrated and confirmed by a numerical example.

Manipulations between eigenstates of 2-level quantum system based on optimal measurements

This paper explores the manipulation between eigenstates in a two-level system by a sequence of instantaneous projective measurements. Three cases of the manipulations are studied: the manipulation of optimal measurement-based control; the optimal measurement-based manipulation with the effect of free evolution of system; and the external control fields being used to compensate for the effect caused by the free evolution. Numerical simulations are conducted to verify the results obtained from the theoretically analytical solutions. The optimal parameters for each manipulation case are obtained. The experimental results indicate that the external control fields can make the optimal measurement-based control more effective.

Efficient reconstruction of density matrices for high dimensional quantum state tomography

The conventional quantum state tomography (QST) needs large number of measurements to reconstruct the quantum state. Thanks to the compressive sensing (CS) theory, one can recover a pure or nearly pure quantum state with an acceptable accuracy given much fewer number of measurements. However, most existing algorithms for CS based QST are rather slow and difficult to be implemented in practice. To fill the gap between the CS theory and practical QST, this paper firstly applies an improved Alternating Direction Multiplier Method (ADMM) combining with the Iterative Shrinkage-Thresholding Algorithm (ISTA), ISTADMM for short, aiming at improving the efficiency of QST problem in particular with much lower number of measurements. The ISTADMM avoids computing the inverse of large-scale matrix, reduces the computational time and required memory space. The computation complexity is reduced from O(d6) for least square (widely used in QST), and O(md4) for Fixed Point-ADMM in our previous work, to ISTADMMs O(md2). The proposed algorithm makes it practical to reconstruct high dimensional quantum states provided fewer number of measurements. The simulations verify the superiority of the proposed algorithm, where it takes 3.13 minutes to reconstruct an 8-qubit density matrix with 96.17% accuracy, which is faster than many existing and our previous work.