Feedback Matrix Research Articles

Two-step hybrid collaborative filtering using deep variational Bayesian autoencoders

Existing recommender systems rely on user and item representations in a fixed continuous low-dimensional latent space. To predict ratings, they use only an implicit feedback matrix, whereas user and item side information is ignored. Furthermore, they use the same arbitrary priors for the user and item latent vectors, reducing the ability of the model to identify the actual latent vectors. Currently, the latent parameters should be learned directly for every user and movie. This is problematic, as it would require both model retraining and learning the latent vector representations when users or items are added to the underlying dataset. To address these issues, we propose a two-step hybrid variational Bayesian autoencoder to characterize the uncertainty of predicted ratings. An encoder is first trained to map data vectors to the latent space so that the latent representations can be dynamically computed. Subsequently, we use the generative process of users and items with their priors as side-specific information to handle matrix sparsity and better learn their latent vectors. Finally, we consider stochastic variational inference to approximate the posterior density of intractable user-item latent vectors. Experiments conducted on two real-world datasets demonstrate the effectiveness of the proposed method compared with state-of-the-art methods.

Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems

The work aims to stabilize the unstable index-1 descriptor systems by Riccati-based feedback stabilization via a modified form of Iterative Rational Krylov Algorithm (IRKA), which is a bi-tangential interpolation-based technique. In the basic IRKA, for the stable systems the Reduced Order Models (ROMs) can be found conveniently, but it is unsuitable for the unstable ones. In the proposed technique, the initial feedback is implemented within the construction of the projectors of the IRKA approach. The solution of the Riccati equation is estimated from the ROM achieved by IRKA and hence the low-rank feedback matrix is attained. Using the reverse projecting process, for the full model the optimal feedback matrix is retrieved from the low-rank feedback matrix. Finally, to validate the aptness and competency of the proposed technique it is applied to unstable index-1 descriptor systems. The comparison of the present work with two previous works is narrated. The simulation is done by numerical computation using MATLAB, and both the tabular method and graphical method are used as the supporting tools of comparative analysis.

Online multi‐parameter estimation of permanent magnet synchronous machine with step‐pulse injection

Online estimation of the machine parameters is essential to fault diagnosis and high-performance control of permanent magnet synchronous machine (PMSM). The signal injection is an effective way to estimate machine parameters. However, the inductance variation caused by signal injection will result in difficulties for the estimated parameters to converge. At the same time, online parameters estimation brings heavy burden to the operation of control system. To solve these two problems, optimized inductance model is built with the step-pulse injection to improve the accuracy of estimation. Compared with the existing method, the step-by-step parameter estimation method is adopted and orders of feedback matrix are reduced, which improves the computation efficiency. The forgetting factor recursive least square (FFRLS) algorithm is adopted to estimate stator resistance, rotor flux linkage and d-, q-axes inductances without acquiring any nominal parameter. The minimum amplitude and appropriate frequency of step-pulse are determined by the parameter error and convergence analysis. The effectiveness of the proposed method is verified via a 1.5 kW PMSM drive platform.

Finite control set model predictive control integrated with disturbance observer for battery energy storage power conversion system

A typical battery energy storage system consists of a combination of battery packs and a grid-tied power conversion system. The control algorithm of the power conversion system plays an important role when interfacing the DC energy stored in battery packs with the conventional AC grid to generate an obedient bidirectional power flow. Finite control set model predictive control is believed to be one of the most effective choices for controlling power conversion systems. However, the performance of such a control strategy heavily depends on the accuracy of the predictive model. Parameter mismatch in the model leads to prediction error, which deteriorates the overall power quality performance of the power conversion system. Therefore, this paper studies a robust finite control set model predictive control method based on a discrete disturbance observer to eliminate the negative effects caused by model inaccuracy and uncertainty. The stability issue of the additional observer is discussed from the perspective of closed-loop poles. Parameter scan is performed to provide assistance in designing the feedback matrix. Finally, simulations and experimental results obtained from a downscaled prototype rated at 4.2 kVA are conducted as a validation of the presented control algorithm.

Method for the transformation of complex automatic control systems to integrable form

The article considers a class of automatic control systems that is described by a multi- dimensional system of ordinary dil'erential equations. The right hand-side of the system additively contains a linear part and the product of a control matrix by a vector that is the sum of a control vector and an external perturbation vector. The control vector is defined by a nonlinear function dependent on the product of a feedback matrix by a vector of current coordinates. The authors solve the problem of constructing a matrix of a nonsingular transformation, which leads the matrix of the linear part of the system to the Jordan normal form or the first natural normal form. The variables included in this transformation allow us to vary the system settings, which are the parameters of both the control matrix and the feedback matrix, as well as to convert the system to an integrable form. Integrable form is understood as a form in which the system can be integrated in a final form or reduced to a set of subsystems of lower orders. Furthermore, the sum of the subsystem orders is equal to the order of the original system. In the article, particular attention is paid to cases when the matrix of the linear part has complex conjugate eigenvalues, including multiple ones.

Minimum Variance Pole Placement in Uncertain Linear Control Systems

The pole-placement issue for linear multi-input multi-output (MIMO) dynamic systems with uncertain parameters has been addressed in this article. A static feedback matrix has been designed for minimizing variances of closed-loop poles (CLPs) and for assigning poles to the nominal system at the desired places. It is assumed that the joint probability density function (PDF) of uncertain parameters is known and the system has more than one input. A new unknown vector is used like an eigenvector for a stochastic closed-loop system matrix to state the problem. The variances of poles are considered as cost functions, and the means of poles are termed constraints. This form of the problem statement has helped us to simply find a solution. In the first step, the optimization problem with constraints was handled by solving the equality constraint, and then, the problem was converted to a classic extended eigenvalue optimization problem. Later, the eigenvalue optimization problem was solved by the Rayleigh quotient and the feedback matrix was accomplished. Finally, this approach was simulated and validated using the MATLAB simulations, and the results were compared with a robust pole-placement method, which MATLAB control toolbox uses. The Monte Carlo simulations showed lower covariance for CLPs around the mean poles as compared to the robust pole-placement method.

Research on Control Strategy of Two Dimensional Output Force Vibration Damping Electric Actuator

The main spiral blades of helicopter and other non fixed wing aircraft are in the asymmetric and unsteady aerodynamic environment for a long time, which will make the body produce large-scale multi-directional low-frequency vibration, which will become the main vibration source of the body. The linear actuator can only produce single direction driving force, which is difficult to meet the high-precision vibration reduction requirements. Based on this, a direct drive vibration control system based on the space-time coupling method of rotating coordinate system is proposed. Firstly, the mathematical model of the output force of the single side of the electric actuator is deduced, and the space-time coupling method of the rotating coordinate system is proposed to derive the mathematical expression of the two-dimensional vibration suppression output force. Secondly, the two-dimensional output force control strategy based on the cross coupling control of multiple motors is proposed. The controller parameters are designed by state space method and the method of characteristic value of the feedback matrix to ensure the stability of the control system. The controller parameters are optimized according to the sensitivity H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control theory to improve the anti-interference of the closed-loop system. Finally, a 14kg prototype is designed by the proposed control strategy, which completes the synchronous verification experiment of position and speed, steady state and dynamic verification experiment of output force. The experimental results show that the coordinated control strategy of multi motors proposed in this paper makes the actuator output force meet the performance requirements of the system vibration reduction and has a good stability.

Real‐time parameter estimation for sensitivity‐based LQ regulator adaptation

AbstractIn this contribution we consider linear quadratic regulator problems subject to parameter perturbations within the system dynamics. Due to the perturbations, optimality of the regulator would be lost. Iteratively recomputing the optimal feedback matrix is likely to be too costly for real‐time applications, but approximated updates using parametric sensitivities can be efficiently derived. Online parameter identification is applied in order to obtain current parameter perturbations to which the controller shall be adapted. Numerical results for the benchmark example of the inverted pendulum on a cart are discussed.

Ackermann’s Method: Revisited, Extended, and Generalized to Uncontrollabe Systems

The celebrated method of Ackermann for eigenvalue assignment of single-input controllable systems is revisited in this paper, contributing an elegant proof. The new proof facilitates a compact formula which consequently permits an extension of the method to what we call incomplete assignment of eigenvalues. The inability of Ackermann’s formula to deal with uncontrollable systems is considered a weakness inherent in the method. The notion of incomplete assignment leads to a straightforward generalization of our method to eigenvalue assignment of uncontrollable systems, thus mitigating such a drawback of a popular method. Further results concerning the incomplete assignment are stated, verified, and commented. Such results reveal the trace of the state matrix $A$ a worthy feature pertinent to an open loop system. Finally, four numerical examples are worked out to demonstrate cases of incomplete, and uncontrollable eigenvalues assignment. The examples consider a case where the structure of the feedback matrix can be easily simplified. The paper ends with a commentary brief concerning some commonly used MATLAB commands for eigenvalue assignment.

New Sensorless Vector Control System With High Load Capacity Based on Improved SMO and Improved FOO

In the existing sensorless vector control system of permanent magnet synchronous motor (PMSM), direct differential calculation or phase-locked loop (PLL) control is often used to estimate the rotor speed, but this method has some problems of weak load capacity and slow dynamic response. A new sensorless vector control method based on an improved sliding mode observer (SMO) and improved full-order observer (FOO) is proposed in this paper. The cut-off frequency of the low-pass filter is designed as a function of speed, the back EMF is fed back into the stator current estimation mathematical model, and the adaptive rate of feedback gains coefficient is proposed for improving the traditional SMO. The disturbance feedback matrix is introduced for improving the traditional FOO, and the estimated load torque is feedforward compensated to the given end of the quadrature current. An integrated system of corresponding algorithms is established, a test platform is built. The experimental results show that the speed and load torque estimation performance of the improved observer is better than that of the traditional observer in the process of sudden load change. The sensorless vector control system based on the proposed observer has a high dynamic response, load capacity, and reliability.

On Necessary and Sufficient Conditions for Exponential Consensus in Dynamic Networks via Uniform Complete Observability Theory

In this article, we deal with the consensus problem of multiple partial-state coupled linear systems, which are neutrally stable. These systems communicate over dynamic undirected networks, which change continuously and can be disconnected at any time. We develop an analysis framework from uniform complete observability theory to work out <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the necessary and sufficient conditions</i> for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">if and only if</i> a jointly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\delta,T)$</tex-math></inline-formula> -connected condition and an observability condition relying only on system and input matrices are satisfied. A lower bound of the convergence rate is also provided. We figure out the proof by applying matrix analysis and linear functional analysis. A simulation example is presented to illustrate our theoretical findings.

Enhanced Low-Frequency Ride-Through for Speed-Sensorless Induction Motor Drives With Adaptive Observable Margin

For speed-sensorless induction motor (IM) drives, the observability of rotor speed is still a challenging problem under steady-state operations at low synchronous frequencies. To cope with this problem, an enhanced magnetizing current-oriented low-frequency ride-through method is proposed for adaptive full-order observers to ensure the observability of rotor speed. The adaptive changes of magnetizing current reference are generated to maintain the speed observable margin near zero synchronous frequency. Compared with existing methods, it avoids the noises caused by direct rotor flux reference calculation. In addition, the feedback matrix is employed to narrow the unstable regenerating region, and enlarge the observable margin. Addressing the detailed implementation, the analyses are provided with respect to output torque constraint, magnetizing current selection, and observability. Finally, the effectiveness of proposed method is validated on a 2.2 kW IM experimental bench during low-frequency ride-through.

Internal stability improvement of a natural gas centrifugal compressor system based on a new optimal output feedback controller using block transformation and grey wolf optimizer

The improvement of the normal operating mode in gas compression systems performs an essential role in enhancing the process of pumping and transporting the natural gas inside and outside the border of Algeria. In this regards, this paper introduces a novel output-feedback controller design with optimal static matrix gains K, which uses to control and maintain its internal stability by reducing the surge phenomenon appeared clearly in the thermodynamical outputs parameters of the studied centrifugal compressor system. The feedback matrix K is calculated based on transforming the dynamical model using the similarity canonical block transformation (CBT) and determining the block own matrix ℱown by using the famous grey wolf optimizer (GWO). In given view of this study, a comparative investigation carried out, using different optimization methods, and two recent algorithms, to attest the advantages of the proposed controller. The obtained results confirm the internal stability robustness in the presence of disturbances and uncertainty of the system parameters up to 50%. The obtained norm of the proposed controller is ||K||=0.69, which guarantees a comfortable interval of internal stability in closed loop system (CLS), stability interval = [0.26, 0.60] with minimum possible energy. The three stability measures of compressor system is still ensured comparing with other algorithms [0.0171, 0.0012, 0.0276]. The proposed controller eliminates the fluctuation in the outputs of the studied system, the discharge pressure (P2) and the discharge temperature (T2), respectively, i.e. the disappearance of the surge phenomenon completely. We mention that the proposed controller is suitable and applicable only in the parametric and the transformable models.

Research on Speed Sensorless Control of Induction Motor Based on Back EMF

This article mainly uses the reduced-order model of induction motor (IM) to study the speed identification. Since the traditional voltage model (VM) and current model (CM) each have certain limitations, a general reduced-order model obtained by combining VM and CM is proposed for flux observation. This method is more conducive to analyzing system stability and determining gain, so that the entire induction motor vector control system reaches complete stability. In addition, for the full-order observer, according to the rapidity of current convergence, the back EMF can also be used to convert the full-order observer into an equivalent reduced-order observer. In this way, state feedback matrix can be avoided, which can greatly reduce the complexity of calculation and be more convenient to analyzing the stability of the system. Through the simulation of this novel back EMF reduced-order model, the feasibility of the system can be verified.

Allpass Feedback Delay Networks

In the 1960s, Schroeder and Logan introduced delay line-based allpass filters, which are still popular due to their computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we extend the theory of allpass systems to any arbitrary connection of delay lines, namely feedback delay networks (FDNs). We present a characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays. Further, we develop a solution to the completion problem, i.e., given an FDN feedback matrix to determine the remaining gain parameters such that the FDN is allpass. Particularly useful for the completion problem are feedback matrices, which yield a homogeneous decay of all system modes. Finally, we apply the uniallpass characterization to previous FDN designs, namely, Schroeder's series allpass and Gardner's nested allpass for single-input, single-output systems, and, Poletti's unitary reverberator for multi-input, multi-output systems and demonstrate the significant extension of the design space.

Feedback control of chaotic systems using multiple shooting shadowing and application to Kuramoto-Sivashinsky equation.

We propose an iterative method to evaluate the feedback control kernel of a chaotic system directly from the system's attractor. Such kernels are currently computed using standard linear optimal control theory, known as linear quadratic regulator theory. This is however applicable only to linear systems, which are obtained by linearizing the system governing equations around a target state. In the present paper, we employ the preconditioned multiple shooting shadowing (PMSS) algorithm to compute the kernel directly from the nonlinear dynamics, thereby bypassing the linear approximation. Using the adjoint version of the PMSS algorithm, we show that we can compute the kernel at any point of the domain in a single computation. The algorithm replaces the standard adjoint equation (that is ill-conditioned for chaotic systems) with a well-conditioned adjoint, producing reliable sensitivities which are used to evaluate the feedback matrix elements. We apply the idea to the Kuramoto-Sivashinsky equation. We compare the computed kernel with that produced by the standard linear quadratic regulator algorithm and note similarities and differences. Both kernels are stabilizing, have compact support and similar shape. We explain the shape using two-point spatial correlations that capture the streaky structure of the solution of the uncontrolled system.

Time-varying group formation tracking control for second-order multi-agent systems with communication delays and multiple leaders

Time-varying group formation tracking control problems for second-order multi-agent systems with communication delays and multiple leaders are addressed in this paper. The followers are divided into multiple subgroups, and each subgroup is driven to complete the time-varying sub-formation and to track the average state of entire leaders simultaneously. A distributed protocol that considers communication delays and uses only local interaction information is presented. According to Lyapunov-like stability approach, sufficient conditions for the multi-agent systems to realize time-varying group formation tracking with multiple leaders are given. A variable-substitution based method is developed to get the unknown feedback matrix of the protocol and an algorithm is given to summarize the steps to construct the protocol. The theoretical results can be used in the problem of multiple targets enclosed by several subgroups of unmanned aerial vehicles. Finally, numerical examples are applied to verify the feasibility of the proposed results.

Web service reliability prediction based on machine learning

Web service reliability is an important mission that keeps web services running normally. Within web service, the web services invoked by users not only depend on the service itself, but also on web load condition (such as latency). Due to the features of web dynamics, traditional reliability methods have become inappropriate; at the same time, the web condition parameter sparsity problem will cause inaccurate reliability prediction. To address these new challenges, in this paper, we propose a new web service reliability prediction method based on machine learning considering user, web service and web condition. First we solve the web condition parameter sparsity problem, then we use the k-means clustering method to aggregate past invocation data, incorporate user, service, and web condition parameters to build a reliability feedback matrix, at last we predict web service reliability by considering specific web condition environments. The experiment shows that our machine learning method is able to solve the data sparsity problem and improve accurate web service reliability prediction, and we discuss how data sparsity and the number of feedback clusters to affect web service reliability prediction.

H∞ Control for Observer-Based Non-Negative Edge Consensus of Discrete-Time Networked Systems.

This article is concerned with observer-based non-negative edge-consensus (OBNNEC) problems of networked discrete-time systems with or without actuator saturation. An algorithm which only uses actual outputs of neighboring edges is proposed by means of an H∞ control method and modified algebraic Riccati equation (MARE)-based technique. The observer matrix and feedback matrix are constructed by solving the MARE and linear matrix inequality (LMI), respectively. Then, sufficient conditions for guaranteeing bounded inputs and non-negative edge states are derived. In addition, the low-gain characteristic of the MARE-based method is instrumental in guaranteeing non-negative edge states and deriving the feasible observer matrix and feedback matrix. Finally, two examples are shown to demonstrate the obtained theoretical results.

Multidimensional control system synthesis for a precision air-conditioner

The article considers the synthesis procedure for multidimensional digital controller embedded into industrial artificial microclimate systems. The methodology is proposed for constructing the complex dynamic mathematical model for industrial air conditioners represented in the state space of a combined multidimensional controlled system. An analysis of possible control system optimization criteria is performed. Also, the synthesis procedure for an optimal multidimensional digital linear quadratic controller is given. The feedback matrix is synthesized that determines the control vector optimal trajectory using controlled system states by minimizing the quadratic quality criterion. The proposed multidimensional linear digital controller has a feature of logical selection for elements of industrial equipment for performing the optimal control of a microclimate conditioner. The proposed approach allows for reconfiguring the synthesis procedure for the industrial conditioners automatic control system on the basis of delimiting the mutual influence of control parameters.