Swarm Optimization-based Algorithm Research Articles

Hybrid ANN models for durability of GFRP rebars in alkaline concrete environment using three swarm-based optimization algorithms

• Hybrid ANN models for estimating the durability of GFRP rebars in alkaline environment. • ANN-GWO was selected for calculating environmental reduction factor based on higher accuracy. • The rate of degradation in GFRP rebars changes with change in temperature. • Guidelines regarding environmental reduction factor to reflect long-term durability of GFRP rebars. This study investigates the non-linearity of GFRP degradation in terms of tensile strength retention (TSR) encompassing five input variables (i.e., diameter of GFRP rebar, volume fraction of fibers, pH of surrounding solution, temperature of surrounding solution, and duration of conditioning). Additionally, the degradation models were extrapolated to calculate environmental reduction factor (C E ). Based on high non-linear capabilities of artificial neural network (ANN) models, hybrid ANN models were created by deploying particle swarm optimization (PSO), grey wolf optimization (GWO) and marine predators algorithm (MPA) to predict the TSR of GFRP rebars conditioned at variable temperatures and durations. Trial and error procedure was adopted to select the optimal hyperparameter of the hybrid models. The developed models were subjected to statistical, accuracy, sensitivity and uncertainty analyses. ANN-GWO model yielded the highest correlation (R ≈ 0.89 and 0.88, MAE = 0.0558 % and 0.0914 %, and RMSE = 7.86 % and 11.67 %) for the training and testing datasets, respectively. Furthermore, Taylor diagram and accuracy matrix revealed that the performance of the models followed the order; ANN-GWO (R overall = 0.885) > ANN-PSO (R overall = 0.806) > ANN-MPA (R overall = 0.821). For GFRP rebars, made of E-glass fibers (volume fraction = 0.62) impregnated in vinyl ester resin conditioned at 28 °C with surrounding pH of 13, the values of C E for bar sizes 9.5 mm, 12.7 mm and 15.9 mm were recorded as 0.75, 0.87 and 0.95, respectively. It is highly recommended to consider the effect of bar size as an important variable in the design of GFRP reinforced concrete structures and keep C E ≈ 0.75 at 28 °C in alkaline environment.

Bio-inspired Machine Learning for Distributed Confidential Multi-Portfolio Selection Problem.

The recently emerging multi-portfolio selection problem lacks a proper framework to ensure that client privacy and database secrecy remain intact. Since privacy is of major concern these days, in this paper, we propose a variant of Beetle Antennae Search (BAS) known as Distributed Beetle Antennae Search (DBAS) to optimize multi-portfolio selection problems without violating the privacy of individual portfolios. DBAS is a swarm-based optimization algorithm that solely shares the gradients of portfolios among the swarm without sharing private data or portfolio stock information. DBAS is a hybrid framework, and it inherits the swarm-like nature of the Particle Swarm Optimization (PSO) algorithm with the BAS updating criteria. It ensures a robust and fast optimization of the multi-portfolio selection problem whilst keeping the privacy and secrecy of each portfolio intact. Since multi-portfolio selection problems are a recent direction for the field, no work has been done concerning the privacy of the database nor the privacy of stock information of individual portfolios. To test the robustness of DBAS, simulations were conducted consisting of four categories of multi-portfolio problems, where in each category, three portfolios were selected. To achieve this, 200 days worth of real-world stock data were utilized from 25 NASDAQ stock companies. The simulation results prove that DBAS not only ensures portfolio privacy but is also efficient and robust in selecting optimal portfolios.

Evolutionary Swarm based Optimization Algorithm for Power Loss Minimization in Distributed Generation System

The electrical energy requirement is increasing day by day as many of the mechanical systems like motor vehicles and industrial engines are compensated with electrical equipment due to its environment friendly nature. However, most of the design of electrical power generation units do not seem to be eco-friendly as that of the electrical motors and drives. Therefore, the concentration has moved towards the non-renewable energy generation possibilities. Power stations that are operated by wind, solar and hydro stations attract the developers due to their minimum maintenance cost and higher operational efficiency. Hence, the combinations of two or three renewable energy sources are clubbed in many places to form a Distributed Generation (DG) setup. Such DG system requires an efficient switching operation for managing the power outcome from different generating stations to meet the load requirement. To meetup such requirement, a combination of Genetic Algorithm (GA) with the Particle Swarm Optimization (PSO) based technique has been developed in this work. A simulated experiment is also conducted in the work to prove the efficiency of the proposed hybrid model over the traditional GA and PSO approaches.

Performance Comparison of Optimization Algorithm Tuned PID Controllers in Positive Output Re-Lift Luo Converter Operation for Electric Vehicle Applications

In this work, a Particle Swarm-Based optimization algorithm is proposed to optimize the PID controller used in the Positive Output Re-Lift Luo converter for the Electric Vehicle application. The novelty of the work lies in developing an improved PID controller to explore the reliability of the re-lift Luo converter. In addition, the optimization improves the effectiveness of the closed-loop system that possesses high voltage gain with esteemed power density and efficiency. With the Particle Swarm Optimization control algorithm, , , and values are tuned in such a way to obtain the appropriate steady-state condition with no peak overshoot or undershoot, much lesser settling time, no steady-state error, and improved dynamic performances. To analyze the system stability and to obtain better results, reduced-order state-space modeling of the Re-lift Luo converter is adopted, which offers high computational speed and accuracy. Initially, a PID controller is designed using the Zeigler Nicholas method, and the results are compared with the genetic algorithm and Particle Swarm Optimization algorithm. The time-domain analysis has been carried out to analyze and compare the converter’s performance. The simulation results were verified experimentally, and the results prove the robustness of the proposed converter with a PID controller optimized using the Particle Swarm Optimization algorithm.

Swarm Optimization for Energy-Based Acoustic Source Localization: A Comprehensive Study

In the last decades, several swarm-based optimization algorithms have emerged in the scientific literature, followed by a massive increase in terms of their fields of application. Most of the studies and comparisons are restricted to high-level languages (such as MATLAB®) and testing methods on classical benchmark mathematical functions. Specifically, the employment of swarm-based methods for solving energy-based acoustic localization problems is still in its inception and has not yet been extensively studied. As such, the present work marks the first comprehensive study of swarm-based optimization algorithms applied to the energy-based acoustic localization problem. To this end, a total of 10 different algorithms were subjected to an extensive set of simulations with the following aims: (1) to compare the algorithms’ convergence performance and recognize novel, promising methods for solving the problem of interest; (2) to validate the importance (in convergence speed) of an intelligent swarm initialization for any swarm-based algorithm; (3) to analyze the methods’ time efficiency when implemented in low-level languages and when executed on embedded processors. The obtained results disclose the high potential of some of the considered swarm-based optimization algorithms for the problem under study, showing that these methods can accurately locate acoustic sources with low latency and bandwidth requirements, making them highly attractive for edge computing paradigms.

Stability analysis based parameter tuning of Social Group Optimization

Swarm-based optimization algorithms have been popularly used these days for optimization of various real world problems but sometimes it becomes hard to estimate the associated characteristics due to their stochastic nature. To ensure a steady performance of these techniques, it is essential to have knowledge about the range of variables, in which a particular algorithm always provides stable performance and performing stability analysis of an algorithm can help in providing some knowledge regarding the same. Many researchers have performed the stability analysis of several optimization algorithms and analyzed their behavior. Social Group Optimization (SGO) is a newly developed algorithm which has been proven to yield promising results when applied to many real world problems but in literature no work can be found on stability analysis of SGO. In this paper, Von Neumann stability analysis approach has been used for performing stability analysis of Social Group Optimization (SGO) to analyze the behavior of its algorithmic parameters and estimate the range in which they always give stable convergence. The results obtained have been supported by sufficient experimental analysis and simulated using eight benchmark function suite along with their shifted and rotated variations which prove that the algorithm performs better within the stable range and hence convergence is ensured.

Image segmentation of Leaf Spot Diseases on Maize using multi-stage Cauchy-enabled grey wolf algorithm

Grey wolf optimizer (GWO) is a widespread metaphor-based algorithm based on the enhanced variants of velocity-free particle swarm optimizer with proven defects and shortcomings in performance. Regardless of the proven defect and lack of novelty in this algorithm, the GWO has a simple algorithm and it may face considerable unbalanced exploration and exploitation trends. However, GWO is easy to be utilized, and it has a low capacity to deal with multi-modal functions, and it quickly falls into the optima trap or fails to find the global optimal solution. To improve the shortcomings of the basic GWO, this paper proposes an improved GWO called multi-stage grey wolf optimizer (MGWO). By dividing the search process into three stages and using different population updating strategies at each stage, the MGWO’s optimization ability is improved while maintaining a certain convergence speed. The MGWO cannot easily fall into premature convergence and has a better ability to get rid of the local optima trap than GWO. Meanwhile, the MGWO achieves a better balance of exploration and exploitation and has a rough balance curve. Hence, the proposed MGWO can obtain a higher-quality solution. Based on verification on the thirty benchmark functions of IEEE CEC2017 as the objective functions, the simulation experiments in which MGWO compared with some swarm-based optimization algorithms and the balance and diversity analysis were conducted. The results verify the effectiveness and superiority of MGWO. Finally, the MGWO was applied to the multi-threshold image segmentation of Leaf Spot Diseases on Maize at four different threshold levels. The segmentation results were analysed by comparing each comparative algorithm’s PSNR, SSIM, and FSIM. The results proved that the MGWO has noticeable competitiveness, and it can be used as an effective optimizer for multi-threshold image segmentation.

The heterogeneous Aquila optimization algorithm.

A new swarm-based optimization algorithm called the Aquila optimizer (AO) was just proposed recently with promising better performance. However, as reported by the proposer, it almost remains unchanged for almost half of the convergence curves at the latter iterations. Considering the better performance and the lazy latter convergence rates of the AO algorithm in optimization, the multiple updating principle is introduced and the heterogeneous AO called HAO is proposed in this paper. Simulation experiments were carried out on both unimodal and multimodal benchmark functions, and comparison with other capable algorithms were also made, most of the results confirmed the better performance with better intensification and diversification capabilities, fast convergence rate, low residual errors, strong scalabilities, and convinced verification results. Further application in optimizing three benchmark real-world engineering problems were also carried out, the overall better performance in optimizing was confirmed without any other equations introduced for improvement.

Optimizing Faculty Workloads and Room Utilization using Heuristically Enhanced WOA

The creation and generation of schedules that are free of conflicts manually every academic semester present higher education institutions with a duty that is laborious and demanding of their resources. The course timetabling optimization, as an education timetabling problem, is a popular example of an NP-hard combinatorial problem. Numerous attempts have been made over the course of the past few decades to find a solution to this problem, but no one has yet developed a foolproof approach that can examine all alternatives to find the best method. The promising swarm-based optimization algorithm called Whale Optimization Algorithm was heuristically enhanced in the present study and is called HEWOA. It was designed as a solution to the course timetabling problem discussed in the current study. HEWOA was able to generate an efficient timetable for the large dataset of 1700 events for an average time of 14.92 seconds only, with an average generation of 7.2 and a best time of 8.38 seconds. These results reveal that the performance of HEWOA was better than that of various hybrids of the Genetic Algorithm that was compared in the present study.

A heuristic swarm-based optimization method using multi-variate normal distributions with self-adaptive variance matrices

In this paper a heuristic swarm-based optimization method developed based on stochastic search and concepts from statistics was presented for optimal design of problems in structural mechanics. Although in recent years many heuristic optimization methods have been developed, none of them can be considered as the most effective method for solving all types of optimization problems. In general, heuristic optimization methods are formulated to follow specific patterns and often include some random parameters. It has been shown that adding stochastic parameters and concepts from statistics to such algorithms can improve their performance and increase the chance of finding global optimal points. Based upon same notion, we have developed a new swarm-based optimization algorithm in which multi-variate normal distributions with self-adaptive variance matrices (MNSV) are used to generate superior solutions in each iteration. The self-adaptive variance matrix in each iteration was calculated using the variance of the best points from solution history. Such a choice improved both exploration and exploitation of the algorithm and led to a trade-off between them from beginning towards the end of the solution. Computational complexity of MNSV algorithm was comparable to that of other swarm-based optimization algorithms and performance of the algorithm was tested through optimal solution of several benchmarks from structural and mechanical engineering. While MNSV algorithm was simple in terms of both formulation and implementation, it was effective in finding optimal solutions and often converged using a smaller number of iterations when compared to other algorithms.

Optimized functional linked neural network for predicting diaphragm wall deflection induced by braced excavations in clays

Deep excavation during the construction of underground systems can cause movement on the ground, especially in soft clay layers. At high levels, excessive ground movements can lead to severe damage to adjacent structures. In this study, finite element analyses (FEM) and the hardening small strain (HSS) model were performed to investigate the deflection of the diaphragm wall in the soft clay layer induced by braced excavations. Different geometric and mechanical properties of the wall were investigated to study the deflection behavior of the wall in soft clays. Accordingly, 1090 hypothetical cases were surveyed and simulated based on the HSS model and FEM to evaluate the wall deflection behavior. The results were then used to develop an intelligent model for predicting wall deflection using the functional linked neural network (FLNN) with different functional expansions and activation functions. Although the FLNN is a novel approach to predict wall deflection; however, in order to improve the accuracy of the FLNN model in predicting wall deflection, three swarm-based optimization algorithms, such as artificial bee colony (ABC), Harris’s hawk’s optimization (HHO), and hunger games search (HGS), were hybridized to the FLNN model to generate three novel intelligent models, namely ABC-FLNN, HHO-FLNN, HGS-FLNN. The results of the hybrid models were then compared with the basic FLNN and MLP models. They revealed that FLNN is a good solution for predicting wall deflection, and the application of different functional expansions and activation functions has a significant effect on the outcome predictions of the wall deflection. It is remarkably interesting that the performance of the FLNN model was better than the MLP model with a mean absolute error (MAE) of 19.971, root-mean-squared error (RMSE) of 24.574, and determination coefficient (R2) of 0.878. Meanwhile, the performance of the MLP model only obtained an MAE of 20.321, RMSE of 27.091, and R2 of 0.851. Furthermore, the results also indicated that the proposed hybrid models, i.e., ABC-FLNN, HHO-FLNN, HGS-FLNN, yielded more superior performances than those of the FLNN and MLP models in terms of the prediction of deflection behavior of diaphragm walls with an MAE in the range of 11.877 to 12.239, RMSE in the range of 15.821 to 16.045, and R2 in the range of 0.949 to 0.951. They can be used as an alternative tool to simulate diaphragm wall deflections under different conditions with a high degree of accuracy.

IntelliSwAS: Optimizing deep neural network architectures using a particle swarm-based approach

Deep learning is in a continuous evolution and many domains benefit from this substantial progress in the development of intelligent solutions. While this progress has been swift, there are more and more applications and the specific requirements of each application domain entails much work done by researchers to adapt existing models or create new ones. This traditional approach has produced many successful designs, but recently, automated methods of finding neural network architectures emerged. We introduce IntelliSwAS approach for optimizing deep neural network architectures for a classification or regression task. Image classification was selected as the task, but IntelliSwAS is generic enough such that it could be successfully applied on other classification or regression problems. A particle swarm-based optimization algorithm is proposed for the automatic search for convolutional neural network architectures. The search technique is enhanced by a machine learning model (DAGRNN) which we designed for predicting the quality of the network architectures and thus increasing the performance of the algorithm. The proposed model is able to process data structured as directed acyclic graphs in general and we applied it specifically on network architectures. The network architecture that we discovered using IntelliSwAS surpassed 89.8% of the competing image classification models that we considered for comparison.

Real Power Loss Reduction by Extreme Learning Machine Based Leontodon Algorithm

In this paper Extreme Learning Machine based Leontodon Algorithm (ELMLA) has been applied for solving the Real Power loss reduction problem. Key objectives of this paper are Real power loss reduction, Voltage stability enhancement and voltage deviation minimization. Leontodon Algorithm (LA) technique is an innovative swarm based optimization algorithm. In evolutionary procedure of LA, the eminence of the seeds engendered by Leontodon is rutted, and the outstanding seeds will be reserved and appraised, whereas the deprived seeds are rejected. In order to define whether a seed is tremendous or not, an enhancement of Leontodon algorithm with extreme learning machine (ELMLA) is projected in this paper. Based on fitness values the Leontodon population is segregated into outstanding and deprived Leontodons. Subsequently outstanding and deprived Leontodons are apportioned corresponding labels as +1 if outstanding or − 1 if deprived), and it has been considered as a training set, which built on extreme learning machine. Lastly, the design is applied to categorize the Leontodon seeds as excellent or deprived. Only outstanding Leontodon seeds are selected to take part in evolution procedure. Legitimacy of the Extreme Learning Machine based Leontodon Algorithm (ELMLA) is substantiated in IEEE 30 bus system (with and devoid of L-index). Actual Real Power loss reduction is reached. Proportion of actual Real Power loss reduction is augmented.

A Survey on Cat Swarm Optimization Algorithm

Swarm based optimization algorithms are a collection of intelligent techniques in the field of Artificial Intelligence (AI) were developed for simulating the intelligent behavior of animals. Over the years ago, problems complexity increased in a means that it is very difficult for basic mathematical approaches to obtain an optimum solution in an optimal time, this leads the researchers to develop various algorithms base on the natural behaviors of living beings for solving problems. This paper present a review for Cat Swarm Optimization (CSO), which is a powerful metaheuristic swarm-based optimization algorithm inspired by behaviors of cats in the Nature for solving optimization problems. Since its first appearances in 2006, CSO has been improved and applied in different fields by many researchers. In this review, we majorly focus on the original CSO algorithm and some improved branches of CSO family algorithms. Some examples of utilizing CSO to solve problems in engineering are also reviewed.

Optimizing hyperparameters of deep reinforcement learning for autonomous driving based on whale optimization algorithm.

Deep Reinforcement Learning (DRL) enables agents to make decisions based on a well-designed reward function that suites a particular environment without any prior knowledge related to a given environment. The adaptation of hyperparameters has a great impact on the overall learning process and the learning processing times. Hyperparameters should be accurately estimated while training DRL algorithms, which is one of the key challenges that we attempt to address. This paper employs a swarm-based optimization algorithm, namely the Whale Optimization Algorithm (WOA), for optimizing the hyperparameters of the Deep Deterministic Policy Gradient (DDPG) algorithm to achieve the optimum control strategy in an autonomous driving control problem. DDPG is capable of handling complex environments, which contain continuous spaces for actions. To evaluate the proposed algorithm, the Open Racing Car Simulator (TORCS), a realistic autonomous driving simulation environment, was chosen to its ease of design and implementation. Using TORCS, the DDPG agent with optimized hyperparameters was compared with a DDPG agent with reference hyperparameters. The experimental results showed that the DDPG’s hyperparameters optimization leads to maximizing the total rewards, along with testing episodes and maintaining a stable driving policy.

A comparison of swarm-based optimization algorithms in linear antenna array synthesis

Today, the design of antenna arrays is very important in providing effective and efficient wireless communication. The purpose of antenna array synthesis is to obtain a radiation pattern with a low side lobe level (SLL) at a desired half power beam width in far-field. The amplitude and position values of the array elements can be optimized to obtain a radiation pattern with suppressed SLLs. In this paper, swarm-based metaheuristic algorithms including particle swarm optimization (PSO), artificial bee colony (ABC), mayfly algorithm (MA) and jellyfish search (JS) are compared to determine the optimal design of linear antenna arrays. Extensive experiments are conducted on designing 10-, 16-, 24- and 32-element linear arrays by determining the amplitude and positions. Experiments are repeated 30 times due to the random nature of swarm-based optimizers, and statistical results show that the performance of the novel algorithms, MA and JS, is better than that of the well-known PSO and ABC methods.

A binary artificial bee colony algorithm and its performance assessment

Artificial bee colony algorithm, ABC for short, is a swarm-based optimization algorithm proposed for solving continuous optimization problems. Due to its simple but effective structure, some binary versions of the algorithm have been developed. In this study, we focus on modification of its xor-based binary version, called as binABC. The solution update rule of basic ABC is replaced with a xor logic gate in binABC algorithm, and binABC works on discretely-structured solution space. The rest of components in binABC are the same as with the basic ABC algorithm. In order to improve local search capability and convergence characteristics of binABC, a stigmergic behavior-based update rule for onlooker bees of binABC and extended version of xor-based update rule are proposed in the present study. The developed version of binABC is applied to solve a modern benchmark problem set (CEC2015). To validate the performance of proposed algorithm, a series of comparisons are conducted on this problem set. The proposed algorithm is first compared with the basic ABC and binABC on CEC2015 set. After its performance validation, six binary versions of ABC algorithm are considered for comparison of the algorithms, and a comprehensive comparison among the state-of-art variants of swarm intelligence or evolutionary computation algorithms is conducted on this set of functions. Finally, an uncapacitated facility location problem set, a pure binary optimization problem, is considered for the comparison of the proposed algorithm and binary variants of ABC algorithm. The experimental results and comparisons show that the proposed algorithm is successful and effective in solving binary optimization problems as its basic version in solving continuous optimization problems.

Comparative study of SBOAs on the tuning procedure of the designed SMPI controller for MIMO VSP/HVDC interconnected model

This paper presents a new application of advanced SMPI controller for a newly introduced interconnected dynamic system with VSP based HVDC links for frequency control problem. This work presents an outgrowth of analysis about the Swarm – Based Optimization Algorithms (SBOAs) in the tuning process of Multivariable Proportional – Integral (MPI) controller, which is called swarm – based MPI (SMPI). PSO, GOA and GWO algorithms are used for tuning process of the designed SMPI. The VSP based HVDC model is added for mitigation of system frequency dynamics with emulating virtual inertia. The proposed SMPI controller are designed for enhancing the dynamic performance of this system’s states during contingencies and they are compared with the conventional designed MPI controller. Deviation characteristics of the step function in MIMO transfer function of the VSP based HVDC model is considered as the common performance index in the proposed algorithms. On the other hand, the role of the proposed SMPI controller is to stabilize such interconnected system while minimizing the associated cost function. Matlab simulations next to the performed Nyquist’s stability anslysis demonstrate how the tuned SMPI can remarkably improve the frequency deviations and the damping of the inter-area oscillations excited during a fault. This enhancement is more obvious especially when SMPI controller for a VSP based virtual inertia emulation is tuned using GWO method.

Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer

The power scheduling problem in a smart home (PSPSH) refers to the timely scheduling operations of smart home appliances under a set of restrictions and a dynamic pricing scheme(s) produced by a power supplier company (PSC). The primary objectives of PSPSH are: (I) minimizing the cost of the power consumed by home appliances, which refers to electricity bills, (II) balance the power consumed during a time horizon, particularly at peak periods, which is known as the peak-to-average ratio, and (III) maximizing the satisfaction level of users. Several approaches have been proposed to address PSPSH optimally, including optimization and non-optimization based approaches. However, the set of restrictions inhibit the approach used to obtain the optimal solutions. In this paper, a new formulation for smart home battery (SHB) is proposed for PSPSH that reduces the effect of restrictions in obtaining the optimal/near-optimal solutions. SHB can enhance the scheduling of smart home appliances by storing power at unsuitable periods and use the stored power at suitable periods for PSPSH objectives. PSPSH is formulated as a multi-objective optimization problem to achieve all objectives simultaneously. A robust swarm-based optimization algorithm inspired by the grey wolf lifestyle called grey wolf optimizer (GWO) is adapted to address PSPSH. GWO has powerful operations managed by its dynamic parameters that maintain exploration and exploitation behavior in search space. Seven scenarios of power consumption and dynamic pricing schemes are considered in the simulation results to evaluate the proposed multi-objective PSPSH using SHB (BMO-PSPSH) approach. The proposed BMO-PSPSH approach’s performance is compared with that of other 17 state-of-the-art algorithms using their recommended datasets and four algorithms using the proposed datasets. The proposed BMO-PSPSH approach exhibits and yields better performance than the other compared algorithms in almost all scenarios.

An optimized LQG servo controller design using LQI tracker for VSP-based AC/DC interconnected systems

This paper proposes a novel application for the optimal Linear Quadratic Gaussian (LQG) servo controller to enable a proper coordination of the AC/HVDC interconnected system with Virtual Synchronous Power (VSP) based inertia emulation. Particularly, the proposed control design takes the process disturbances and measurement noise of the studied VSP-HVDC system into account, while few studies have focused on this perspective. The proposed LQG controller with modifications is designed by means of a combination of Kalman Filter (state estimator) and an added Linear Quadratic Integrator (LQI) to observe the system model’s states and track the reference commands while rejecting the effects of system noise. Besides, we utilize a swarm-based optimization algorithm to operate as the search process for the tuning of the elements in the weighting matrices involved in the controller design. The role of the proposed optimal LQG controller is to stabilize such AC/DC interconnected system with VSP-based inertia emulator while minimizing the associated performance index. According to the obtained simulation results, in addition to the advancement from the VSP-based approach for damping frequency oscillations excited by faults, application of the proposed LQG servo controller can achieve the targets on both estimating the state variables and tracking the reference signals with satisfactory performance, comparing with the conventional LQG regulator.