Search results for: constraint optimal

Authors: Jeffrey L. Duffany

Abstract:

An optimal solution for a large number of constraint satisfaction problems can be found using the technique of substitution and elimination of variables analogous to the technique that is used to solve systems of equations. A decision function f(A)=max(A2) is used to determine which variables to eliminate. The algorithm can be expressed in six lines and is remarkable in both its simplicity and its ability to find an optimal solution. However it is inefficient in that it needs to square the updated A matrix after each variable elimination. To overcome this inefficiency the algorithm is analyzed and it is shown that the A matrix only needs to be squared once at the first step of the algorithm and then incrementally updated for subsequent steps, resulting in significant improvement and an algorithm complexity of O(n3).

Keywords: Algorithm, complexity, constraint, np-complete.

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Authors: Shigeaki Sakurai, Youichi Kitahata, Ryohei Orihara

Abstract:

This paper proposes a method that discovers sequential patterns corresponding to user-s interests from sequential data. This method expresses the interests as constraint patterns. The constraint patterns can define relationships among attributes of the items composing the data. The method recursively decomposes the constraint patterns into constraint subpatterns. The method evaluates the constraint subpatterns in order to efficiently discover sequential patterns satisfying the constraint patterns. Also, this paper applies the method to the sequential data composed of stock price indexes and verifies its effectiveness through comparing it with a method without using the constraint patterns.

Keywords: Sequential pattern mining, Constraint pattern, Attribute constraint, Stock price indexes

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Authors: Mat Syai'in, Adi Soeprijanto, Takashi Hiyama

Abstract:

An optimal power flow (OPF) based on particle swarm optimization (PSO) was developed with more realistic generator security constraint using the capability curve instead of only Pmin/Pmax and Qmin/Qmax. Neural network (NN) was used in designing digital capability curve and the security check algorithm. The algorithm is very simple and flexible especially for representing non linear generation operation limit near steady state stability limit and under excitation operation area. In effort to avoid local optimal power flow solution, the particle swarm optimization was implemented with enough widespread initial population. The objective function used in the optimization process is electric production cost which is dominated by fuel cost. The proposed method was implemented at Java Bali 500 kV power systems contain of 7 generators and 20 buses. The simulation result shows that the combination of generator power output resulted from the proposed method was more economic compared with the result using conventional constraint but operated at more marginal operating point.

Keywords: Optimal Power Flow, Generator Capability Curve, Particle Swarm Optimization, Neural Network

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Authors: Khodamorad Nabaki, Jianhu Shen, Xiaodong Huang

Abstract:

This paper develops a method for considering the critical fatigue stress as a constraint in the Bi-directional Evolutionary Structural Optimization (BESO) method. Our aim is to reach an optimal design in which high cycle fatigue failure does not occur for a specific life time. The critical fatigue stress is calculated based on modified Goodman criteria and used as a stress constraint in our topology optimization problem. Since fatigue generally does not occur for compressive stresses, we use the p-norm approach of the stress measurement that considers the highest tensile principal stress in each point as stress measure to calculate the sensitivity numbers. The BESO method has been extended to minimize volume an object subjected to the critical fatigue stress constraint. The optimization results are compared with the results from the compliance minimization problem which shows clearly the merits of our newly developed approach.

Keywords: Topology optimization, BESO method, p-norm, fatigue constraint.

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Authors: Mat Syai'in, Adi Soeprijanto

Abstract:

An Optimal Power Flow based on Improved Particle Swarm Optimization (OPF-IPSO) with Generator Capability Curve Constraint is used by NN-OPF as a reference to get pattern of generator scheduling. There are three stages in Designing NN-OPF. The first stage is design of OPF-IPSO with generator capability curve constraint. The second stage is clustering load to specific range and calculating its index. The third stage is training NN-OPF using constructive back propagation method. In training process total load and load index used as input, and pattern of generator scheduling used as output. Data used in this paper is power system of Java-Bali. Software used in this simulation is MATLAB.

Keywords: Optimal Power Flow, Generator Capability Curve, Improved Particle Swarm Optimization, Neural Network

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Authors: Young-Seok Choi

Abstract:

We present a new framework of the data-reusing (DR) adaptive algorithms by incorporating a constraint on noise, referred to as a noise constraint. The motivation behind this work is that the use of the statistical knowledge of the channel noise can contribute toward improving the convergence performance of an adaptive filter in identifying a noisy linear finite impulse response (FIR) channel. By incorporating the noise constraint into the cost function of the DR adaptive algorithms, the noise constrained DR (NC-DR) adaptive algorithms are derived. Experimental results clearly indicate their superior performance over the conventional DR ones.

Keywords: Adaptive filter, data-reusing, least-mean square (LMS), affine projection (AP), noise constraint.

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Authors: Abdenour Bounsiar, Edith Grall, Pierre Beauseroy

Abstract:

In this paper we are interested in classification problems with a performance constraint on error probability. In such problems if the constraint cannot be satisfied, then a rejection option is introduced. For binary labelled classification, a number of SVM based methods with rejection option have been proposed over the past few years. All of these methods use two thresholds on the SVM output. However, in previous works, we have shown on synthetic data that using thresholds on the output of the optimal SVM may lead to poor results for classification tasks with performance constraint. In this paper a new method for supervised classification with rejection option is proposed. It consists in two different classifiers jointly optimized to minimize the rejection probability subject to a given constraint on error rate. This method uses a new kernel based linear learning machine that we have recently presented. This learning machine is characterized by its simplicity and high training speed which makes the simultaneous optimization of the two classifiers computationally reasonable. The proposed classification method with rejection option is compared to a SVM based rejection method proposed in recent literature. Experiments show the superiority of the proposed method.

Keywords: rejection, Chow's rule, error-reject tradeoff, SupportVector Machine.

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Authors: Kuo-Lung Lor, Chi-Hsuan Tsou, Yeun-Chung Chang, Chung-Ming Chen

Abstract:

For evaluating the severity of Chronic Obstructive Pulmonary Disease (COPD), one is interested in inspecting the airway wall thickening due to inflammation. Although airway segmentations have being well developed to reconstruct in high order, airway wall segmentation remains a challenge task. While tackling such problem as a multi-surface segmentation, the interrelation within surfaces needs to be considered. We propose a new method for three-dimensional airway wall segmentation using spring structural active contour model. The method incorporates the gravitational field of the image and repelling force field of the inner lumen as the soft constraint and the geometric spring structure of active contour as the hard constraint to approximate a three-dimensional coupled surface readily for thickness measurements. The results show the preservation of topology constraints of coupled surfaces. In conclusion, our springy, soft-tissue-like structure ensures the globally optimal solution and waives the shortness following by the inevitable improper inner surface constraint.

Keywords: active contour model, airway wall, COPD, geometric spring structure

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Authors: Young-Seok Choi

Abstract:

We present a family of data-reusing and affine projection algorithms. For identification of a noisy linear finite impulse response channel, a partial knowledge of a channel, especially noise, can be used to improve the performance of the adaptive filter. Motivated by this fact, the proposed scheme incorporates an estimate of a knowledge of noise. A constraint, called the adaptive noise constraint, estimates an unknown information of noise. By imposing this constraint on a cost function of data-reusing and affine projection algorithms, a cost function based on the adaptive noise constraint and Lagrange multiplier is defined. Minimizing the new cost function leads to the adaptive noise constrained (ANC) data-reusing and affine projection algorithms. Experimental results comparing the proposed schemes to standard data-reusing and affine projection algorithms clearly indicate their superior performance.

Keywords: Data-reusing, affine projection algorithm, error constraint, system identification.

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Authors: Young-Seok Choi

Abstract:

This paper presents a normalized subband adaptive filtering (NSAF) algorithm to cope with the sparsity condition of an underlying system in the context of compressive sensing. By regularizing a weighted l1-norm of the filter taps estimate onto the cost function of the NSAF and utilizing a subgradient analysis, the update recursion of the l1-norm constraint NSAF is derived. Considering two distinct weighted l1-norm regularization cases, two versions of the l1-norm constraint NSAF are presented. Simulation results clearly indicate the superior performance of the proposed l1-norm constraint NSAFs comparing with the classical NSAF.

Keywords: Subband adaptive filtering, sparsity constraint, weighted l1-norm.

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Authors: P.S.Prakash, S.Selvan

Abstract:

QoS Routing aims to find paths between senders and receivers satisfying the QoS requirements of the application which efficiently using the network resources and underlying routing algorithm to be able to find low-cost paths that satisfy given QoS constraints. The problem of finding least-cost routing is known to be NP hard or complete and some algorithms have been proposed to find a near optimal solution. But these heuristics or algorithms either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we analyzed two algorithms namely Characterized Delay Constrained Routing (CDCR) and Optimized Delay Constrained Routing (ODCR). The CDCR algorithm dealt an approach for delay constrained routing that captures the trade-off between cost minimization and risk level regarding the delay constraint. The ODCR which uses an adaptive path weight function together with an additional constraint imposed on the path cost, to restrict search space and hence ODCR finds near optimal solution in much quicker time.

Keywords: QoS, Delay, Routing, Optimization

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Authors: Parham Azimi, Hamid Reza Charmchi

Abstract:

In this research, we have developed a new efficient heuristic algorithm for the dynamic facility layout problem with budget constraint (DFLPB). This heuristic algorithm combines two mathematical programming methods such as discrete event simulation and linear integer programming (IP) to obtain a near optimum solution. In the proposed algorithm, the non-linear model of the DFLP has been changed to a pure integer programming (PIP) model. Then, the optimal solution of the PIP model has been used in a simulation model that has been designed in a similar manner as the DFLP for determining the probability of assigning a facility to a location. After a sufficient number of runs, the simulation model obtains near optimum solutions. Finally, to verify the performance of the algorithm, several test problems have been solved. The results show that the proposed algorithm is more efficient in terms of speed and accuracy than other heuristic algorithms presented in previous works found in the literature.

Keywords: Budget constraint, Dynamic facility layout problem, Integer programming, Simulation

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Authors: R. Rajabpour, N. Talebbeydokhti, M. H. Ahmadi

Abstract:

In recent years, new techniques for solving complex problems in engineering are proposed. One of these techniques is JPSO algorithm. With innovative changes in the nature of the jump algorithm JPSO, it is possible to construct a graph-based solution with a new algorithm called G-JPSO. In this paper, a new algorithm to solve the optimal control problem Fletcher-Powell and optimal control of pumps in water distribution network was evaluated. Optimal control of pumps comprise of optimum timetable operation (status on and off) for each of the pumps at the desired time interval. Maximum number of status on and off for each pumps imposed to the objective function as another constraint. To determine the optimal operation of pumps, a model-based optimization-simulation algorithm was developed based on G-JPSO and JPSO algorithms. The proposed algorithm results were compared well with the ant colony algorithm, genetic and JPSO results. This shows the robustness of proposed algorithm in finding near optimum solutions with reasonable computational cost.

Keywords: G-JPSO, operation, optimization, pumping station, water distribution networks.

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Authors: Aniruddha Bhattacharya, Pranab Kumar Chattopadhyay

Abstract:

Optimal reactive power flow is an optimization problem with one or more objective of minimizing the active power losses for fixed generation schedule. The control variables are generator bus voltages, transformer tap settings and reactive power output of the compensating devices placed on different bus bars. Biogeography- Based Optimization (BBO) technique has been applied to solve different kinds of optimal reactive power flow problems subject to operational constraints like power balance constraint, line flow and bus voltages limits etc. BBO searches for the global optimum mainly through two steps: Migration and Mutation. In the present work, BBO has been applied to solve the optimal reactive power flow problems on IEEE 30-bus and standard IEEE 57-bus power systems for minimization of active power loss. The superiority of the proposed method has been demonstrated. Considering the quality of the solution obtained, the proposed method seems to be a promising one for solving these problems.

Keywords: Active Power Loss, Biogeography-Based Optimization, Migration, Mutation, Optimal Reactive Power Flow.

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Authors: Jeffrey L. Duffany

Abstract:

The equivalence class subset algorithm is a powerful tool for solving a wide variety of constraint satisfaction problems and is based on the use of a decision function which has a very high but not perfect accuracy. Perfect accuracy is not required in the decision function as even a suboptimal solution contains valuable information that can be used to help find an optimal solution. In the hardest problems, the decision function can break down leading to a suboptimal solution where there are more equivalence classes than are necessary and which can be viewed as a mixture of good decision and bad decisions. By choosing a subset of the decisions made in reaching a suboptimal solution an iterative technique can lead to an optimal solution, using series of steadily improved suboptimal solutions. The goal is to reach an optimal solution as quickly as possible. Various techniques for choosing the decision subset are evaluated.

Keywords: np-complete, complexity, algorithm.

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Authors: M. Mohebbi, K. Shakeri

Abstract:

In the real application of active control systems to mitigate the response of structures subjected to sever external excitations such as earthquake and wind induced vibrations, since the capacity of actuators is limited then the actuators saturate. Hence, in designing controllers for linear and nonlinear structures under sever earthquakes, the actuator saturation should be considered as a constraint. In this paper optimal design of active controllers for nonlinear structures by considering the actuator saturation has been studied. To this end a method has been proposed based on defining an optimization problem which considers the minimizing of the maximum displacement of the structure as objective when a limited capacity for actuator has been used as a constraint in optimization problem. To evaluate the effectiveness of the proposed method, a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of pre-stressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used as active control mechanism and algorithm. To enhance the efficiency of the controllers, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been found by using the Distributed Genetic Algorithm (DGA). According to the results it has been concluded that the proposed method has been effective in considering the actuator saturation in designing optimal controllers for nonlinear frames. Also it has been shown that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers for considering the actuator saturation.

Keywords: Active control, Actuator Saturation, Nonlinear, Optimization.

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Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: P. S. Prakash, S. Selvan

Abstract:

QoS Routing aims to find paths between senders and receivers satisfying the QoS requirements of the application which efficiently using the network resources and underlying routing algorithm to be able to find low-cost paths that satisfy given QoS constraints. The problem of finding least-cost routing is known to be NP-hard or complete and some algorithms have been proposed to find a near optimal solution. But these heuristics or algorithms either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we concentrate an algorithm that finds a near-optimal solution fast and we named this algorithm as optimized Delay Constrained Routing (ODCR), which uses an adaptive path weight function together with an additional constraint imposed on the path cost, to restrict search space and hence ODCR finds near optimal solution in much quicker time.

Keywords: QoS, Delay, Routing, Optimization.

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Authors: M. Mohebbi, K. Shakeri

Abstract:

Since the actuator capacity is limited, in the real application of active control systems under sever earthquakes it is conceivable that the actuators saturate, hence the actuator saturation should be considered as a constraint in design of optimal controllers. In this paper optimal design of active controllers for nonlinear structures by considering actuator saturation, has been studied. The proposed method for designing optimal controllers is based on defining an optimization problem which the objective has been to minimize the maximum displacement of structure when a limited capacity for actuator has been used. To this end a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of prestressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used. To achieve the best results, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been optimized by the Distributed Genetic Algorithm (DGA). Results show the effectiveness of the proposed method in considering actuator saturation. Also based on the numerical simulations it can be concluded that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers which consider the actuator saturation.

Keywords: Active control, Actuator Saturation, Distributedgeneticalgorithms, Nonlinear.

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Authors: Abdolreza Hatamlou, Yusef Farhang, Mohammad Reza Meybodi

Abstract:

Variable ordering heuristics are used in constraint satisfaction algorithms. Different characteristics of various variable ordering heuristics are complementary. Therefore we have tried to get the advantages of all heuristics to improve search algorithms performance for solving constraint satisfaction problems. This paper considers combinations based on products and quotients, and then a newer form of combination based on weighted sums of ratings from a set of base heuristics, some of which result in definite improvements in performance.

Keywords: Constraint Satisfaction Problems, Variable Ordering Heuristics, Combination, Search Algorithms

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Authors: Sheeba V.S, Elizabeth Elias

Abstract:

Optimization of filter banks based on the knowledge of input statistics has been of interest for a long time. Finite impulse response (FIR) Compaction filters are used in the design of optimal signal adapted orthonormal FIR filter banks. In this paper we discuss three different approaches for the design of interpolated finite impulse response (IFIR) compaction filters. In the first method, the magnitude squared response satisfies Nyquist constraint approximately. In the second and third methods Nyquist constraint is exactly satisfied. These methods yield FIR compaction filters whose response is comparable with that of the existing methods. At the same time, IFIR filters enjoy significant saving in the number of multipliers and can be implemented efficiently. Since eigenfilter approach is used here, the method is less complex. Design of IFIR filters in the least square sense is presented.

Keywords: Principal Component Filter Bank, InterpolatedFinite Impulse Response filter, Orthonormal Filter Bank, Eigen Filter.

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Authors: S. A. Faizi, S. Yoshitomi

Abstract:

The optimal design procedure of buckling restrained braces (BRBs) in reinforced concrete (RC) building structures can provide the distribution of horizontal stiffness of BRBs at each story, which minimizes story drift response of the structure under the constraint of specified total stiffness of BRBs. In this paper, a simple rule is proposed to convert continuous horizontal stiffness of BRBs into sectional sizes of BRB which are available from standardized section list assuming realistic structural design stage.

Keywords: Buckling restrained brace, building engineering, optimal damper placement, structural engineering.

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Authors: Songtao Chang, Yongji Wang, Lei Liu, Dangjun Zhao

Abstract:

Reentry trajectory optimization is a multi-constraints optimal control problem which is hard to solve. To tackle it, we proposed a new algorithm named CDEN(Constrained Differential Evolution Newton-Raphson Algorithm) based on Differential Evolution( DE) and Newton-Raphson.We transform the infinite dimensional optimal control problem to parameter optimization which is finite dimensional by discretize control parameter. In order to simplify the problem, we figure out the control parameter-s scope by process constraints. To handle constraints, we proposed a parameterless constraints handle process. Through comprehensive analyze the problem, we use a new algorithm integrated by DE and Newton-Raphson to solve it. It is validated by a reentry vehicle X-33, simulation results indicated that the algorithm is effective and robust.

Keywords: reentry vehicle, trajectory optimization, constraint optimal, differential evolution.

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Authors: Abdel-Reza Hatamlou, Mohammad Reza Meybodi

Abstract:

In this paper we present a hybrid search algorithm for solving constraint satisfaction and optimization problems. This algorithm combines ideas of two basic approaches: complete and incomplete algorithms which also known as systematic search and local search algorithms. Different characteristics of systematic search and local search methods are complementary. Therefore we have tried to get the advantages of both approaches in the presented algorithm. The major advantage of presented algorithm is finding partial sound solution for complicated problems which their complete solution could not be found in a reasonable time. This algorithm results are compared with other algorithms using the well known n-queens problem.

Keywords: Constraint Satisfaction Problem, Hybrid SearchAlgorithm.

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Authors: Ömer Faruk Baykoç, Ümit Sami Sakalli

Abstract:

In this paper, we propose a fuzzy aggregate production planning (APP) model for blending problem in a brass factory which is the problem of computing optimal amounts of raw materials for the total production of several types of brass in a period. The model has deterministic and imprecise parameters which follows triangular possibility distributions. The brass casting APP model can not always be solved by using common approaches used in the literature. Therefore a mathematical model is presented for solving this problem. In the proposed model, the Lai and Hwang-s fuzzy ranking concept is relaxed by using one constraint instead of three constraints. An application of the brass casting APP model in a brass factory shows that the proposed model successfully solves the multi-blend problem in casting process and determines the optimal raw material purchasing policies.

Keywords: Aggregate production planning, Blending, brasscasting, possibilistic programming.

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Authors: F. Fissou Amigue, S. Ndjakomo Essiane, S. Pérabi Ngoffé, G. Abessolo Ondoa, G. Mengata Mengounou, T. P. Nna Nna

Abstract:

This document proposes a method for determining the optimal point of integration of distributed generation (DG) in distribution grid. Slime mould optimization is applied to determine best node in case of one and two injection point. Problem has been modeled as an optimization problem where the objective is to minimize joule loses and main constraint is to regulate voltage in each point. The proposed method has been implemented in MATLAB and applied in IEEE network 33 and 69 nodes. Comparing results obtained with other algorithms showed that slime mould optimization algorithms (SMOA) have the best reduction of power losses and good amelioration of voltage profile.

Keywords: Optimization, distributed generation, integration, slime mould algorithm.

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Authors: Cuong D. Dao, Rob J.I. Basten, Andreas Hartmann

Abstract:

This paper studies the optimal maintenance planning of preventive maintenance and renewal activities for components in a single railway track when the available time for maintenance is limited. The rail-track system consists of several types of components, such as rail, ballast, and switches with different preventive maintenance and renewal intervals. To perform maintenance or renewal on the track, a train free period for maintenance, called a possession, is required. Since a major possession directly affects the regular train schedule, maintenance and renewal activities are clustered as much as possible. In a highly dense and utilized railway network, the possession time on the track is critical since the demand for train operations is very high and a long possession has a severe impact on the regular train schedule. We present an optimization model and investigate the maintenance schedules with and without the possession capacity constraint. In addition, we also integrate the social-economic cost related to the effects of the maintenance time to the variable possession cost into the optimization model. A numerical example is provided to illustrate the model.

Keywords: Rail-track components, maintenance, optimal clustering, possession capacity.

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Authors: S. V. Kasmir Raja, P. Herbert Raj

Abstract:

The overlay approach has been widely used by many service providers for Traffic Engineering (TE) in large Internet backbones. In the overlay approach, logical connections are set up between edge nodes to form a full mesh virtual network on top of the physical topology. IP routing is then run over the virtual network. Traffic engineering objectives are achieved through carefully routing logical connections over the physical links. Although the overlay approach has been implemented in many operational networks, it has a number of well-known scaling issues. This paper proposes a new approach to achieve traffic engineering without full-mesh overlaying with the help of integrated approach and equal subset split method. Traffic engineering needs to determine the optimal routing of traffic over the existing network infrastructure by efficiently allocating resource in order to optimize traffic performance on an IP network. Even though constraint-based routing [1] of Multi-Protocol Label Switching (MPLS) is developed to address this need, since it is not widely tested or debugged, Internet Service Providers (ISPs) resort to TE methods under Open Shortest Path First (OSPF), which is the most commonly used intra-domain routing protocol. Determining OSPF link weights for optimal network performance is an NP-hard problem. As it is not possible to solve this problem, we present a subset split method to improve the efficiency and performance by minimizing the maximum link utilization in the network via a small number of link weight modifications. The results of this method are compared against results of MPLS architecture [9] and other heuristic methods.

Keywords: Constraint based routing, Link Utilization, Subsetsplit method and Traffic Engineering.

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Authors: G. Chandana Sushma, T. R. Jyothsna

Abstract:

This paper presents optimal Phasor Measurement Unit (PMU) Placement in network using a genetic algorithm approach as it is infeasible and require high installation cost to place PMUs at every bus in network. This paper proposes optimal PMU allocation considering observability and redundancy utilizing Genetic Algorithm (GA) approach. The nonlinear constraints of buses are modeled to give accurate results. Constraints associated with Zero Injection (ZI) buses and radial buses are modeled to optimize number of locations for PMU placement. GA is modeled with ZI bus constraints to minimize number of locations without losing complete observability. Redundancy of every bus in network is computed to show optimum redundancy of complete system network. The performance of method is measured by Bus Observability Index (BOI) and Complete System Observability Performance Index (CSOPI). MATLAB simulations are carried out on IEEE -14, -30 and -57 bus-systems and compared with other methods in literature survey to show the effectiveness of the proposed approach.

Keywords: Constraints, genetic algorithm, observability, phasor measurement units, redundancy, synchrophasors, zero injection bus.

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Authors: N. Popovich, P. Yan

Abstract:

In this paper, the process of obtaining Q and R matrices for optimal pitch aircraft control system has been described. Since the innovation of optimal control method, the determination of Q and R matrices for such system has not been fully specified. The value of Q and R for optimal pitch aircraft control application, have been simulated and calculated. The suitable results for Q and R have been observed through the performance index (PI). If the PI is small “enough", we would say the Q & R values are suitable for that certain type of optimal control system. Moreover, for the same value of PI, we could have different Q and R sets. Due to the rule-free determination of Q and R matrices, a specific method is brought to find out the rough value of Q and R referring to rather small value of PI.

Keywords: Aircraft, control, digital, optimal, Q and R matrices

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