Search results for: stochastic optimal control technique

Authors: María L. Jalón, Feargal Brennan

Abstract:

A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: Non-stationary stochastic optimization, oscillating water column, temporal variability, wave energy.

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Authors: Takayuki Shiina

Abstract:

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of rootmean- squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous - time.

Keywords: Mathematical expectation, filtration, anomalous noise, memory.

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Authors: Hitoshi Takata, Tomohiro Hachino, Masaki Horai, Kazuo Komatsu

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In this paper, we are concerned with the design and its simulation studies of a modified extremum seeking control for nonlinear systems. A standard extremum seeking control has a simple structure, but it takes a long time to reach an optimal operating point. We consider a modification of the standard extremum seeking control which is aimed to reach the optimal operating point more speedily than the standard one. In the modification, PD acceleration term is added before an integrator making a principal control, so that it enables the objects to be regulated to the optimal point smoothly. This proposed method is applied to Monod and Williams-Otto models to investigate its effectiveness. Numerical simulation results show that this modified method can improve the time response to the optimal operating point more speedily than the standard one.

Keywords: Extremum seeking control, Monod model, Williams- Otto model, PD acceleration term, Optimal operating point.

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

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In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

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This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model.

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Authors: Yin Yin Pey, Leok Poh Chua, Wei Long Siauw

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Linear stochastic estimation and quadratic stochastic estimation techniques were applied to estimate the entire velocity flow-field of an open cavity with a length to depth ratio of 2. The estimations were done through the use of instantaneous velocity magnitude as estimators. These measurements were obtained by Particle Image Velocimetry. The predicted flow was compared against the original flow-field in terms of the Reynolds stresses and turbulent kinetic energy. Quadratic stochastic estimation proved to be more superior than linear stochastic estimation in resolving the shear layer flow. When the velocity fluctuations were scaled up in the quadratic estimate, both the time-averaged quantities and the instantaneous cavity flow can be predicted to a rather accurate extent.

Keywords: Open cavity, Particle Image Velocimetry, Stochastic estimation, Turbulent kinetic energy.

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Authors: P. Beraldi, M. E. Bruni

Abstract:

Data Envelopment Analysis (DEA) is one of the most widely used technique for evaluating the relative efficiency of a set of homogeneous decision making units. Traditionally, it assumes that input and output variables are known in advance, ignoring the critical issue of data uncertainty. In this paper, we deal with the problem of efficiency evaluation under uncertain conditions by adopting the general framework of the stochastic programming. We assume that output parameters are represented by discretely distributed random variables and we propose two different models defined according to a neutral and risk-averse perspective. The models have been validated by considering a real case study concerning the evaluation of the technical efficiency of a sample of individual firms operating in the Italian leather manufacturing industry. Our findings show the validity of the proposed approach as ex-ante evaluation technique by providing the decision maker with useful insights depending on his risk aversion degree.

Keywords: DEA, Stochastic Programming, Ex-ante evaluation technique, Conditional Value at Risk.

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Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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Authors: Madhukar Nagare, Pankaj Dutta

Abstract:

Inventory decisional environment of short life-cycle products is full of uncertainties arising from randomness and fuzziness of input parameters like customer demand requiring modeling under hybrid uncertainty. Prior inventory models incorporating fuzzy demand have unfortunately ignored stochastic variation of demand. This paper determines an unambiguous optimal order quantity from a set of n fuzzy observations in a newsvendor inventory setting in presence of fuzzy random variable demand capturing both fuzzy perception and randomness of customer demand. The stress of this paper is in providing solution procedure that attains optimality in two steps with demand information availability in linguistic phrases leading to fuzziness along with stochastic variation. The first step of solution procedure identifies and prefers one best fuzzy opinion out of all expert opinions and the second step determines optimal order quantity from the selected event that maximizes profit. The model and solution procedure is illustrated with a numerical example.

Keywords: Fuzzy expected value, Fuzzy random demand, Hybrid uncertainty, Optimal order quantity, Single-period inventory

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Authors: Amira M. Attia, Karim H. Youssef, Nabil H. Abbasy

Abstract:

Energy consumption schedule (ECS) technique shifts usage of loads from on peak hours and redistributes them throughout the day according to residents’ operating time preferences. This technique is used as form of indirect control from utility to improve the load curve and hence its load factor and reduce customer’s total electric bill as well. Similarly, load shifting technique achieves ECS purposes but as direct control form applied from utility. In this paper, ECS is simulated twice as optimal constrained mathematical formula, solved by using CVX program in MATLAB^® R2013b. First, it is utilized for single residential building with ten apartments to determine max allowable energy consumption per hour for each residential apartment. Then, it is used for single apartment with number of shiftable domestic devices, where operating schedule is deduced using previous simulation output results as constraints. The paper ends by giving differences between ECS technique and load shifting technique via literature and simulation. Based on results assessment, it will be shown whether using ECS or load shifting is more beneficial to both customer and utility.

Keywords: Energy consumption schedule, load shifting technique, comparison.

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Authors: Shu Lü, Shouming Zhong, Zixin Liu

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In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neural networks, stochastic, time-varying delays.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: A. A. Hussen, I. N. Jleta

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Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effects of these random errors, they must be accurately modeled. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors.

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Authors: R. Sharma, M. Gopal

Abstract:

This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-space. The approach creates a synergy between an approximate evolving model and approximate cost-to-go values to produce a sequence of improving policies finally converging to the optimal policy through an intelligent and structured search of the policy space. The approach modifies the policy update step of the policy iteration so as to result in a speedy and stable convergence to the optimal policy. We apply the algorithm to a non-holonomic mobile robot control problem and compare its performance with other Reinforcement Learning (RL) approaches, e.g., a) Q-learning, b) Watkins Q(λ), c) SARSA(λ).

Keywords: Markov Decision Process (MDP), Mobile robot, Policy iteration, Simulation.

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Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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Authors: W. Chayinthu, K-N. Areerak, K-L. Areerak, A. Srikaew

Abstract:

This paper presents the optimal controller design of the generator control unit in the aircraft power system. The adaptive tabu search technique is applied to tune the controller parameters until the best terminal output voltage of generator is achieved. The output response from the system with the controllers designed by the proposed technique is compared with those from the conventional method. The transient simulations using the commercial software package show that the controllers designed from the adaptive tabu search algorithm can provide the better output performance compared with the result from the classical method. The proposed design technique is very flexible and useful for electrical aircraft engineers.

Keywords: Cascade PI controllers, DQ method, Adaptive tabusearch, Generator control unit, Aircraft power system, Modeling, Simulation, Artificial Intelligence.

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Authors: Shyam S.N. Perera

Abstract:

An optimal control problem for a mathematical model of efficiency of antiviral therapy in hepatitis B virus infections is considered. The aim of the study is to control the new viral production, block the new infection cells and maintain the number of uninfected cells in the given range. The optimal controls represent the efficiency of antiviral therapy in inhibiting viral production and preventing new infections. Defining the cost functional, the optimal control problem is converted into the constrained optimization problem and the first order optimality system is derived. For the numerical simulation, we propose the steepest descent algorithm based on the adjoint variable method. A computer program in MATLAB is developed for the numerical simulations.

Keywords: Virus infection model, Optimal control, Adjoint system, Steepest descent

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Authors: Y. Areepong

Abstract:

The objective of this paper is to present explicit analytical formulas for evaluating important characteristics of Double Moving Average control chart (DMA) for Poisson distribution. The most popular characteristics of a control chart are Average Run Length ( 0 ARL ) - the mean of observations that are taken before a system is signaled to be out-of control when it is actually still incontrol, and Average Delay time ( 1 ARL ) - mean delay of true alarm times. An important property required of 0 ARL is that it should be sufficiently large when the process is in-control to reduce a number of false alarms. On the other side, if the process is actually out-ofcontrol then 1 ARL should be as small as possible. In particular, the explicit analytical formulas for evaluating 0 ARL and 1 ARL be able to get a set of optimal parameters which depend on a width of the moving average ( w ) and width of control limit ( H ) for designing DMA chart with minimum of 1 ARL

Keywords: Optimal parameters, Average Run Length, Average Delay time, Double Moving Average chart.

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Authors: S. Hamid Mirmohammadi, Shahrazad Tamjidzad

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This paper is concerned with the single-item continuous review inventory system in which demand is stochastic and discrete. The budget consumed for purchasing the ordered items is not restricted but it incurs extra cost when exceeding specific value. The unit purchasing price depends on the quantity ordered under the all-units discounts cost structure. In many actual systems, the budget as a resource which is occupied by the purchased items is limited and the system is able to confront the resource shortage by charging more costs. Thus, considering the resource shortage costs as a part of system costs, especially when the amount of resource occupied by the purchased item is influenced by quantity discounts, is well motivated by practical concerns. In this paper, an optimization problem is formulated for finding the optimal (r, Q) policy, when the system is influenced by the budget limitation and a discount pricing simultaneously. Properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs.

Keywords: (r, Q) policy, Stochastic demand, backorders, limited resource, quantity discounts.

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Authors: Bassem Roushdy, Nahed Sobhy, Abdelrhim Abdelhamid, Ahmed Mahmoud

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Most papers model Joint Replenishment Problem (JRP) as a (kT,S) where kT is a multiple value for a common review period T,and S is a predefined order up to level. In general the (T,S) policy is characterized by a long out of control period which requires a large amount of safety stock compared to the (R,Q) policy. In this paper a probabilistic model is built where an item, call it item(i), with the shortest order time between interval (T)is modeled under (R,Q) policy and its inventory is continuously reviewed, while the rest of items (j) are periodically reviewed at a definite time corresponding to item

Keywords: Inventory management, Joint replenishment, policy evaluation, stochastic process

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Authors: Ghulam Zakria, Zailin Guan , Yasser Riaz Awan, Wan Lizhi

Abstract:

There are many real world problems in which parameters like the arrival time of new jobs, failure of resources, and completion time of jobs change continuously. This paper tackles the problem of scheduling jobs with random due dates on multiple identical machines in a stochastic environment. First to assign jobs to different machine centers LPT scheduling methods have been used, after that the particular sequence of jobs to be processed on the machine have been found using simple stochastic techniques. The performance parameter under consideration has been the maximum lateness concerning the stochastic due dates which are independent and exponentially distributed. At the end a relevant problem has been solved using the techniques in the paper..

Keywords: Quantity Production Flow Shop, LPT Scheduling, Stochastic Scheduling, Maximum Lateness, Random Due Dates

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

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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: 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: Deepak Chhabra, Gian Bhushan, Pankaj Chandna

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The present work deals with the optimal placement of piezoelectric actuators on a thin plate using Modified Control Matrix and Singular Value Decomposition (MCSVD) approach. The problem has been formulated using the finite element method using ten piezoelectric actuators on simply supported plate to suppress first six modes. The sizes of ten actuators are combined to outline one actuator by adding the ten columns of control matrix to form a column matrix. The singular value of column control matrix is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with GA. Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions using Linear Quadratic regulator) scheme. It is observed that MCSVD approach has given the position of patches adjacent to each-other, symmetric to the centre axis and given greater vibration suppression than other previously published results on SVD. 

Keywords: Closed loop Average dB gain, Genetic Algorithm (GA), LQR Controller, MCSVD, Optimal positions, Singular Value Decomposition (SVD) Approaches.

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Authors: Kittipob Kondee, Chutima Prommak

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In this paper, we propose an optimization technique that can be used to optimize the placements of reference nodes and improve the location determination performance for the multi-floor building. The proposed technique is based on Simulated Annealing algorithm (SA) and is called MSMR-M. The performance study in this work is based on simulation. We compare other node-placement techniques found in the literature with the optimal node-placement solutions obtained from our optimization. The results show that using the optimal node-placement obtained by our proposed technique can improve the positioning error distances up to 20% better than those of the other techniques. The proposed technique can provide an average error distance within 1.42 meters.

Keywords: Indoor positioning System, Optimization System design, Multi-Floor Building, Wireless Sensor Networks.

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: Model predictive control, optimal control, crystal growth, process control.

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even-dough decreases at these extreme wind speeds but are not infinite. Moreover, we also fund that it is possible to stabilize the power coefficient (stabilizing the output power)above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: Probability, Stochastic, Probability density function, Turbulence.

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Authors: K. Kusakana

Abstract:

A hybrid energy system is a combination of renewable energy sources with back up, as well as a storage system used to respond to given load energy requirements. Given that the electrical output of each renewable source is fluctuating with changes in weather conditions, and since the load demand also varies with time; one of the main attributes of hybrid systems is to be able to respond to the load demand at any time by optimally controlling each energy source, storage and back-up system. The induced optimization problem is to compute the optimal operation control of the system with the aim of minimizing operation costs while efficiently and reliably responding to the load energy requirement. Current optimization research and development on hybrid systems are mainly focusing on the sizing aspect. Thus, the aim of this paper is to report on the state-of-the-art of optimal operation control of hybrid renewable energy systems. This paper also discusses different challenges encountered, as well as future developments that can help in improving the optimal operation control of hybrid renewable energy systems.

Keywords: Renewable energies, hybrid systems, optimization, operation control.

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Authors: A. Aissani, H. Benaoudia

Abstract:

Stochastic comparison has been an important direction of research in various area. This can be done by the use of the notion of stochastic ordering which gives qualitatitive rather than purely quantitative estimation of the system under study. In this paper we present applications of comparison based uncertainty related to entropy in Reliability analysis, for example to design better systems. These results can be used as a priori information in simulation studies.

Keywords: Uncertainty, Stochastic comparison, Reliability, serie's system, imperfect repair.

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