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smoothed functional algorithm with Norm-limited Update Vector for Identification of Continuous-time Fractional-order Hammerstein Models

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IETE JOURNAL OF RESEARCH 2024年第2期70卷 1814-1832页

作者： Mok, RenHao Ahmad, Mohd Ashraf Univ Malaysia Pahang Pekan Pahang Malaysia Univ Malaysia Pahang UMP Fac Elect & Elect Engn Technol Pekan Pahang Malaysia

This article proposes an identification method of continuous-time fractional-order Hammerstein model using smoothed functional algorithm with a norm-limited update vector (NL-SFA). In particular, the standard smoothed functional algorithm (SFA) based method is modified by implementing a limit function in the update vector of the standard SFA based method to solve the issue of high tendency of divergence during the identification process. As a result of this, the proposed NL-SFA based method is applied to identify the variables of the linear and non-linear subsystems in the Hammerstein model. While most of the actual linear subsystems can be naturally expressed in a continuous-time domain, the implementation of the fractional-order could also reduce the computational complexity in finding a more accurate reduced-order model. Moreover, three experiments of the Hammerstein model identification based on a numerical example, an actual twin-rotor system, and an actual flexible manipulator system were carried out in this study to verify the effectiveness of the proposed NL-SFA-based method. The numerical and experimental results were analyzed to correspond to the measurement of the objective function and variable identification error and time-domain and frequency-domain responses. Conclusively, the proposed NL-SFA-based method can provide stable convergence and significantly better accuracy of the Hammerstein model in the numerical example, the actual twin-rotor system, and the flexible manipulator system compared to the standard SFA. Moreover, the proposed NL-SFA also provides slightly competitive identification accuracy with the existing norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and the average multi-verse optimizer sine cosine algorithm (AMVO-SCA) based methods.

关键词： smoothed functional algorithm Continuous-time Fractional-order Hammerstein model Variable identification

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Fast and optimal tuning of fractional order PID controller for AVR system based on memorizable-smoothed functional algorithm

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ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH 2022年 35卷

作者： Mok, RenHao Ahmad, Mohd Ashraf Univ Malaysia Pahang Fac Elect & Elect Engn Technol Pekan Malaysia

Voltage regulation in automatic voltage regulator (AVR) system has been one of the most challenging engineering problem due to the uncertain load condition. Therefore, the control of AVR system by using PID based controller is one of the essential approach to maintain the performance of the AVR system. Subsequently, the application of FOPID controller in AVR system is gaining more attention recently. This is because the FOPID has additional control parameters at the derivative and integral parts than the PID controller, which has the advantage to improve the output response of AVR system while retaining the robustness and simple construction as the PID controller. Nevertheless, many existing optimization tools for tuning the FOPID controller, which are based on multi-agent based optimization, require large number of function evaluation in their algorithm that could lead to high computational burden. Therefore, this study proposes a modified smoothed function algorithm (MSFA) based method to tune the FOPID controller of AVR system since it requires fewer number of function evaluation per iteration. Moreover, the proposed MSFA based method also can solve the unstable convergence issue in the original smoothed function algorithm (SFA), thus able to provide better convergence accuracy. The simulations of step response analysis, Bode plot analysis, trajectory tracking analysis, disturbance rejection analysis, and parameter variation analysis are conducted to evaluate the effectiveness of the proposed MSFA-FOPID controller of AVR system. Consequently, the results obtained from the simulations revealed that the proposed method is highly effective and significantly improved as compared to the other existing FOPID controllers. (C) 2022 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： smoothed functional algorithm Automatic voltage regulator Fractional PID controller Gradient based Optimization

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Multi-Time Scale smoothed functional With Nesterov's Acceleration

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IEEE ACCESS 2021年 9卷 113489-113499页

作者： Sharma, Abhinav Lakshmanan, K. Gupta, Ruchir Gupta, Atul PDPM Indian Inst Informat Technol Jabalpur Dept Comp Sci Jabalpur 482005 Madhya Pradesh India IIT Banaras Hindu Univ BHU Varanasi Dept Comp Sci Varanasi 221005 Uttar Pradesh India Jawaharlal Nehru Univ JNU Dept Comp Sci Delhi 110067 India

smoothed functional (SF) algorithm estimates the gradient of the stochastic optimization problem by convolution with a smoothening kernel. This process helps the algorithm to converge to a global minimum or a point close to it. We study a two-time scale SF based gradient search algorithm with Nesterov's acceleration for stochastic optimization problems. The main contribution of our work is to prove the convergence of this algorithm using the stochastic approximation theory. We propose a novel Lyapunov function to show the associated second-order ordinary differential equations' (o.d.e.) stability for a non-autonomous system. We compare our algorithm with other smoothed functional algorithms such as Quasi-Newton SF, Gradient SF and Jacobi Variant of Newton SF on two different optimization problems: first, on a simple stochastic function minimization problem, and second, on the problem of optimal routing in a queueing network. Additionally, we compared the algorithms on real weather data in a weather prediction task. Experimental results show that our algorithm performs significantly better than these baseline algorithms.

关键词： Approximation algorithms Linear programming Convergence Prediction algorithms Markov processes Cost function Trajectory Multi-Stage queueing networks Nesterov's acceleration simulation smoothed functional algorithm stochastic approximation algorithms stochastic optimization

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Quasi-Newton smoothed functional algorithms for unconstrained and constrained simulation optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第3期66卷 533-556页

作者： Lakshmanan, K. Bhatnagar, Shalabh Amrita Sch Engn Dept Comp Sci & Engn Bangalore 560035 Karnataka India Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India

We propose a multi-time scale quasi-Newton based smoothed functional (QN-SF) algorithm for stochastic optimization both with and without inequality constraints. The algorithm combines the smoothed functional (SF) scheme for estimating the gradient with the quasi-Newton method to solve the optimization problem. Newton algorithms typically update the Hessian at each instant and subsequently (a) project them to the space of positive definite and symmetric matrices, and (b) invert the projected Hessian. The latter operation is computationally expensive. In order to save computational effort, we propose in this paper a quasi-Newton SF (QN-SF) algorithm based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) update rule. In Bhatnagar (ACM TModel Comput S. 18(1): 27-62, 2007), a Jacobi variant of Newton SF (JN-SF) was proposed and implemented to save computational effort. We compare our QN-SF algorithm with gradient SF (G-SF) and JN-SF algorithms on two different problems - first on a simple stochastic function minimization problem and the other on a problem of optimal routing in a queueing network. We observe from the experiments that the QN-SF algorithm performs significantly better than both G-SF and JN-SF algorithms on both the problem settings. Next we extend the QN-SF algorithm to the case of constrained optimization. In this case too, the QN-SF algorithm performs much better than the JN-SF algorithm. Finally we present the proof of convergence for the QN-SF algorithm in both unconstrained and constrained settings.

关键词： Simulation Stochastic optimization Stochastic approximation algorithms smoothed functional algorithm Quasi-Newton methods Constrained optimization Multi-stage queueing networks

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Stochastic algorithms for Discrete Parameter Simulation Optimization

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2011年第4期8卷 780-793页

作者： Bhatnagar, Shalabh Mishra, Vivek Kumar Hemachandra, Nandyala Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India Indian Inst Technol Dept Ind Engn & Operat Res Bombay 400076 Maharashtra India

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm. Note to Practitioners-Even though SPSA and SFA have been devised in the literature for continuous optimization problems, our results indicate that they can be powerful techniques even when they are adapted to discrete optimization settings. OCBA is widely recognized as one of the most powerful methods for discrete optimization when the parameter sets are of small or moderate size. On a setting involving a parameter set of size 100, we observe that when the computing budget is small, both SPSA and OCBA show similar performance and are better in comparison to SFA, however, as the computing budget is increased, SPSA and SFA show better performance than OCBA. Both our algorithms also show good performance when the parameter set has a size of 10(8). SFA is seen to show the best overall performance. Unlike most other DPSO algorithms in the literature, an advantage with our algorithms is that they are easily implementable regardless of the size of the parameter sets and show good performance in both scenarios.

关键词： Discrete parameter simulation optimization long-run average cost objective simultaneous perturbation stochastic approximation smoothed functional algorithm

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Optimal Parameter Trajectory Estimation in Parameterized SDEs: An algorithmic Procedure

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ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION 2009年第2期19卷 1–27页

作者： Bhatnagar, Shalabh Karmeshu Mishra, Vivek Kumar Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India Jawaharlal Nehru Univ Sch Comp & Syst Sci New Delhi 110067 India

We consider the problem of estimating the optimal parameter trajectory over a finite time interval in a parameterized stochastic differential equation (SDE), and propose a simulation-based algorithm for this purpose. Towards this end, we consider a discretization of the SDE over finite time instants and reformulate the problem as one of finding an optimal parameter at each of these instants. A stochastic approximation algorithm based on the smoothed functional technique is adapted to this setting for finding the optimal parameter trajectory. A proof of convergence of the algorithm is presented and results of numerical experiments over two different settings are shown. The algorithm is seen to exhibit good performance. We also present extensions of our framework to the case of finding optimal parameterized feedback policies for controlled SDE and present numerical results in this scenario as well.

关键词： Optimal parameter trajectory parameterized stochastic differential equations (SDEs) simulation optimization smoothed functional algorithm

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Multiscale chaotic SPSA and smoothed functional algorithms for simulation optimization

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SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL 2003年第10期79卷 568-580页

作者： Bhatnagar, S Borkar, VS Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India Tata Inst Fundamental Res Sch Technol & Comp Sci Bombay 400005 Maharashtra India

The authors propose a two-timescale version of the one-simulation smoothed functional (SF) algorithm with extra averaging. They also propose the use of a chaotic simple deterministic iterative sequence for generating random samples for averaging. This sequence is used for generating the N independent and identically distributed (i.i.d.), Gaussian random variables in the SF algorithm. The convergence analysis of the algorithms is also briefly presented. The authors show numerical experiments on the chaotic sequence and compare performance with a good pseudo-random generator. Next they show experiments in two different settings-a network of M/G/1 queues with feedback and the problem of finding a closed-loop optimal policy (within a prespecified class) in the available bit rate (ABR) service in asynchronous transfer mode (ATM) networks, using all the algorithms. The authors observe that algorithms that use the chaotic sequence show better performance in most cases than those that use the pseudo-random generator.

关键词： smoothed functional algorithm SPSA algorithm chaotic iterative sequence simulation optimization hidden Markov model

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