Order reduction of linear discrete systems using a genetic algorithm

Satakshi,; Mukherjee, S.; Mittal, R. C.

doi:10.1016/j.apm.2004.09.016

Cited by 31 publications

(12 citation statements)

References 6 publications

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“…Figure 9 & 10, illustrates the frequency and impulse response of the abated 2 nd order system and the original higher 4 th order system along with other methods found in the literature [31,32,33,34]. It is evident that the abated systems' response nearly matches the response of the original system.…”

Section: Illustrative Examplesmentioning

confidence: 80%

GA based Order Abatement Technique for Linear Dynamic Systems for Continues Time System and Discrete Time System

SINGH,

SINGH

2024

Preprint

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In this paper a hybrid technique of order abatement is introduced for Higher Order Linear Dynamic Systems (HOLDSs) for continuous and discrete time system. The denominator dynamics of the original HOLDSs is abated with continued fraction method, yet the abated numerator is extracted using the Genetic Algorithm. The abated system is attained by combining the benefits of the above two methods. The motive of the suggested technique is to conserve the characteristics of the HOLDSs system in abated system by minimizing the Integral Square Error(ISE). The proposed technique assures the conservation of steady-state stability along with the transient stability of the original HOLDS. A comprehensive comparison study is conducted using two HOLDS cases of continuous time system and two cases of discrete time system from the literature. The ISEs, Time-response and Frequency- response are calculated and plotted with the help of Simulink/MATLAB and compared with the other reduction techniques from the literature. The results demonstrate that the suggested technique provides less ISE than alternative approaches and the time and frequency responses closely resemble the response of the original system.

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Section: Illustrative Examplesmentioning

confidence: 80%

GA based Order Abatement Technique for Linear Dynamic Systems for Continues Time System and Discrete Time System

SINGH,

SINGH

2024

Preprint

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“…In this section, we present two numerical examples to illustrate the aforementioned results. Example Given a stable discrete linear system

(\overset{normalΣ}{true})

used in with the parameters as follows:

Ā = [\begin{matrix} 0.0701 & 0.093 & - 0.0174 & 0.0126 & - 0.043 & - 0.0436 & 0.0288 & - 0.0384 \\ 0.5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0.5 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0.25 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0.125 & 0 \end{matrix}], \bar{B} = [\begin{matrix} 0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{matrix}],

\bar{C} = [\begin{matrix} 0.1402 & 0.1860 & - 0.0348 & 0.0252 & - 0.0860 & - 0.0872 & 0.0576 & - 0.0768 \end{matrix}] .

…”

Section: Numerical Examplesmentioning

confidence: 99%

Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance

Sun

Lam²

2015

Intl J Robust & Nonlinear

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This paper is concerned with the optimal time-weighted H 2 model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to find a mean square stable MJLS of lower order such that the time-weighted H 2 norm of the corresponding error system is minimized for a given mean square stable discrete MJLSs. The notation of time-weighted H 2 norm of discrete MJLS is defined for the first time, and then a computational formula of this norm is given, which requires the solution of two sets of recursive discrete Markovian jump Lyapunov-type linear matrix equations. Based on the time-weighted H 2 norm formula, we propose a gradient flow method to solve the optimal time-weighted H 2 model reduction problem. A necessary condition for minimality is derived, which generalizes the standard result for systems when Markov jumps and the time-weighting term do not appear. Finally, numerical examples are used to illustrate the effectiveness of the proposed approach.M. SUN AND J. LAM where x.k/ 2 R n represents the state variable of the system, u.k/ 2 R p is the control input vector, and´.k/ 2 R m is the output. The parameter Â.k/ stands for the state of a Markov

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“…Due to their extensive competencies in maintaining systems' stability ensuing transition between high-order and reduced-order systems, employment of modernized meta-heuristics approaches towards settling encountered challenges across MOR structures has indeed received vast attention among scholastic communities in recent years. This is primarily exemplified by Mukherjee et al [6] regarding the implementation of a Genetic Algorithm (GA) for systematic model order reduction. The Big Bang Big Crunch (BBBC) method was then recommended by [7] for a similar purpose without foregoing the existing stability of the initial system.…”

Section: Introductionmentioning

confidence: 99%

A novel hybrid of Nonlinear Sine Cosine Algorithm and Safe Experimentation Dynamics for model order reduction

Suid

Ahmad

2022

Automatika

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The current study introduces the hybridization of the Nonlinear Sine Cosine Algorithm (NSCA) and Safe Experimentation Dynamics (SED) as a novel optimization method for model order reduction of high-order single-input single-output (SISO) systems. Reciprocated synergism between both meta-heuristic algorithms is achieved by appropriating the nonlinear positionupdated mechanism of NSCA for enhanced exploration/exploitation competencies and proficiency of SED in maximizing stagnation avoidance within the local optima. Named the NSCA-SED algorithm, the applicability of the proposed method is assessed by scholastic adoption of a sixth-order numerical transfer function towards two independent high-order systems enclosing Double-Pendulum Overhead Crane and Flexible Manipulator. Experimentation results further suggested NSCA-SED as the superior alternative in terms of execution robustness and consistency excellence against other available optimization-based methods for tackling model order reduction. Exemplified simulations sequentially demonstrated considerable improvements by the employment of NSCA-SED over conventional SCA following respective enhanced proportions of 97.17%, 13.17% and 29.03% for Example 1, Example 2 and Example 3.

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Order reduction of linear discrete systems using a genetic algorithm

Cited by 31 publications

References 6 publications

GA based Order Abatement Technique for Linear Dynamic Systems for Continues Time System and Discrete Time System

GA based Order Abatement Technique for Linear Dynamic Systems for Continues Time System and Discrete Time System

Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance

A novel hybrid of Nonlinear Sine Cosine Algorithm and Safe Experimentation Dynamics for model order reduction

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Order reduction of linear discrete systems using a genetic algorithm

Cited by 31 publications

References 6 publications

GA based Order Abatement Technique for Linear Dynamic Systems for Continues Time System and Discrete Time System

GA based Order Abatement Technique for Linear Dynamic Systems for Continues Time System and Discrete Time System

Model reduction of discrete Markovian jump systems with time‐weighted H2 performance

A novel hybrid of Nonlinear Sine Cosine Algorithm and Safe Experimentation Dynamics for model order reduction

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Model reduction of discrete Markovian jump systems with time‐weighted H₂ performance