Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

Radhoush, Saeed; Samavat, M.; Vali, Mohammad Ali

doi:10.1080/21642583.2014.919887

Cited by 7 publications

(8 citation statements)

References 20 publications

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“…The transient responses of u ( t ) and x ( t ) obtained are compared with their corresponding values from other optimal control approaches, as demonstrated in Figure 14. As it can be observed, the analytical solution obtained from the parallel AGP algorithm with the configuration of u ( x ( t ) , t ) has successfully converged to the exact numerical solution of the Riccati equation, whilst the convergence of both wavelet combination approach (Radhoush et al, 2014) and the configuration of u ( x ( t ) ) to the exact numerical solution are not satisfactory.…”

Section: Typical Case Studies Of Optimization Using the Agp Algorithmmentioning

confidence: 97%

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The archived-based genetic programming for optimal design of linear/non-linear controllers

Mohammadi

Nariman-Zadeh

Jamali

2020

Transactions of the Institute of Measurement and Control

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Evaluation of control signal function is one of the critical subjects in the optimal control problems. The optimal control is usually obtained by optimizing a performance index that is a weighted combination of control effort and state trajectories in the quadratic form, typically known as quadratic performance index (QPI). For the simple case of linear time-invariant (LTI) systems, problems are commonly solved using the well-established governing Riccati equation; however, obtaining the analytical solutions for linear time-variant (LTV) and nonlinear systems has always been highly debated in the optimal control problems. In this study, a newly developed type of Genetic Programming called the archived-based genetic programming (AGP) is presented. Using this algorithm, the analytical solutions for any type of optimal control problems can be obtained faster and more efficiently than the ordinary GPs. Subsequently, due to the inefficiency of QPI in capturing the general behavior of signals, a new performance index named the absolute performance index (API) is proposed in this study. Since the developed AGP algorithm could find the analytical solutions irrespective of the conventional mathematical calculations, it can be effectively implemented to solve the introduced API measures. According to the analytical results, it is observed that in a given problem, the solutions of API are more compatible with the design goals compared with QPI. Furthermore, it is shown that some new forms of the control signals such as impulse solutions, which may not be obtained using QPI, can only be estimated using API in defining the optimal control problems.

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Section: Typical Case Studies Of Optimization Using the Agp Algorithmmentioning

confidence: 97%

“…In order to assess the AGP efficacy to obtain the analytical solutions of the LTV problems, an LTV system, studied by Radhoush et al (2014), has been selected here. The main aim in this problem is minimizing a QPI that prompts the state to converge towards zero in one second.…”

Section: Typical Case Studies Of Optimization Using the Agp Algorithmmentioning

confidence: 99%

The archived-based genetic programming for optimal design of linear/non-linear controllers

Mohammadi

Nariman-Zadeh

Jamali

2020

Transactions of the Institute of Measurement and Control

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“…It normally causes a control signal represented as an optimal control only for its better transient responses in higher norm. Since the optimal solution of time-varying systems is not as easy as those of time-invariant systems, much effort has been devoted to the optimal solutions of these systems (Radhoush et al (2014)). The control law for such problems would be obtained as followswhere the functions R and B are defined in equations (62) and (63), and K(t) is given in Radhoush et al (2014).…”

Section: Utilization Of the Presented Approachmentioning

confidence: 99%

“…Since the optimal solution of time-varying systems is not as easy as those of time-invariant systems, much effort has been devoted to the optimal solutions of these systems (Radhoush et al (2014)). The control law for such problems would be obtained as followswhere the functions R and B are defined in equations (62) and (63), and K(t) is given in Radhoush et al (2014). The time-varying feature of the control law results in the solution of the Riccati equation for linear time-varying problems where the gain matrix could be function of time.…”

Section: Utilization Of the Presented Approachmentioning

confidence: 99%

Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

Ebrahimzadeh

Khanduzi

Beik³

et al. 2021

Journal of Vibration and Control

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Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.

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“…The topic of time variation in the context of optimal control has been widely addressed [1][2][3][4][5]. Here the focus is instead on handling variation of several weights in a cost function that combines multiple performance goals.…”

Section: -mentioning

confidence: 99%

Time-Varying Weights in Multi-Objective Optimal Control for Flexible Wing Aircraft

Hashemi

Nguyen

Drew

2019

AIAA Scitech 2019 Forum

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A multi-objective optimal control technique is modified to accommodate changing cost function weights and is used to control a flexible wing aircraft model. Variation of the weights is used to adjust the relative importance of each objective according to either a prescribed function of time or of the state. Several techniques for obtaining a practical approximation to the optimal control solution are presented, and stability of a specific weight structure with the optimal controller is demonstrated. Functionality of the multi-objective control design with weight variation is demonstrated in simulation of a flexible wing transport aircraft and is shown to improve performance over the fixed weight version both at a constant flight condition and across changing flight conditions.

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Optimal control of linear time-varying systems using the Chebyshev wavelets (a comparative approach)

Cited by 7 publications

References 20 publications

The archived-based genetic programming for optimal design of linear/non-linear controllers

The archived-based genetic programming for optimal design of linear/non-linear controllers

Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

Time-Varying Weights in Multi-Objective Optimal Control for Flexible Wing Aircraft

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