A Discrete Dynamical System and Its Applications

Carrasco-Gutierrez, Carlos Enrique; Sosa, Wilfredo

doi:10.1590/0101-7438.2019.039.03.0457

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…Important concepts of inverse optimal control are given below [80]- [82]. Consider a nonlinear, discrete and affine system given as [83]- [85]:…”

Section: Inverse Optimal Controlmentioning

confidence: 99%

A Novel Adaptive LSSVR-Based Inverse Optimal Controller With Integrator for Nonlinear Non-Affine Systems

Sanci,

Uçak,

Günel

2023

IEEE Access

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In this study, a novel inverse optimal controller based on NARMA-L2 modelling technique and online least squares support vector regression (LSSVR) method has been proposed for nonlinear nonaffine systems. Firstly, the nonlinear autoregressive with exogenous inputs (NARX) model of the system is obtained using online LSSVR method, then this model is decomposed into NARMA-L2 submodels. Hence, the non-affine system model is converted to a nonlinear affine system model. The obtained NARMA-L2 submodels are used in computing the inverse optimal control law. Furthermore, the parameters of the inverse optimal controller have also been optimized online using the Levenberg-Marquadt algorithm. The performance of the proposed LSSVR based inverse optimal controller using NARMA-L2 model has been evaluated by simulations carried out on two benchmark systems, and the results show that the LSSVR based NARMA-L2 model and inverse optimal controller attain good modelling and control performances.

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“…Important concepts of inverse optimal control are given below [80]- [82]. Consider a nonlinear, discrete and affine system given as [83]- [85]:…”

Section: Inverse Optimal Controlmentioning

confidence: 99%

A Novel Adaptive LSSVR-Based Inverse Optimal Controller With Integrator for Nonlinear Non-Affine Systems

Sanci,

Uçak,

Günel

2023

IEEE Access

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“…In this section three main aspects of the inverse optimal control design will be explored for general nonlinear discrete systems [15,17]. For doing so, let us define the general structure of the system under analysis as follows [18,19].…”

Section: Inverse Optimal Control Designmentioning

confidence: 99%

Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach

2020

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This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential equations that are discretized using the forward difference method. The main advantages of using the discrete-inverse optimal control to regulate state variables in dynamic systems are (i) the control input is an optimal signal as it guarantees the minimum of the Hamiltonian function, (ii) the control signal makes the dynamical system passive, and (iii) the control input ensures asymptotic stability in the sense of Lyapunov. Numerical simulations in the MATLAB environment allow demonstrating the effectiveness and robustness of the studied control design for state variables regulation with a wide gamma of dynamic behaviors as a function of the assigned control gains.

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Neural Network Based Adaptive Inverse Optimal Control for Non-Affine Nonlinear Systems

Sancı,

Öke Günel

2024

Neural Process Lett

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In this paper, a novel methodology is introduced for the inverse optimal control of non-affine, nonlinear and discrete-time systems. Although inverse optimal control of affine systems is studied in detail in technical literature, there is no adequate research about its implementation on non-affine systems. here are two main contributions of this work. Firstly using the input–output data of the system to be controlled its NARMA-L2 model is obtained using a multi-layer feedforward neural network, this step provides a conversion from a non-affine to affine system model. After the affine system model is obtained, the inverse optimal control law is applied. The second contribution of this paper is the computation of the inverse optimal control signal. The selection of the P matrix in the control law is crucial since its value directly affects the control performance. Here a novel method is proposed where an adaptive and optimal P matrix is computed online using a recurrent neural network to minimize a predefined cost function. The performance of the proposed control method is evaluated by simulations performed on benchmark problems. The robustness of the method is also tested by additional simulations where noise and disturbance is imposed on the system. The obtained results justify the applicability of the proposed approach.

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A Discrete Dynamical System and Its Applications

Cited by 3 publications

References 4 publications

A Novel Adaptive LSSVR-Based Inverse Optimal Controller With Integrator for Nonlinear Non-Affine Systems

A Novel Adaptive LSSVR-Based Inverse Optimal Controller With Integrator for Nonlinear Non-Affine Systems

Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach

Neural Network Based Adaptive Inverse Optimal Control for Non-Affine Nonlinear Systems

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