Finite-time composite control for a class of singularly perturbed nonlinear systems via successive Galerkin approximation

Kim, Y.-J.; Kim, B.-S.; Lim, Myo Taeg

doi:10.1049/ip-cta:20045146

Cited by 9 publications

(18 citation statements)

References 11 publications

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“…The transfer functions for slow and fast subsystem are denoted by (30) and (31), respectively. The composite model is signified as a sum of slow and fast subsystem and a very little item ( ) [37] composite ( ) = slow ( )…”

Section: Jian Niu Methodmentioning

confidence: 99%

“…It was tested to a DC motor driven inverted pendulum system and it provides realistic and satisfactory simulation results. Multivariable control by Kim et al [30] used successive Galerkin approximation (SGA) method. This method causes the complexity in computations to increase with respect to the order of the system.…”

Section: Introductionmentioning

confidence: 99%

“…To the best of author knowledge, there are two methods to obtain the singularly perturbation system, which are by analytical [21,[29][30][31] and linear analysis [32][33][34][35]. Singularly perturbation system obtained based on linear analysis is discussed and has been applied in this research.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Singularly Perturbation Method Applied To Multivariable PID Controller Design

Razali

Wahab

Balaguer

et al. 2015

Mathematical Problems in Engineering

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Proportional integral derivative (PID) controllers are commonly used in process industries due to their simple structure and high reliability. Efficient tuning is one of the relevant issues of PID controller type. The tuning process always becomes a challenging matter especially for multivariable system and to obtain the best control tuning for different time scales system. This motivates the use of singularly perturbation method into the multivariable PID (MPID) controller designs. In this work, wastewater treatment plant and Newell and Lee evaporator were considered as system case studies. Four MPID control strategies, Davison, Penttinen-Koivo, Maciejowski, and Combined methods, were applied into the systems. The singularly perturbation method based on Naidu and Jian Niu algorithms was applied into MPID control design. It was found that the singularly perturbed system obtained by Naidu method was able to maintain the system characteristic and hence was applied into the design of MPID controllers. The closed loop performance and process interactions were analyzed. It is observed that less computation time is required for singularly perturbed MPID controller compared to the conventional MPID controller. The closed loop performance shows good transient responses, low steady state error, and less process interaction when using singularly perturbed MPID controller.

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Section: Jian Niu Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Singularly Perturbation Method Applied To Multivariable PID Controller Design

Razali

Wahab

Balaguer

et al. 2015

Mathematical Problems in Engineering

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“…A first attempt for the optimization of coupled nonlinear systems was reported in , where the authors proposed a coupling perturbation method for near‐optimum design. Approximate solutions of independent reduced‐order HJB equations using successive Galerkin approximation (SGA) have been proposed as alternative methods for solving the weakly coupled nonlinear optimal control problem. Unfortunately, the SGA method suffers from a computational complexity that increases with the dimension of the system under consideration.…”

Section: Introductionmentioning

confidence: 99%

“…These results were based on a recursive reduced‐order scheme in order to solve the algebraic Riccati equation. Following this reduced‐order scheme for solving the algebraic Riccati equation, the authors in proposed a nonlinear optimal control for a weakly coupled nonlinear system based on the solution of two independent reduced‐order HJB equations using SGA . The main drawback of this method is the off‐line design and that the computational complexity increases with the dimension of the system.…”

Section: Introductionmentioning

confidence: 99%

Approximate optimal adaptive control for weakly coupled nonlinear systems: A neuro‐inspired approach

GarcíaźCarrillo

Vamvoudakis

Hespanha

2015

Adaptive Control & Signal

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Summary This paper proposes a new approximate dynamic programming algorithm to solve the infinite‐horizon optimal control problem for weakly coupled nonlinear systems. The algorithm is implemented as a three‐critic/four‐actor approximators structure, where the critic approximators are used to learn the optimal costs, while the actor approximators are used to learn the optimal control policies. Simultaneous continuous‐time adaptation of both critic and actor approximators is implemented, a method commonly known as synchronous policy iteration. The adaptive control nature of the algorithm requires a persistence of excitation condition to be a priori guaranteed, but this can be relaxed by using previously stored data concurrently with current data in the update of the critic approximators. Appropriate robustifying terms are added to the controllers to eliminate the effects of the residual errors, leading to asymptotic stability of the equilibrium point of the closed‐loop system. Simulation results show the effectiveness of the proposed approach for a sixth‐order dynamical example. Copyright © 2015 John Wiley & Sons, Ltd.

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Suboptimal control for nonlinear slow‐fast coupled systems using reinforcement learning and Takagi–Sugeno fuzzy methods

Liu

Yang

Luo

et al. 2021

Adaptive Control & Signal

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Summary In this article, by using singular perturbation theory, reinforcement learning (RL), and Takagi–Sugeno (T‐S) fuzzy methods, a RL‐fuzzy‐based composite suboptimal control method is proposed for nonlinear slow‐fast coupled systems (SFCSs) with unknown slow dynamics. First, the SFCSs is decomposed into slow and fast subsystems and the original optimal control problem is reduced to two subproblems. Then, for the slow subsystem, a nonlinear coordinate transformation is introduced to transform the nonquadratic slow utility function into the quadratic form. Unmeasurable virtual slow subsystem state is reconstructed by the state measurements of original system and slow controller design algorithm is proposed in the framework of RL by utilizing the actor‐critic neural networks to approximate the controller and cost function. For the fast subsystem, T‐S fuzzy model is established and state measurements of the original system are exploited to reconstruct the unmeasurable fast subsystem state. Fast controller is designed with the approach of parallel distributed compensation. The obtained slow and fast controllers form the composite suboptimal controller for the original SFCSs. Considering the state reconstruction error, convergence of the slow controller design algorithm, suboptimality of the composite controller, and stability of the closed‐loop SFCSs are analyzed. Finally, the effectiveness of our proposed method is illustrated by examples.

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Finite-time composite control for a class of singularly perturbed nonlinear systems via successive Galerkin approximation

Cited by 9 publications

References 11 publications

Singularly Perturbation Method Applied To Multivariable PID Controller Design

Singularly Perturbation Method Applied To Multivariable PID Controller Design

Approximate optimal adaptive control for weakly coupled nonlinear systems: A neuro‐inspired approach

Suboptimal control for nonlinear slow‐fast coupled systems using reinforcement learning and Takagi–Sugeno fuzzy methods

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