Data‐driven terminal iterative learning control with high‐order learning law for a class of non‐linear discrete‐time multiple‐input–multiple output systems

Chi, Ronghu; Liu, Yu; Hou, Zhongsheng; Jin, Shangtai

doi:10.1049/iet-cta.2014.0754

Cited by 48 publications

(16 citation statements)

References 33 publications

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“…In this paper, the following assumptions are imposed.Assumption The identical initial condition is assumed, that is, y k (0) = y 0 , ∀ k , and y 0 is a constant vector.Assumption The nonlinear function g N (⋅) is bounded with bounded arguments, and its derivatives with respect to U k are continuous and bounded. Without loss of generality, we assume that

L_{g}^{\min} < (‖‖, g_{N}^{'} (() \cdot)) \leq L_{g}^{\max}

for all time instants and iterations where

g_{N}^{'} (() \cdot) = \frac{∂ g_{N} (() \cdot)}{∂ U_{k}^{T}}

and

L_{g}^{\min}

L_{g}^{\max}

are 2 positive constants.Theorem (Chi et al): If nonlinear system satisfies Assumptions and , then there exists a matrix Ξ k such that system can be transferred to a linear model in the iteration domain without any linearization approximation:

y_{k} ((), N) = y_{k - 1} ((), N) + Ξ_{k} normalΔ U_{k},

and

L_{g}^{\min} \leq (‖‖, {boldΞ}_{k}) \leq L_{g}^{\max}

is bounded for any iteration k ,

Ξ_{k} = [\begin{matrix} center \\ center \frac{∂ g_{1, N}^{*}}{∂ {boldu}_{k}^{T} (0)} & center \frac{∂ g_{1, N}^{*}}{∂ {boldu}_{k}^{T} (1)} & center \dots & center \frac{∂ g_{1, N}^{*}}{∂ {boldu}_{k}^{T} (N - 1)} \end{matrix}]

…”

Section: Problem Formulation and Dynamical Linearizationmentioning

confidence: 99%

“…In addition, the convergence analysis was conducted mainly under a linear system framework. More recently, 2 high‐order data‐driven TILC methods were presented in Chi et al, but only an asymptotic convergence is proved. As it is known, monotonic convergence is a more desirable performance with more practical relevance than the asymptotic one .…”

Section: Introductionmentioning

confidence: 99%

“…To evaluate the performance of high‐order ILC, some works have been done by simulation study to illustrate that the high‐order ILC can achieve a better performance with enhanced robustness than the low‐order one. However, in theory, the question whether the control performance of high‐order ILC is superior or inferior to that of the low‐order ILC is still open.…”

Section: Introductionmentioning

confidence: 99%

“…(1) The proposed data‐driven high‐order optimal terminal iterative learning control (OTILC) uses more terminal error information, rather than control inputs as in Chi et al, of previous iterations to improve the control performance. Virtually, the tracking errors are more efficient in reflecting the influence of the system uncertainties than the control inputs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Data‐driven high‐order terminal iterative learning control with a faster convergence speed

Chi

Huang

Hou³

et al. 2017

Intl J Robust & Nonlinear

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In this paper, a novel high-order optimal terminal iterative learning control (highorder OTILC) is proposed via a data-driven approach for nonlinear discrete-time systems with unknown orders in the input and output. The objective is to track the desired values at the endpoint of the operation cycle. The terminal tracking errors over more than one previous iterations are used to enhance the high-order OTILC's performance with faster convergence. From rigor of the analysis, the monotonic convergence of the terminal tracking error is proved along the iteration direction. More importantly, the condition for a high-order OTILC to outperform the low-order ones is first established by this work. The learning gain is not fixed but iteratively updated by using the input and output (I/O) data, which enhances the flexibility of the proposed controller for modifications and expansions. The proposed method is datadriven in which no explicit models are used except for the input and output data.The applications to a highly nonlinear continuous stirred tank reactor and a highly nonlinear fed-batch fermentater demonstrate the effectiveness of the proposed high-order OTILC design. KEYWORDSdata-driven approach, faster convergent speed, high-order algorithm, monotonic convergence, terminal iterative learning control

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L_{g}^{\min} < (‖‖, g_{N}^{'} (() \cdot)) \leq L_{g}^{\max}

for all time instants and iterations where

g_{N}^{'} (() \cdot) = \frac{∂ g_{N} (() \cdot)}{∂ U_{k}^{T}}

and

L_{g}^{\min}

L_{g}^{\max}

y_{k} ((), N) = y_{k - 1} ((), N) + Ξ_{k} normalΔ U_{k},

and

L_{g}^{\min} \leq (‖‖, {boldΞ}_{k}) \leq L_{g}^{\max}

is bounded for any iteration k ,

Ξ_{k} = [\begin{matrix} center \\ center \frac{∂ g_{1, N}^{*}}{∂ {boldu}_{k}^{T} (0)} & center \frac{∂ g_{1, N}^{*}}{∂ {boldu}_{k}^{T} (1)} & center \dots & center \frac{∂ g_{1, N}^{*}}{∂ {boldu}_{k}^{T} (N - 1)} \end{matrix}]

…”

Section: Problem Formulation and Dynamical Linearizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Data‐driven high‐order terminal iterative learning control with a faster convergence speed

Chi

Huang

Hou³

et al. 2017

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…A high-order learning control law terminal iterative learning control (TILC) is developed to improve control performance. The new developed control law is a data-driven control strategy, where any other model information of the control plant do not need except for the I/O measurements [15]. The model-free sliding mode controllers have been applied to control the azimuth and pitch positions in two single input single output control loops and it has proved its effectiveness over intelligent PI control system [16].…”

Section: Introductionmentioning

confidence: 99%

Improved Load Frequency Control Using a Fast Acting Active Disturbance Rejection Controller

Rahman

Chowdhury

2017

Energies

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System frequency may change from defined values while transmitting power from one area to another in an interconnected power system due to various reasons such as load changes and faults. This frequency change causes a frequency error in the system. However, the system frequency should always be maintained close to the nominal value even in the presence of model uncertainties and physical constraints. This paper proposes an Active Disturbance Rejection Controller (ADRC)-based load frequency control (LFC) of an interconnected power system. The controller incorporates effects of generator inertia and generator electrical proximity to the point of disturbances. The proposed controller reduces the magnitude error of the area control error (ACE) of an interconnected power system compared to the standard controller. The simulation results verify the effectiveness of proposed ADRC in the application of LFC of an interconnected power system.

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Bounded‐input iterative learning control: Robust stabilization via a minimax approach

Driessen

Sadegh

Kwok

2016

Adaptive Control & Signal

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SummaryIn this paper, we consider the design problem of making the convergence of the bounded‐input, multi‐input iterative learning controller presented in our previous work robust to errors in the model‐based value of the input‐output Jacobian matrix via a minimax (min‐max or 'minimize the worst case') approach. We propose to minimize the worst case (largest) value of the infinity‐norm of the matrix whose norm being less then unity implies convergence of the controller. This matrix is the one associated with monotonicity of a sequence of input error norms. The input‐output Jacobian uncertainty is taken to be an additive linear one. Theorem 3.1 and its proof show that the worst‐case infinity‐norm is actually minimized by choosing either the inverse of the centroid of the set of possible input‐output Jacobians or a zero matrix. And an explicit expression is given for both the criteria used to choose between the two matrices and the resulting minimum worst‐case infinity norm. We showed previously that the matrix norm condition associated with monotonicity of a sequence of output‐error norms is not sufficient to assure convergence of the bounded‐input controller. The importance of knowing which norm condition is the relevant one is demonstrated by showing that the set of minimizers of the minimax problem formulated with the wrong norm does not contain in general minimizers of the maximum relevant norm and moreover can lead to a gain matrix that destroys the assured convergence of the bounded‐input controller given in previous work. Copyright © 2016 John Wiley & Sons, Ltd.

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Data‐driven terminal iterative learning control with high‐order learning law for a class of non‐linear discrete‐time multiple‐input–multiple output systems

Cited by 48 publications

References 33 publications

Data‐driven high‐order terminal iterative learning control with a faster convergence speed

Data‐driven high‐order terminal iterative learning control with a faster convergence speed

Improved Load Frequency Control Using a Fast Acting Active Disturbance Rejection Controller

Bounded‐input iterative learning control: Robust stabilization via a minimax approach

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