Adaptive output regulation of a class of discrete-time nonlinear systems based on output feedback and NN feedforward control

Mizumoto, Ikuro; Tanaka, Naoki; Tokimatsu, Toru

doi:10.1109/cdc.2010.5717981

Cited by 13 publications

(8 citation statements)

References 17 publications

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“…For this ASPR augmented system, an output feedback‐based adaptive control system combined with a Radial Basis Function (RBF) adaptive neural network (NN) feedforward input is designed as follows :

\begin{matrix} true \\ right \begin{matrix} u (k) & = & u_{e} (k) + v (k), u_{e} (k) = - K (k) {\overset{e}{true}}_{a} (k) \\ v (k) & = & \hat{W} {(k)}^{T} S (ω (k)) \\ K (k) & = & {\overset{σ}{true}}_{1} K (k - 1) + {\overset{σ}{true}}_{1} γ {\overset{e}{true}}_{a} (k) {\overset{e}{true}}_{a} (k) - P_{K} (k) \\ {\bar{σ}}_{1} & = & 0true \frac{1}{1 + σ_{1}}, σ_{1} > 0 \\ \hat{W} (k) & = & {\overset{σ}{true}}_{2} \hat{W} (k - 1) - {\overset{σ}{true}}_{2} Γ S (ω (k)) {\overset{e}{true}}_{a} (k) \\ {\bar{σ}}_{2} & = & 0true \frac{1}{1 + σ_{2}}, σ_{2} > 0 \end{matrix} \end{matrix}

where

\hat{W} = [{\overset{w}{true}}_{1}, ..., {\overset{w}{true}}_{l}]

…”

Section: Adaptive Control System Designmentioning

confidence: 99%

“…It should be noted that the error

{\bar{e}}_{a}

given in cannot be directly available because of causality problems. However, taking an equivalent transformation of , the augmented error signal

{\bar{e}}_{a}

can be obtained by

\begin{matrix} true \\ right {\bar{e}}_{a} (k) & = & left \frac{{\hat{e}}_{a} (k) - {\bar{σ}}_{1} d_{f} K (k - 1) {\hat{e}}_{a} (k)}{1 + {\bar{σ}}_{1} d_{f} γ {\hat{e}}_{a}^{2} (k)} \end{matrix}

using the available signals so that the control input can be implemented directly without causality problems .…”

Section: Adaptive Control System Designmentioning

confidence: 99%

“…For the adaptive control system shown above, the following theorem holds : Theorem Suppose that the reference signal

y_{r} (k),

which the output

y (k)

is required to track, is generated by the following exosystem:

\begin{matrix} true \\ right ω (k + 1) & = & left A_{r} ω (k) \\ right y_{r} (k) & = & left c_{r}^{T} ω (k) \end{matrix}

where

bold-italicω (k) \in R^{q}

is a state vector of the exosystem with

bold-italicω (0) = bold-italic bold0

and

y_{r} (0) = 0

. Now, there exist an ideal state

x^{*} (k)

and an ideal input

v^{*} (k)

which attain perfect tracking such that

\begin{matrix} true \\ right {bold-italicx}^{*} (k + 1) & = & left bold-italicA {bold-italicx}^{*} (k) + bold-italicb v^{*} (k) \\ right y (k) & = & left {bold-italicc}^{T} {bold-italicx}^{*} (k) \equiv y_{r} (k) \end{matrix}

and they are given by functions of

bold-italicω (k)

such as

x^{*} (k) = bold-italicπ

…”

Section: Adaptive Control System Designmentioning

confidence: 99%

“…For this ASPR augmented system, an output feedback-based adaptive control system combined with a Radial Basis Function (RBF) adaptive neural network (NN) feedforward input is designed as follows [11]:…”

Section: Adaptive Control System Designmentioning

confidence: 99%

See 3 more Smart Citations

PFC Design via FRIT Approach for Adaptive Output Feedback Control of Discrete‐Time Systems

Mizumoto

Takagi

Fukui

et al. 2014

Electrical Engineering Japan

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SUMMARY This paper deals with a design problem of an adaptive output feedback control for discrete‐time systems with a parallel feedforward compensator (PFC), which is designed for making the augmented controlled system “Almost Strictly Positive Real” (ASPR). A PFC design scheme by a fictitious reference iterative tuning (FRIT) approach with only using an input/output experimental data set will be proposed for discrete‐time systems in order to design an adaptive output feedback control system. Furthermore, the effectiveness of the proposed PFC design method will be confirmed through numerical simulations by designing an adaptive control system with adaptive NN (neural network) for an uncertain discrete‐time system. © 2014 Wiley Periodicals, Inc. Electr Eng Jpn, 187(1): 24–32, 2014; Published online in Wiley Online Library (http://wileyonlinelibrary.com). DOI 10.1002/eej.22456

show abstract

\begin{matrix} true \\ right \begin{matrix} u (k) & = & u_{e} (k) + v (k), u_{e} (k) = - K (k) {\overset{e}{true}}_{a} (k) \\ v (k) & = & \hat{W} {(k)}^{T} S (ω (k)) \\ K (k) & = & {\overset{σ}{true}}_{1} K (k - 1) + {\overset{σ}{true}}_{1} γ {\overset{e}{true}}_{a} (k) {\overset{e}{true}}_{a} (k) - P_{K} (k) \\ {\bar{σ}}_{1} & = & 0true \frac{1}{1 + σ_{1}}, σ_{1} > 0 \\ \hat{W} (k) & = & {\overset{σ}{true}}_{2} \hat{W} (k - 1) - {\overset{σ}{true}}_{2} Γ S (ω (k)) {\overset{e}{true}}_{a} (k) \\ {\bar{σ}}_{2} & = & 0true \frac{1}{1 + σ_{2}}, σ_{2} > 0 \end{matrix} \end{matrix}

where

\hat{W} = [{\overset{w}{true}}_{1}, ..., {\overset{w}{true}}_{l}]

…”

Section: Adaptive Control System Designmentioning

confidence: 99%

“…It should be noted that the error

{\bar{e}}_{a}

given in cannot be directly available because of causality problems. However, taking an equivalent transformation of , the augmented error signal

{\bar{e}}_{a}

can be obtained by

\begin{matrix} true \\ right {\bar{e}}_{a} (k) & = & left \frac{{\hat{e}}_{a} (k) - {\bar{σ}}_{1} d_{f} K (k - 1) {\hat{e}}_{a} (k)}{1 + {\bar{σ}}_{1} d_{f} γ {\hat{e}}_{a}^{2} (k)} \end{matrix}

using the available signals so that the control input can be implemented directly without causality problems .…”

Section: Adaptive Control System Designmentioning

confidence: 99%

“…For the adaptive control system shown above, the following theorem holds : Theorem Suppose that the reference signal

y_{r} (k),

which the output

y (k)

is required to track, is generated by the following exosystem:

\begin{matrix} true \\ right ω (k + 1) & = & left A_{r} ω (k) \\ right y_{r} (k) & = & left c_{r}^{T} ω (k) \end{matrix}

where

bold-italicω (k) \in R^{q}

is a state vector of the exosystem with

bold-italicω (0) = bold-italic bold0

and

y_{r} (0) = 0

. Now, there exist an ideal state

x^{*} (k)

and an ideal input

v^{*} (k)

which attain perfect tracking such that

\begin{matrix} true \\ right {bold-italicx}^{*} (k + 1) & = & left bold-italicA {bold-italicx}^{*} (k) + bold-italicb v^{*} (k) \\ right y (k) & = & left {bold-italicc}^{T} {bold-italicx}^{*} (k) \equiv y_{r} (k) \end{matrix}

and they are given by functions of

bold-italicω (k)

such as

x^{*} (k) = bold-italicπ

…”

Section: Adaptive Control System Designmentioning

confidence: 99%

Section: Adaptive Control System Designmentioning

confidence: 99%

See 2 more Smart Citations

PFC Design via FRIT Approach for Adaptive Output Feedback Control of Discrete‐Time Systems

Mizumoto

Takagi

Fukui

et al. 2014

Electrical Engineering Japan

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, in such cases, it has been indicated that affects from the introduced PFC result in degradation of the control performance in the output tracking control because the adaptive controller is designed for the augmented system with the PFC. As a counter measure to this problem, a method introducing a feedforward signal generated by an adaptive RBF NN (radial basis function neural networks) has been proposed for output feedback systems [16]. We will consider to expand this method to adaptive PID control.…”

Section: Introductionmentioning

confidence: 99%

Output tracking control of discrete-time nonlinear systems by adaptive PID based on output feedback passivity

Mizumoto

Takagi

2014

Proceeding of the 11th World Congress on Intelligent Control and Automation

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In this paper, we propose a design scheme of an adaptive PID tracking control system for discrete-time nonlinear SISO systems. The proposed method utilizes the OFSP properties of the controlled system, so that the stability of the resulting adaptive control system can be guaranteed with certainty. A robust adaptive PID design scheme for the OFSP augmented system with a parallel feedforward compensator without causality problems was developed by introducing an adaptive NN feedforward control signal. * ( + 1) = ( * ( )) + * ( )and they are given by functions of ( ) such as * ( ) = ( ( )) and * ( ) = ( ( )).Assumption 2: ( ( )) and ℎ( ( )) are globally Lipschitz.

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ASPR based Output Feedback Control with an Adaptive Predictive Feedfoward Input for MIMO Systems

Mizumoto

Fujii

2017

IFAC-PapersOnLine

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Adaptive output regulation of a class of discrete-time nonlinear systems based on output feedback and NN feedforward control

Cited by 13 publications

References 17 publications

PFC Design via FRIT Approach for Adaptive Output Feedback Control of Discrete‐Time Systems

PFC Design via FRIT Approach for Adaptive Output Feedback Control of Discrete‐Time Systems

Output tracking control of discrete-time nonlinear systems by adaptive PID based on output feedback passivity

ASPR based Output Feedback Control with an Adaptive Predictive Feedfoward Input for MIMO Systems

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