Optimal tracking of time-varying systems with the overdetermined recursive instrumental variable algorithm

Alameda-Hernández, E.; Blanco, D.; Ruíz, Diego P.; Carrión, M.C.

doi:10.1049/iet-cta:20060260

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…Therefore, the recursive form of the IV method is more preferable. Many RIV methods have been studied for the linear system identification problems [22][23][24], in which the IV matrix at time index k + 1 has the block form as…”

Section: Forgetting Factor Based Rivmentioning

confidence: 99%

“…T is given in (24). However, the penultimate term in the IV matrix G k + 1 is not the same as g k T .…”

Section: Taylor Serial Expansion Based Rivmentioning

confidence: 99%

“…Therefore, the recursive form of the IV method is more preferable. Many RIV methods have been studied for the linear system identification problems [22–24], in which the IV matrix at time index

k + 1

has the block form as

G_{k + 1} = (][, \begin{matrix} 1em4pt \\ ℓ G_{k} \\ g_{k + 1}^{T} \end{matrix}),

where

0 \leq ℓ \leq 1

is the forgetting factor and

g_{k + 1}^{T}

is the last row of

G_{k + 1}

. For the pseudo‐linear form given in (10), the same idea can be used by choosing

ℓ = 1

and assuming that the block form of

G_{k + 1}

is available [27, 30].…”

Section: Localisation Algorithmsmentioning

confidence: 99%

“…To reduce the bias, it is directly perceived through the common sense to introduce the bias reduction technique such as the IV method into the recursive solution similar to that in the batched methods. Although there exists kinds of recursive IV (RIV) methods in the linear system identification problems, which obtains the RIV matrix approximately applying a forgetting factor to the current measurement [20][21][22][23][24][25][26]. However, due to the non-linearity between the position and measurements, it is difficult to obtain the IV matrix recursively as the traditional RIV estimator does [26,27].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Recursive instrumental variable method for locating a scanning emitter by a single observer using time of interception

Zhang

Guo

2017

IET Radar Sonar & Navi

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The recursive solution to passive localisation of a scanning emitter using time of interception (TOI) by a single moving observer is investigated in this study. First, the correlated measurement noise in the traditional pseudo-linear model for the scanning emitter localisation is decoupled by introducing the first noise corrupted direction of arrival as a nuisance parameter. A recursive pseudo-linear least square (RPLS) estimator is then developed by transforming the TOI of the scanning emitter into the direction difference of arrival model. However, there is bias in this method due to the correlation between the measurement matrix and the noise. To reduce the bias, the instrumental variable (IV) method is used, and two recursive IV (RIV) estimators, forgetting factor based RIV (F2RIV) and Taylor series expansion based RIV (TSRIV), are proposed. It approximates the IV matrix recursively using the Taylor series expansion in the TSRIV estimator. Simulations show that the TSRIV estimator alleviates the bias compared with the RPLS estimator dramatically and can reach the Cramer-Rao lower bound at moderate measurement noise levels. Moreover, it is more stable and has shorter convergence time than the F2RIV estimator.

show abstract

Section: Forgetting Factor Based Rivmentioning

confidence: 99%

“…T is given in (24). However, the penultimate term in the IV matrix G k + 1 is not the same as g k T .…”

Section: Taylor Serial Expansion Based Rivmentioning

confidence: 99%

k + 1

has the block form as

G_{k + 1} = (][, \begin{matrix} 1em4pt \\ ℓ G_{k} \\ g_{k + 1}^{T} \end{matrix}),

where

0 \leq ℓ \leq 1

is the forgetting factor and

g_{k + 1}^{T}

is the last row of

G_{k + 1}

. For the pseudo‐linear form given in (10), the same idea can be used by choosing

ℓ = 1

and assuming that the block form of

G_{k + 1}

is available [27, 30].…”

Section: Localisation Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Recursive instrumental variable method for locating a scanning emitter by a single observer using time of interception

Zhang

Guo

2017

IET Radar Sonar & Navi

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show abstract

“…The prime objective of regulation problems [5–11] is to find a control policy that brings the desired states to origin in finite amount of time while minimising a cost function. On the other hand, optimal tracking control problem (OTCP) [12–15] entails finding control policies that will make the desired states (output of the system) track a time varying reference trajectory. Traditionally, the OTCP requires development of two different controllers: (i) transient controller and (ii) steady‐state control [4, 15].…”

Section: Introductionmentioning

confidence: 99%

H∞ tracking control via variable gain gradient descent‐based integral reinforcement learning for unknown continuous time non‐linear system

Mishra

Ghosh

2020

IET Control Theory & Appl

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Optimal tracking of continuous‐time non‐linear systems has been extensively studied in literature. However, in several applications, absence of knowledge about system dynamics poses a severe challenge in solving the optimal tracking problem. This has found growing attention among researchers recently, and integral reinforcement learning based method augmented with actor neural network (NN) have been deployed to this end. However, very few studies have been directed to model‐free H∞ optimal tracking control that helps in attenuating the effect of disturbances on the system performance without any prior knowledge about system dynamics. To this end, a recursive least square‐based parameter update was recently proposed. However, gradient descent‐based parameter update scheme is more sensitive to real‐time variation in plant dynamics. Experience replay (ER) technique has been shown to improve the convergence of NN weights by utilising past observations iteratively. Motivated by these, this study presents a novel parameter update law based on variable gain gradient descent and ER technique for tuning the weights of critic, actor and disturbance NNs. The presented update law leads to improved model‐free tracking performance under L2‐bounded disturbance. Simulation results are presented to validate the presented update law.

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Higher-order statistics for power systems: Effects of the sampling frequency on ergodicity

Alameda-Hernández

Montoya

Mercado-Vargas

et al. 2016

Applied Mathematical Modelling

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Optimal tracking of time-varying systems with the overdetermined recursive instrumental variable algorithm

Cited by 5 publications

References 16 publications

Recursive instrumental variable method for locating a scanning emitter by a single observer using time of interception

Recursive instrumental variable method for locating a scanning emitter by a single observer using time of interception

H∞ tracking control via variable gain gradient descent‐based integral reinforcement learning for unknown continuous time non‐linear system

Higher-order statistics for power systems: Effects of the sampling frequency on ergodicity

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