Optimal Feedback Control for Linear Systems with Input Delays Revisited

Zhou, Yusheng; Wang, Zaihua

doi:10.1007/s10957-014-0532-8

Cited by 11 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Compared to feedback controllers (i.e., PD and proportional-integral-derivative), which are not optimal in the presence of delays, optimal controllers can model the control of human standing ( Kiemel et al, 2002 ; Kuo, 1995 ; Kuo, 2005 ; van der Kooij et al, 1999 ; van der Kooij et al, 2001 ) and theoretically stabilize human standing with large (>500 ms) delays ( Kuo, 1995 ). This ability, however, rapidly declines with increasing center of mass accelerations ( Kuo, 1995 ), including those driven by external disturbances ( Zhou and Wang, 2014 ). Although feedback and optimal controllers assume that the nervous system linearly and continuously modulates the balancing torques to stand ( Fitzpatrick et al, 1996 ; Masani et al, 2006 ; van der Kooij and de Vlugt, 2007 ; Vette et al, 2007 ), intermittent corrective balance actions ( Asai et al, 2009 ; Bottaro et al, 2005 ; Gawthrop et al, 2011 ; Loram et al, 2011 ; Loram et al, 2005 ) may represent a solution when time delays rule out continuous control ( Gawthrop and Wang, 2006 ; Arsan et al, 1999 ).…”

Section: Discussionmentioning

confidence: 99%

Learning to stand with unexpected sensorimotor delays

Rasman

Forbes

Peters

et al. 2021

eLife

View full text Add to dashboard Cite

Human standing balance relies on self-motion estimates that are used by the nervous system to detect unexpected movements and enable corrective responses and adaptations in control. These estimates must accommodate for inherent delays in sensory and motor pathways. Here, we used a robotic system to simulate human standing in the anteroposterior direction about the ankles and impose sensorimotor delays into the control of balance. Imposed delays destabilized standing, but through training, participants adapted and re-learned to balance with the delays. Before training, imposed delays attenuated vestibular contributions to balance and triggered perceptions of unexpected standing motion, suggesting increased uncertainty in the internal self-motion estimates. After training, vestibular contributions partially returned to baseline levels and larger delays were needed to evoke perceptions of unexpected standing motion. Through learning, the nervous system accommodates balance sensorimotor delays by causally linking whole-body sensory feedback (initially interpreted as imposed motion) to self-generated balance motor commands.

show abstract

Section: Discussionmentioning

confidence: 99%

Learning to stand with unexpected sensorimotor delays

Rasman

Forbes

Peters

et al. 2021

eLife

View full text Add to dashboard Cite

show abstract

“…Fractional optimal control of a system having a performance index with delayed terms. Some texts study the optimal control problem consists of a quadratic performance index with delayed terms, for example see [32,43]. Assume that for all types of the given systems, we have…”

Section: 6mentioning

confidence: 99%

Caputo fractional derivative operational matrices of Legendre and Chebyshev wavelets in fractional delay optimal control

Malmir¹

2022

NACO

View full text Add to dashboard Cite

<p style='text-indent:20px;'>Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo derivative operational matrices are used in quadratic optimization of systems having fractional or integer orders differential equations. Using these operational matrices, a new quadratic programming wavelet-based method without doing any integration operation for finding solutions of quadratic optimal control of traditional linear/nonlinear fractional time-delay constrained/unconstrained systems is introduced. General strategies for handling different types of the optimal control problems are proposed.</p>

show abstract

“…In (24), the current control input Δ ( ) uses the future state vector ( + ). It is necessary to predict the future state vector to ensure that the controller is executable.…”

Section: Theorem 1 If (A1) and (A2) Hold Andmentioning

confidence: 99%

“…Substituting (26) into (24), the feedback control law of the augmented error system (11) can be obtained as follows:…”

Section: Theorem 1 If (A1) and (A2) Hold Andmentioning

confidence: 99%

“…The optimal regulation problem was studied for systems with input delay and designed optimal feedback controllers by using the duality principle and the maximum principle [21][22][23]. The design process was simplified by introducing a quadratic performance index with corresponding input delay in [24]. A nested predictor was established to effectively compensate for the time delay for linear systems with both state and input delays [25,26].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Application of Predictor Feedback in Designing a Preview Controller for Discrete-Time Systems with Input Delay

Liao

Deng

2016

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper presents a method for designing a type one servomechanism for a discrete-time linear system with input delay subject to a previewable desired output and a nonmeasurable constant disturbance. The tracking problem of a delay system is transformed into a regulation problem of a delay-free system via constructing an augmented error system and a variable substitution. A controller is obtained with delay compensation and preview compensation based on preview control theory and the predictor method. When the state vector is not directly measurable, a full-dimensional observer is offered. The effectiveness of the design method is demonstrated by numerical simulations.

show abstract

Optimal Feedback Control for Linear Systems with Input Delays Revisited

Cited by 11 publications

References 34 publications

Learning to stand with unexpected sensorimotor delays

Learning to stand with unexpected sensorimotor delays

Caputo fractional derivative operational matrices of Legendre and Chebyshev wavelets in fractional delay optimal control

The Application of Predictor Feedback in Designing a Preview Controller for Discrete-Time Systems with Input Delay

Contact Info

Product

Resources

About