Stability of learning control with disturbances and uncertain initial conditions

Heinzinger, G.; Fenwick, David R.; Paden, B.; Miyazaki, Fumio

doi:10.1109/9.109644

Cited by 256 publications

(118 citation statements)

References 7 publications

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“…Then the following theorem can be obtained which shows that the iterative learning control laws described by (5) and (6) can guarantee the asymptotic convergence of the output error of discrete time-delay system (1).…”

Section: Iterative Learning Controllersmentioning

confidence: 99%

“…Remark 3.2 In this paper, we have employed a class of iterative learning control laws described by (5) and (6), which may regarded as the first-order updating laws. It is not difficult, from the method used in the proof of Theorem 3.1, that the result obtained here is extended to the problem of iterative learning control with high-order updating laws.…”

Section: 9 2006mentioning

confidence: 99%

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Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

Wu¹

2006

IEEJ Trans.EIS

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In a number of practical control problems, there is a class of repetitive dynamical systems, such as robotic control systems, neuromuscular stimulation systems, and so on. For such repetitive dynamical systems, the so-called iterative learning control laws have been introduced. Generally speaking, by employing an iterative learning control algorithm, one can gradually improve or perfect the system performance of a specified task, based on the previous performances of the identical tasks.It is well known that the main advantage of the iterative learning control strategy is to require less a priori knowledge about the system dynamics and less computational effort than many other types of control strategies. Therefore, the problem of iterative learning control for repetitive dynamical systems has received considerable attention, and many results have been obtained. In particular, there are some works in which an iterative learning control scheme has been applied to the analysis and design of continuous dynamical systems with time-delay. On the other hand, the iterative learning control problem of discrete dynamical systems is also considered in the control literature, and some methods are presented to deal with such a class of iterative learning control problems. However, few efforts are made to consider the problem of iterative learning control for discrete dynamical systems with time-delay. It seems that for discrete timedelay dynamical systems, the similar results have not been reported yet in the control literature.In this paper, we consider a discrete-time dynamical system with time-delay, described byn is the current value of the state, u(m) ∈ R m is the control (or input) vector, y(m) ∈ R l is the output vector, A, B, C are constant matrices of appropriate dimensions, and the matrix Eµ, µ = 1, 2, . . . , r, represent the delayed state perturbations. Moreover, the time-varying delay hµ(m) is assumed to be any bounded nonnegative integer function which is not required to be known for the system designer. That is, 0 ≤ hµ(m) ≤hµ, wherehµ is a positive integer.The initial condition for the system with time delays is given by (1) is also assumed to be unknown at each iteration.For discrete time-delay system (1), it is supposed that a desired output trajectory yr(m) ∈ R l is given for a finite time interval m ∈ Γ N 0 := {0, 1, 2, . . . , N}. Then, the error between the desired output and the actual output trajectories of the discrete time-delay system can be represented by e(m) = yr(m) − y(m)· · · · · · · · · · · · · · · · · · · · · · · · · · · (3)where m ∈ Γ Here, we use the superscript k to denote the iteration number of learning processes. Therefore,[k] (m) represent the corresponding vectors at the kth iteration. Now, the main objective of this paper is to find the iterative learning control laws for discrete time-delay system (1) with the unknown initial state such that the output error e(m) between the given desired output yr(m) and the actual output y(m) is identical for all m ∈ Γ N 0 , through the iterativ...

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Section: Iterative Learning Controllersmentioning

confidence: 99%

Section: 9 2006mentioning

confidence: 99%

Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

Wu¹

2006

IEEJ Trans.EIS

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“…Note, however, that the main difficulty with the feasibility of inversion arises during the first part of the trajectory due to unmatched initial conditions 48 . After a certain catch-up time, trajectory following is relatively easy.…”

Section: Ilc With Improved Performancementioning

confidence: 99%

Control and Optimization of Batch Chemical Processes

Bonvin

François

2017

Coulson and Richardson's Chemical Engineering

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A batch process is characterized by the repetition of time-varying operations of finite duration. Due to the repetition, there are two independent "time" variables, namely, the run time during a batch and the batch index. Accordingly, the control and optimization objectives can be defined for a given batch or over several batches. This chapter describes the various control and optimization strategies available for the operation of batch processes. These include online and run-to-run control on the one hand, and repeated numerical optimization and optimizing control on the other. Several case studies are presented to illustrate the various approaches Keywords Batch control, predictive control, iterative learning control, run-to-run control, batch process optimization, dynamic optimization, optimizing control, run-to-run optimization.

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“…We consider a class of multi-input-multi-output nonlinear time-varying systems described by the following state-space equations [16,17]:…”

Section: A Sufficient Condition For Convergence and Robustness Of Ilcmentioning

confidence: 99%

Iterative learning control with sampled-data feedback for robot manipulators

Delchev¹,

Boiadjiev²,

Kawasaki³

et al. 2014

Archives of Control Sciences

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This paper deals with the improvement of the stability of sampled-data (SD) feedback control for nonlinear multiple-input multiple-output time varying systems, such as robotic manipulators, by incorporating an off-line model based nonlinear iterative learning controller. The proposed scheme of nonlinear iterative learning control (NILC) with SD feedback is applicable to a large class of robots because the sampled-data feedback is required for model based feedback controllers, especially for robotic manipulators with complicated dynamics (6 or 7 DOF, or more), while the feedforward control from the off-line iterative learning controller should be assumed as a continuous one. The robustness and convergence of the proposed NILC law with SD feedback is proven, and the derived sufficient condition for convergence is the same as the condition for a NILC with a continuous feedback control input. With respect to the presented NILC algorithm applied to a virtual PUMA 560 robot, simulation results are presented in order to verify convergence and applicability of the proposed learning controller with SD feedback controller attached.

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Stability of learning control with disturbances and uncertain initial conditions

Cited by 256 publications

References 7 publications

Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

Control and Optimization of Batch Chemical Processes

Iterative learning control with sampled-data feedback for robot manipulators

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