Iterative learning control for a class of uncertain nonlinear systems with current state feedback

Liu, Jian; Zhang, Yamiao; Ruan, Xiaoe

doi:10.1080/00207721.2019.1645235

Cited by 16 publications

(5 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since CB is nonsingular and lim k→∞ x k (s + 1) = x d (s + 1), using (15) and (20) together with the continuity of f Φ (s + 1, x k (s + 1)) with respect to x k (s + 1) gives lim k→∞ ūk (s + 1) = ūd (s + 1).…”

Section: Convergencementioning

confidence: 99%

“…When the system state is measurable, the D/Arimoto-type ILC update laws with current state feedback can not only perfectly solve the overshoot problem but also improve the convergence rate even though there exists the unknown system dynamics information. [18][19][20] Kurek and Zaremba 18 considered the Arimoto-type ILC update law with current state feedback for multi-input-multi-output (MIMO) LTI discrete-time system with the input-output coupling matrix (IOCM) being full-row rank, and utilized the 2-D technique to analyze the convergence of system output sequence. It was shown that there are the state feedback gain matrix and the learning gain matrix such that within one trial the control system can track the desired trajectory.…”

Section: Introductionmentioning

confidence: 99%

“…By backwardly iterating technique, Liu et al 19 revealed the action mechanism between state feedback gain matrix and output error for MIMO LTI discrete-time system with the IOCM being full-row rank, and shown how to leverage the known parts of system dynamics to design the state feedback gain matrix for better tracking performance. Liu et al 20 proposed an Arimoto-type ILC scheme with nonlinear state feedback for a class of SISO discrete-time affine nonlinear systems, and shown how to utilize the available system dynamics to design the state feedback item for better tracking performance. Moreover, it was reported in Reference 20 that the (locally Lipschitz) continuities of nonlinear system function and state feedback with respect to the state is enough to ensure the (exponential) convergence of ILC process.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Equivalence and convergence of two iterative learning control schemes with state feedback

Zhang

Liu

Ruan

2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This article considers the equivalence and convergence of two iterative learning control (ILC) schemes with state feedback for a class of multi-input-multi-output discrete-time nonlinear systems in which each desired trajectory corresponds to a unique desired input or an infinite number of desired inputs. First, we strictly prove that the two ILC schemes are equivalent if they have the identical initial system inputs. Moreover, by the input space transformation method and mathematical induction we establish the necessary and sufficient criterion for the convergence of system output, input and state sequences. It is shown that the (locally Lipschitz) continuity is enough to guarantee the (exponential) convergence. Generally, the learned desired input depends on the values of the initial signals, the learning gain matrix and the state feedback item. By designing them with appropriate structures, the dependence is disappeared. Third, we show how to leverage the available information of system dynamics to design the learning gain matrix and state feedback for better tracking performance. Finally, we provide an example to illustrate the usefulness of our findings, in which we introduce the energy of learnable desired input to evaluate the learning performance.

show abstract

Section: Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equivalence and convergence of two iterative learning control schemes with state feedback

Zhang

Liu

Ruan

2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…The authors of [17] proposed an ILC algorithm using 2D robust control theory and discussed the asymptotic stability of uncertain intermittent systems in both the iterative and time directions. For a time-varying and time delay intermittent process with parameter uncertainty, a feedback ILC algorithm was discussed in [20], and a learning-based identification technique for uncertain parameters in a system was obtained based on 2D system theory.…”

Section: Introductionmentioning

confidence: 99%

Iterative Learning Control for Actuator Fault Uncertain Systems

Wang¹,

Dong

Chen

et al. 2022

Symmetry

View full text Add to dashboard Cite

An iterative learning fault-tolerant control method is designed for an actuator fault intermittent process with simultaneous uncertainties for the system parameters. First, an intermittent fault tolerance controller is designed using 2D system theory, and the iterative learning control (ILC) intermittent process is transformed into a 2D Roesser model. Secondly, sufficient conditions for the controller’s existence are analyzed using the linear matrix inequality (LMI) technique, and the control gain matrices are obtained by convex optimization with LMI constraints. Under these conditions for all additive uncertainties for the system parameters and admissible failures, the controller can ensure closed-loop fault-tolerant performance in both the time and batch directions, and it can also meet the H∞ robust performance level against outside disturbances. Eventually, the algorithm’s computational complexity is analyzed, and the effectiveness of the algorithm is verified by simulation with respect to an injection molding machine model. Compared with traditional ILC laws, which do not consider actuator faults, the proposed algorithm has a better convergence speed and stability when the time-invariant and time-variant actuator faults occur during implementation.

show abstract

“…The core mission of the ILC mechanism is to design an adequate control input law for achieving perfect repetitive tracking throughout the whole operation duration as the iterations increase. The conventional control laws can be based on proportional-type, derivative-type, and/or integral-type tracking errors, which are exploited to supply sufficient conditions for guaranteeing either an asymptotical or a monotonic convergence (e.g., [5][6][7][8][9]). Nevertheless, the conventional control input law is usually embedded with a constant learning gain, with no evaluation of the tracking performance, and its convergence condition is dependent upon the system parameter information.…”

Section: Introductionmentioning

confidence: 99%

The Convergence of Data-Driven Optimal Iterative Learning Control for Linear Multi-Phase Batch Processes

2022

Self Cite

View full text Add to dashboard Cite

For multi-phase batch processes with different dimensions whose dynamics can be described as a linear discrete-time-invariant system in each phase, a data-driven optimal ILC was explored using multi-operation input and output data that subordinate a tracking performance criterion. An iterative learning identification was constructed to estimate the system Markov parameters by minimizing the evaluation criterion that consists of the residual of the real outputs from the predicted outputs and two adjacent identifications. Meanwhile, the estimated Markov parameters matrix was embedded into the learning control process in the form of an interaction. By virtue of inner product theory, the monotonic descent of the estimation error was derived, which does not restrict the weighting factor at all. Furthermore, algebraic derivation demonstrates that the tracking is strictly monotonically convergent if the estimation error falls within an appropriate domain. Numerical simulations were carried out to illustrate the validity and the effectiveness of the proposed method.

show abstract

Iterative learning control for a class of uncertain nonlinear systems with current state feedback

Cited by 16 publications

References 40 publications

Equivalence and convergence of two iterative learning control schemes with state feedback

Equivalence and convergence of two iterative learning control schemes with state feedback

Iterative Learning Control for Actuator Fault Uncertain Systems

The Convergence of Data-Driven Optimal Iterative Learning Control for Linear Multi-Phase Batch Processes

Contact Info

Product

Resources

About