Iterative Dynamic Linearization Research Articles

Multi-lagged-input iterative dynamic linearization based data-driven adaptive iterative learning control

This article presents a multi-lagged-input based data-driven adaptive iterative learning control (M-DDAILC) method for nonlinear multiple-input-multiple-output (MIMO) systems by virtue of multi-lagged-input iterative dynamic linearization (IDL). The original nonlinear and non-affine MIMO system is equivalently transformed into a linear input-output incremental counterpart without loss of dynamics. The proposed learning law utilizes the desired trajectory to cancel the influence from iteration-by-iteration variations, as well as additional multi-lagged inputs to improve control performance. The developed iterative estimation law is more effective and also makes estimation of the unknown parameters easier because the dynamics for each parameter to represent are decreased by dividing the system into multiple components in the multi-lagged-input IDL formulation. Moreover, the proposed M-DDAILC does not need an explicit and accurate model. It is proved to be iteratively convergent with rigorous analysis. Both a numerical example and a practical application to a permanent magnet linear motor are provided to verify the validity and applicability of the proposed method.

Computationally Efficient Data-Driven Higher Order Optimal Iterative Learning Control.

Based on a nonlifted iterative dynamic linearization formulation, a novel data-driven higher order optimal iterative learning control (DDHOILC) is proposed for a class of nonlinear repetitive discrete-time systems. By using the historical data, additional tracking errors and control inputs in previous iterations are used to enhance the online control performance. From the online data, additional control inputs of previous time instants within the current iteration are utilized to improve transient response. The data-driven property of the proposed method implies that no model information except for the I/O data is utilized. The computational complexity is reduced by avoiding matrix inverse operation in the proposed DDHOILC approach due to the nonlifted linear formulation of the original model. The asymptotic convergence is proved rigorously. Furthermore, the convergence property is analyzed and evaluated via three performance indexes. By elaborately selecting the higher order factors, the higher order learning control law outperforms the lower order one in terms of convergence performance. Simulation results verify the effectiveness of the proposed approach.

Constraint data‐driven optimal terminal ILC of end product quality for a class of I/O constrained batch processes

AbstractIn order to deal with the I/O constraints in a practical plant, a soft limiter is often added into the control design procedure directly; however, the performance of the soft limiter based control approach will be degraded greatly due to the use of the soft constraints. This paper proposes a data‐driven optimal terminal iterative learning control (constraint‐DDOTILC) approach for the end product quality control of batch processes with I/O hard constraints. To deal with nonlinearities, a novel iterative dynamic linearization method without omitting any information of the original plant is introduced such that the derived linearized data‐driven model is completely equivalent to the original nonlinear system. By transferring all the constraints on the system output, control input, and the change rate of input signals into a linear inequality, a novel constraint‐DDOTILC is developed by minimizing an objective function under the derived linear matrix inequality constraint. The optimal learning gain of the constraint‐DDOTILC can be updated iteratively according to the input and output measurements to enhance the flexibility for modifications and expansions of the controlled plant. Both theoretical analysis and simulation results confirm the effectiveness of the proposed constraint‐DDOTILC.

Constrained data-driven optimal iterative learning control

A constrained optimal ILC for a class of nonlinear and non-affine systems, without requiring any explicit model information except for the input and output data, is proposed in this work. In order to address the nonlinearities, an iterative dynamic linearization method without omitting any information of the original plant is introduced in the iteration direction. The derived linearized data model is equivalent to the original nonlinear system and reflects the real-time dynamics of the controlled plant, rather than a static approximate model. By transferring all the constraints on the system output, control input, and the change rate of input signals into a linear matrix inequality, a novel constrained data-driven optimal ILC is developed by minimizing a predesigned objective function. The optimal learning gain is unfixed and updated iteratively according to the input and output measurements, which enhances the flexibility regarding modifications and expansions of the controlled plant. The results are further extended to the point-to-point control tasks where the exact tracking performance is required only at certain points and a constrained data-driven optimal point-to-point ILC is proposed by only utilizing the error measurements at the specified points only.