An iterative learning algorithm founded on the normalization principle and inverse triangular dynamic initial error compensation

Dual-Stage Iterative Learning Control With Markov Parameters Toward Pointwise Convergence Evaluation

The study proposes iterative Learning Control (ILC) for single-input, single-output, discrete-time, time-invariant linear systems, where system outputs are expressed by the convolution of Markov parameters and historical input data. In the proposed method, the input signals and system parameters are updated in a pointwise manner after every trial. Then, normalization signals are introduced to ensure the boundedness of the magnitude of both the input signals and the estimated parameters. The main feature of the proposed method is the pointwise evaluation of the convergence rate for the input signals to the desired ones. The theoretical analysis is conducted under the assumption that the sign of the initial first Markov parameter estimate is selected to be the same as that of the true value. It should be noted that the convergence of tracking errors could be achieved even when the estimated parameters do not converge to the true values. The feature contrasts with the existing model-based ILC, where the control performance is significantly dependent on the precision of the estimated parameters. Finally, a numerical example is shown that supports the analysis of the proposed method.

Robust Iterative Learning Control with Higher-Order Feedback for Variable-Trial-Length Nonlinear Systems Under Input Saturation and Disturbances

This paper studies a robust composite higher-order feedback iterative learning control method for affine nonlinear discrete-time systems. The considered system is subject to input saturation, randomly varying trial lengths, random initial state shifts, and external disturbances. In the controller formulation phase, a Bernoulli stochastic sequence is used to model the data dropout phenomenon caused by non-uniform trial lengths. To address information loss caused by varying trial lengths, a composite control law is developed by combining a higher-order feedforward learning term with a real-time feedback term. The proposed method uses input and error information from several previous trials to compensate for the loss of learning information caused by non-uniform trial lengths. Based on mathematical induction, it is shown that the mathematical expectation of the tracking error gradually converges towards a strictly bounded residual neighborhood. It can be clearly shown that the analytical limits of this area are related to the magnitude of external disturbances and the variations in the initial state. Moreover, in optimal circumstances, the suggested algorithm ensures the rigorous asymptotic convergence of the anticipated error to zero. Finally, numerical simulations support the theoretical analysis and show that the proposed method maintains satisfactory tracking performance under the considered nonideal factors.

Inverse optimal control of general nonlinear systems based on adaptive dynamic programming

Robust Model Reference Adaptive Control with Combined Adaptation under Finite Excitation Condition

In adaptive control, parametric uncertainties in linear-in-parameter form consist of unknown parameters and known regressor signals. Convergence of the unknown parameters to their ideal values requires the regressor to satisfy a persistent excitation (PE) condition, which depends on future data and is therefore infeasible to guarantee online. Memory-based parameter update laws address this by enabling ideal parameter convergence under the online-verifiable finite excitation (FE) condition. In this paper, a new algorithm is proposed to construct a memory term via the Modified Gram-Schmidt orthogonalization procedure for a class of multi-input multi-output nonlinear systems with an unknown diagonal control effectiveness matrix and bounded nonparametric uncertainties. Under the finite excitation condition, the constructed memory term yields an identity coefficient matrix in the parameter estimation error dynamics. The identity coefficient matrix eliminates the need for time-varying adaptation gains, enables an explicit ultimate bound on the parameter estimation error, and preserves the structure of the nonparametric uncertainty bound under the memory term. Building on this, a combined adaptation law is developed for controller gain estimation under FE. The closed-loop tracking and estimation errors are shown to decay exponentially to a neighborhood of the origin, characterized by an explicit ultimate bound, with a decay rate that depends solely on user-defined gains and system constants, independent of the level of regressor excitation. This removes the dependence of the convergence rate on the level of regressor excitation, a key limitation of existing approaches such as concurrent learning, memory regressor extension, and DREM.

Improved Fixed-Time Gradient-Based Multivariable Extremum Seeking Algorithm

While the fixed-time gradient-based multivariable extremum seeking (FxTGMES) algorithm guarantees convergence within a bounded time independent of initial conditions, its nonlinear power terms often induce excessively large initial control gains. This inherently leads to pronounced transient overshoot and degrades the overall dynamic response. To address this issue, an improved fixed-time gradient-based multivariable extremum seeking (IFxTGMES) algorithm is proposed by integrating a dynamic compensation network. Specifically, a low-pass filter is employed to attenuate the high-gain-induced transient overshoot, while a proportional-derivative (PD) feedback loop is introduced to provide phase lead compensation, effectively neutralizing the inherent phase lag caused by the filter. Simulation results verify that the proposed IFxTGMES algorithm successfully suppresses the initial transient overshoot and enhances dynamic response quality, while strictly preserving the fixed-time convergence property.

Feedforward Iterative Learning Control Compensated Fractional‐Order Model‐Free Adaptive Control

Model‐free adaptive control (MFAC) can carry out various tasks using only input and output (I/O) data, providing advantages such as lower operational costs, higher scalability, and easier implementation. In this article, to further improve tracking performance, a fractional‐order model‐free adaptive control (FOMFAC) with P‐type feedforward iterative learning controller for uncertain discrete‐time nonlinear systems is proposed. First, the FOMFAC law is designed by using an optimization input criterion function based on a fractional‐order (FO) equivalent model, which contains more input and output data information. Then, an iterative learning control (ILC) scheme is proposed as the feedforward component term to achieve fast convergence. Different from the existing plug‐in method, the stability of the whole closed‐loop control system is rigorously proved. Finally, the presented simulation evidence substantiates both the theoretical validity and practical superiority of the novel control method.