A data-driven dynamic internal model control (D $^{3}$ IMC) scheme is proposed for unknown nonlinear nonaffine systems bypassing modeling steps. Different from the traditional internal model constructed by either a first-principle or an identified model, a dynamic internal model (DIM) is developed in this work using I/O data where a compact form dynamic linearization approach is introduced for addressing the nonlinearity and nonaffine structure. Then, the D $^{3}$ IMC is proposed with both a nominal control algorithm and an uncertainty compensation control algorithm. The former can quickly respond to the feedback errors and the latter can compensate the model-plant mismatch and external disturbances. Meanwhile, the adaptive parameter updating law in the proposed D $^{3}$ IMC method inherits the robustness against uncertainties. A nominal D $^{3}$ IMC is also designed without including the compensator when there is no exogenous disturbance since the adaptive mechanism can handle system uncertainty. Further, the results are extended and a full-form dynamic linearization-based D $^{3}$ IMC is developed to address control of nonlinear systems with more complex dynamics. All the proposed D $^{3}$ IMC methods are data-driven without need of an explicit model, and thus they are significant extensions from the traditional model-based IMC. Simulation study verifies the results.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.

In this article, a higher order indirect adaptive iterative learning control (HO-iAILC) scheme is developed for nonlinear nonaffine systems. The inner loop adopts a $P$ -type controller whose set-point is updated iteratively by learning from the iterations. To this end, an ideal nonlinear learning control law is designed in the outer loop. It is then transferred to a linear parametric-learning controller with a corresponding parameter estimation law by introducing an iterative dynamic linearization (IDL) method. This IDL method is also used to gain an iterative linear data model of the nonlinear system. A parameter iterative updating algorithm is utilized for estimating the unknown parameters of the obtained linear data model. Finally, the HO-iAILC is presented that utilizes additional error information to improve the control performance and employs two iterative adaptive mechanisms to deal with uncertainties. The convergence of the proposed HO-iAILC scheme is proved by using two basic mathematical tools, namely: 1) contraction mapping and 2) mathematical induction. Simulation studies are conducted for the verification of the theoretical results.

In this article, an indirect adaptive iterative learning control (iAILC) scheme is proposed for both linear and nonlinear systems to enhance the P-type controller by learning from set points. An adaptive mechanism is included in the iAILC method to regulate the learning gain using input–output measurements in real time. An iAILC method is first designed for linear systems to improve control performance by fully utilizing model information if such a linear model is known exactly. Then, an iterative dynamic linearization (IDL)-based iAILC is proposed for a nonlinear nonaffine system, whose model is completely unknown. The IDL technique is employed to deal with the strong nonlinearity and nonaffine structure of the systems such that a linear data model can be attained consequently for the algorithm design and performance analysis. The convergence of the developed iAILC schemes is proved rigorously, where contraction mapping, two-dimensional (2-D) Roesser’s system theory, and mathematical induction are employed as the basic analysis tools. Simulation studies are provided to verify the developed theoretical results.

In this paper, an event-triggered P-type iterative learning control (ILC) scheme is developed, where the control input update only occurs in the event-triggered iterations. The event-triggered iterations are determined by a pre-defined event-triggering condition, which is composed of two parts, one is the threshold condition to ensure convergence, the other is derived from the Lyapunov stability principle to ensure stability. The convergence analysis theorem is deduced mathematically. Further, using similar steps, event-triggered PD-type ILC and event-triggered PID-type ILC are proposed. Finally, the simulation results illustrate that the presented algorithms can ensure that the error converges and make the control input update less frequently, so as to realise the goal of saving resources.

In this work, a new indirect iterative learning control (ILC) method with an iterative dynamical identification of the set-point command is proposed. The ILC law of the set-point is derived from the dynamical linearization of a nonlinear ideal ILC law. Then, the estimation law of the parameter in the ILC law is derived from the optimization of a cost function. At last, simulations demonstrate the advantages of the proposed scheme.