Sliding mode iterative learning control for non-linear systems with uncertainties

A new iterative learning algorithm for nonlinear systems based on updated Newton method is investigated. The exchange row updated method is employed to derive the approximation of derivatives of the output function. The inverse of approximation of derivatives of the output function can be obtained by simple recurrent formula. This new algorithm has advantage of simplified calculation of the iterative learning control law in every iterative learning process. Sufficient conditions for convergence of this new updated Newton algorithm are given and proved. Moreover, a secant-type iterative learning control of new updated Newton method is presented. This approach avoid calculating partial derivatives such that the calculate work is largely reduced.

Iterative learning control demands the same initial state in each iteration, which is equal to the desired state. But this condition is unattainable in practice. This paper addresses the problem of some fixed initial state in iterative learning control for high-order nonlinear system. It presents a new control algorithm. In the process of tracking, this algorithm can rectify the initial errors through a step-by-step rectifying controller. The controller rectifies the x n at first, then x n−1 after finishing the rectifying actions of x n , and so on. All of these rectifying actions are finished in a small interval. Furthermore, the algorithm has shown effective in the improvement of tracking performance through simulation.

Lots of iterative learning control (ILC) algorithms have been developed to improve tracking performance of systems that track same trajectory repetitively. In this paper, we use an open-closed-loop PD-type ILC scheme for the control of a class of nonlinear systems. Sufficient condition for guaranteeing the convergence of the learning scheme is given under a few reasonable assumptions, and then proved with linear operator theory. It is shown that the proportional coefficients of the ILC scheme is not a factor for guaranteeing the convergence, the condition is weaker than known results for similar ILC schemes.

Most of the existing iterative learning control algorithms proposed for time-delay systems are based on the condition that the time-delay is precisely available, and the initial state is reset to the desired one or a fixed value at the start of each operation, which makes great limitation on the practical application of corresponding results. In this paper, a new iterative learning control algorithm is studied for a class of nonlinear system with uncertain state delay and arbitrary initial error. This algorithm needs to know only the boundary estimation of the state delay, and the initial state is updated, while the convergence of the system is guaranteed. Without state disturbance and output measurement noise, the system output will strictly track the desired trajectory after successive iteration. Furthermore, in the presence of state disturbance and measurement noise, the tracking error will be bounded uniformly. The convergence is strictly proved mathematically, and sufficient conditions are obtained. A numerical example is shown to demonstrate the effectiveness of the proposed approach.

To deal with iterative learning control of nonlinear systems with non‐repeatable control tasks, an adaptive PID‐type iterative learning controller is presented in this paper. The control structure is constructed based on a time‐varying boundary layer so that the initial state error problem can be solved and possible undesirable chattering behavior can be removed. The PID‐type iterative learning controller is designed by using the fact that a PID controller can be used as an approximator for an optimal controller in a compact set. An error equation is derived to represent the relation between the control input and system tracking error. Since the optimal PID gains for the best approximation are in general unavailable, the control parameters are tuned between successive iterations to ensure internal stability and error convergence. Under this adaptive PID‐type iterative learning controller, the referenced trajectory is allowed to be iteration‐varying which means that it is not required to be the same at each iteration. It is shown that all the adjustable parameters and the internal signals remain bounded for all iterations. Furthermore, the norm of tracking error vector at each time instant will asymptotically converge to a tunable residual set.

This paper presents a decentralized learning controller for large-scale nonlinear systems. A new learning method which is based on a performance index of sliding mode control is used to derive an iterative learning algorithm to obtain control actions. The effectiveness and the performance of the proposed approach are illustrated by the simulation results of a two-inverted pendulum system and a two-link manipulator. The attractive features also include a smaller residual error and robustness against nonlinear interactions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In order to improve the convergence speed of iterative learning control and reduce the fluctuation of the system error, a class of linear steady-state systems is considered. The convergence of the algorithm and error fluctuations are studied by introducing the variable-gain idea into the D-type iterative learning control algorithm with variable forgetting factor. According to the related properties of the λ norm theory, the convergence of the improved iterative learning algorithm is proved. Compared with iterative learning control with forgetting factor and iterative learning control with variable gain, MATLAB simulation analysis is performed. The simulation results show that the algorithm is effective. The improved iterative learning law not only makes the iterative error smoother, but also improves the convergence speed.

A conditional iterative learning control (ILC) is derived for uncertain non-linear systems to track repetitive trajectory under the alignment initial condition. The learning of the conditional ILC is performed, only if the tracking error is dominated by the input instead of the initial conditions. The major advantage of this method is that it can simultaneously handle non-parametric uncertainties and the alignment initial condition. A simulation example is presented to illustrate the performance and implementation of the conditional ILC.

Iterative learning control (ILC) is a simple and effective method for the control of systems that perform same task repetitively. In this paper, open-closed-loop D-type ILC problem is investigated for a class of nonlinear time-varying systems. Under a few reasonable assumptions, sufficient condition for guaranteeing the convergence of the learning scheme is given and then proved with linear operator theory. The condition is independent of the specific form of the state space model, also it is weaker than known results for D-type ILC scheme.

The piezoelectric micro-positioning platform(PMP) has advantages in high displacement resolution and fast response, however, the serious hysteresis nonlinearity in the PMP restricts its positioning accuracy. This paper presents a discretization of Krasnosel’skii-Pokrovskii model to describe the hysteresis nonlinearity of the PMP. Then, the density function is identified online by the adaptive linear neural network. To compensate the intrinsic hysteresis nonlinearity in the PMP, a feedforward compensation control method is implemented by an innovative iterative learning control algorithm. Moreover, a hybrid control method based on iterative learning and fractional order PID control is proposed to further improve the control accuracy. A series of comparative experiments are carried out to validate the feasibility and effectiveness of the proposed control method.

A novel iterative learning control (ILC) algorithm was developed and applied to an active flow control problem. The technique uses pulsed air jets to delay flow separation on a two-element high-lift wing. The ILC algorithm uses position-based pressure measurements to update the actuation. The method was experimentally tested on a wing model in a 0.9 m × 0.6 m low-speed wind tunnel at the University of Southampton. Compressed air and fast switching solenoid valves were used as actuators to excite the flow, and the pressure distribution around the chord of the wing was measured as a feedback control signal for the ILC controller. Experimental results showed that the actuation was able to delay the separation and increase the lift by approximately 10%–15%. By using the ILC algorithm, the controller was able to find the optimum control input and maintain the improvement despite sudden changes of the separation position.

An adaptive iterative learning controller (ILC) is proposed for a class of nonlinear systems with hysteresis described by Bouc-Wen model. First, the property of Bouc-Wen mode is discussed and the upper bound is derived .Then an iterative learning controller is proposed through the Lyapunov-like function. This controller can eliminate the oscillation and overshoot caused by hysteresis effectively. Finally, simulation results are provided to illustrate the effectiveness of the proposed controller.

In this paper, a new iterative learning algorithm is proposed for repetitive nonlinear systems. The control system employs a combination of state feedback and iterative learning control (ILC) in which the coefficients of states are learned similar to ILC methods. The control system is in a closed loop format both in iteration domain (because of ILC) and in time domain (because of feedback control) which improves the robustness of the conventional ILC. The convergence of the control algorithm is also proved. Finally, simulation results for a 5-DOF manipulator have been presented to illustrate that the proposed algorithm is more robust than a first order P type ILC method at the presence of white Gaussian noise as a nonrepeating disturbance.

With the accelerating integration of renewable energy into new power system, load frequency control (LFC) plays a crucial role in maintaining system stability and reliability. Traditional LFC methods usually adopt fixed control strategies, which are vulnerable to the dynamic characteristics of the system. This vulnerability is especially evident during complex load fluctuations and the continuous decrease in system inertia, highlighting the need to enhance controller performance. Moreover, with the expanding role of communication networks in frequency modulation, this paper proposes a novel LFC strategy for power systems. This strategy utilizes an adaptive event-triggered mechanism based on iterative learning. The adaptive event-triggered mechanism is employed to reduce the transmission requirements of the communication network, and an iterative learning control algorithm is incorporated to improve frequency modulation performance. The effectiveness of this method is verified through simulations under various operating conditions. The results show that the adaptive event-triggered mechanism can dynamically adjust the execution frequency of the control strategy, thereby reducing communication burdens and energy losses. Additionally, the iterative learning control strategy not only improves the system response speed and stability but also enables the system to tolerate a larger event-triggered threshold, thus better coordinating with the adaptive event-triggered mechanism.

Iterative learning contouring control: Theory and application to biaxial systems