In this article, an echo state network (ESN)-based backstepping adaptive iterative learning control scheme is proposed for nonlinear strict-feedback systems performing the same operation repeatedly over a finite-time interval. Different from most of the output tracking approaches, an error-tracking approach is presented using the backstepping technique, such that the tracking error can follow a prespecified error trajectory without any requirement on the initial value of system states. Then, a novel Lyapunov function is constructed to deal with the unknown state-dependent gain function of the controller design. The uncertain nonlinearities are approximated by employing ESNs with simple feedback structures, and the weight update laws are developed by combining the parameter adaptation in the time domain and iteration domain. Moreover, the proposed control scheme is further extended to handle the strict-feedback systems with input saturations. Through the Lyapunov-like synthesis, the closed-loop stability and error convergence of the proposed error-tracking control scheme are analyzed in the presence of the approximation errors. Numerical simulations are provided to verify the effectiveness of the proposed scheme.

This article proposes a prescribed-time robust repetitive learning control scheme for uncertain permanent magnet synchronous motor (PMSM) servo systems. An error-tracking approach is developed through constructing a desired error trajectory, such that the exact settling time of the error convergence can be achieved without using any switching mechanism in controller design. In order to achieve high-precision steady-state tracking accuracy, a fully saturated repetitive learning law is developed to reduce the residual periodic steady-state error and drive the tracking error to converge into a sufficiently small region around the origin, such that the rapid transient response and high-precision steady-state tracking accuracy of the PMSM servo system can be both guaranteed simultaneously. Comparative experiments are provided to verify the effectiveness of the proposed method.

An adaptive fuzzy iterative learning control(AFILC) method is presented to address the state tracking issue of constrained systems with arbitrary initial state errors and unknown control gain. A novel desired error trajectory is systematically developed in the polynomial form to relax the identical initial condition, which allows for arbitrary setting of initial values for all the system state errors. The proposed desired error trajectory can also relax the iteration-invariance restriction on the reference signals due to the independence of the reference trajectories. An asymmetric integral fractional barrier Lyapunov function is developed, keeping the tracking error within the preassigned boundary. Moreover, there is no need to estimate the unknown control gain function in the controller design, reducing computation burden. Numerical simulations and experiments in the permanent magnet synchronous motor experimental platform are provided to illustrate the efficacy of the proposed method. Note to Practitioners —Most practical systems often perform repetitive tasks in industrial processes, such as the repetitive handling process of manipulators, and the rotation process of motors, etc. Iterative learning control method is model independent, and fully utilizes the repetitive characteristics during system operation. However, due to irregular initial state drifts caused by locating operations at different iterations, the identical initial condition is often violated in practical iterative learning control applications. This paper presents an adaptive fuzzy iterative learning control method to address the state tracking issue of constrained systems with arbitrary initial state errors and unknown control gain. The problem of inconsistent initial values is addressed by designing a desired error trajectory in the polynomial form, such that arbitrary setting of initial values for all the system state errors is allowed. For safe operation in practice, an asymmetric integral fractional barrier Lyapunov function is developed to keep the tracking error within the preassigned boundary. The satisfactory experimental results on the permanent magnet synchronous motor experimental platform also demonstrate the practical effectiveness of the proposed method.

In engineering applications, high-precision tracking control is crucial for robotic manipulators to successfully complete complex operational tasks. To achieve this goal, this study proposes an adaptive tunable predefined-time backstepping control strategy for uncertain robotic manipulators with external disturbances and model uncertainties. By establishing a novel practical predefined-time stability criterion, a tunable predefined-time backstepping controller is systematically presented, allowing the upper bound of tracking error settling time to be precisely determined by adjusting only one control parameter. To accurately address lumped uncertainty, two updating laws are designed: a fuzzy weight updating law and a boundary adaptive updating law, which together reduce dependence on system model knowledge. In addition, the singularity problem in the predefined-time design process is effectively avoided by constructing the hyperbolic tangent function. The efficacy of the proposed control strategy is verified through numerical simulations.

This study provides an adaptive filtered prescribed-time position control scheme for motor driving servo systems. A desired error trajectory is constructed by employing a smoothly decreasing continuous function, such that the prescribed-time position tracking control of the motor driving servo system can be equivalently transformed into the error tracking control design. Then, a prescribed-time controller is developed to drive the position tracking error to track the desired error trajectory, such that the error convergence can be achieved at the prescribed settling time. Besides, a novel adaptive filter is presented to avoid differentiating virtual control variables in recursive procedures and ensure the filter error convergence into a small bound near the origin within the preset finite time. Some experiments on a practical motor driving servo system are performed to verify the effectiveness of the proposed method.

The use of manipulators can improve sustainable energy utilization efficiency and increase sustainable manufacturing practices for solar tracking systems and manufactures, and thus it is significant to guarantee a high tracking accuracy for manipulators. In this paper, an error-tracking adaptive iterative learning control (AILC) method is proposed for a constrained flexible-joint manipulator (FJM) with initial errors. Due to the existence of the repeated positioning drift, the accuracy of the actual manipulator and the sustainable energy utilization efficiency are affected, which motivates the error-tracking approach proposed in this paper to deal with the repeat positioning problem. The desired error trajectory is constructed, such that the tracking error can follow the desired error trajectory without arbitrary initial values and iteration-varying tasks. Then, the system uncertainties are approximated by the capability of fuzzy logic systems (FLSs), and the combined adaptive laws are designed to update the weight and the approximating error of FLSs. Considering the safety operation of the flexible-joint manipulator, both input and output constraints are considered, a quadratic-fractional barrier Lyapunov function (QFBLF) is constructed, such that the system output is always within the constrained region. Therefore, the proposed method can guarantee the output tracking accuracy of manipulators under arbitrary initial values and iteration-varying tasks and keep the system output within the constraints to improve the transient performance, such that the energy utilization and accessory manufacturing efficiency can be improved. Through the Lyapunov synthesis, it is proved that the tracking error can converge to zero as the number of iterations goes to infinity. Finally, comparative simulations are carried out to verify the effectiveness of the proposed method.