The existing adaptive iterative learning control approaches with variable constraints mainly consider the matched uncertainties and only ensure the boundedness of parameter estimation errors. In this paper, an adaptive iterative learning control (AILC) method with prescribed performance constraints and improved parameter estimations is developed for a class of uncertain nonlinear strict-feedback systems. The prescribed performance control is achieved through generating a preset error trajectory in each iteration within the performance envelope and making the error of the actual tracking error versus the preset one small enough all the time. The improvement of the parameter estimation performance is realized by reconstructing the parameter estimation errors and using them to modify the differential-difference adaptive laws. The control algorithm is designed based on the dynamic surface control method and thus free from the “differential explosion” problem. It is guaranteed via the Lyapunov theory that all signals of the closed-loop system are semi-global bounded, the system output could track the given reference trajectory with the prescribed performance in each iteration and the$\mathcal {L}_{2}$norms of the estimation errors are uniformly ultimately bounded along the iteration-axis. Additionally, two simulation examples illustrate the effectiveness and advantages of the proposed adaptive iterative learning control method.

This paper investigates the practical prescribed-time control problem for uncertain high-order strict-feedback systems (SFSs) using the fully actuated system (FAS) approach, unlike previous research that primarily focuses on asymptotic stability control for such systems. First, the uncertain high-order SFSs are transformed into a high-order FAS. Next, a performance function is introduced to perform a coordinate transformation on the FAS, turning the original control problem into a boundedness issue for the transformed system. Then, neural networks are used to approximate the system’s uncertain terms, and a controller is designed for the transformed system based on the FAS approach. Using Lyapunov theory, it is proved that all signals in the closed-loop system are uniformly ultimately bounded, and the system output can converge to a specified region within a prescribed time. Finally, the effectiveness of the proposed control method is demonstrated through simulations of the RLC circuit system, a numerical example and an electromechanical system.

This article examines the normal form of a multiple-input-multiple-output (MIMO) linear time-varying (LTV) system. It explores the transformation of such a system into its normal form using an LTV transformation, if it possesses a general relative degree that may not be uniform (strict). Based on the obtained normal form, the internal and external dynamics as well as the inverse system of the LTV system are investigated. Additionally, the zero dynamics can be effectively parameterized. Moreover, by employing the derived LTV normal form, the proportional-derivative output-feedback stabilization and output tracking problems are resolved. Finally, an illustrative example is presented to showcase the effectiveness of the proposed controllers.