This article develops a novel cost function (performance index function) to overcome the obstacles in solving the optimal tracking control problem for a class of nonlinear systems with known system dynamics via adaptive dynamic programming (ADP) technique. For the traditional optimal control problems, the assumption that the controlled system has zero equilibrium is generally required to guarantee the finiteness of an infinite horizon cost function and a unique solution. In order to solve the optimal tracking control problem of nonlinear systems with nonzero equilibrium, a specific cost function related to tracking errors and their derivatives is designed in this article, in which the aforementioned assumption and related obstacles are removed and the controller design process is simplified. Finally, comparative simulations are conducted on an inverted pendulum system to illustrate the effectiveness and advantages of the proposed optimal tracking control strategy.

Preserving data privacy in data-driven modeling for the Industrial Internet of Things (IIoT) has become critically important due to the susceptibility of communication data from numerous devices to cyber-attacks. Given its multi-subsystem integration, nonlinear interactions, and networking characteristics, IIoT can be modeled as nonlinear networked systems (NNSs). This paper presents a federated learning-based offset-free distributed control (FL-OFDC) method for NNSs with multiple subsystems to preserve data privacy and achieve offset-free control, with potential applications to IIoT. First, a novel FL algorithm with personalized optimization (FLPO) is proposed to simultaneously obtain global and local models using a simple algorithm framework, which can preserve data privacy and address the heterogeneity issue among subsystems. Subsequently, a novel information-theoretic bound for the generalization error of the FLPO algorithm with iteration properties is constructed using individual sample mutual information. Next, an FL-OFDC scheme for NNSs under external disturbances is developed to eliminate the offset, and its closed-loop stability criteria are derived. Finally, a chemical process network, that is, a specific case of IIoT, is employed to demonstrate the practicality of the FLPO and FL-OFDC methods.

Sliding mode control strategies have been widely used for tracking robot manipulators and have demonstrated their effectiveness. However, certain issues still persist. One of them is that tracking error may converge to a bounded region surrounding the origin, due to the sliding surface failing to reach zero. This can be so because system's motion depends on the designed sliding surface. In this article, a new sliding surface is proposed to enhance tracking performance with a fast convergence rate and minimum steady-state error. The sliding surface is formulated using the sliding variable value at the previous sampling instant, and the technique is therefore referred to as time-delay sliding mode control. The proposed control strategy offers several advantages: first, it achieves better precision without the need for increasing the number of tunable parameters; second, it can be readily extended to different types of sliding surfaces, without the need for complex architectures to decrease the steady-state error; third, it is robust against unknown dynamics and payload. Numerical simulations and practical experiments are reported to demonstrate the effectiveness of the proposed approach in enhancing tracking performance.

In this article, a combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) output tracking control strategy was proposed for a family of nonlinear systems with unknown drift function and control input gain function. In such a method, a neural network (NN) is used to approximate the controller directly. The main merits of the proposed strategy are given as follows: first, not only the NN parameters, such as weights, centers, and widths but also the learning rates of NN parameter updating laws are updated online via the proposed learning algorithm based on Barzilai-Borwein technique; and second, the controller design process can be further simplified, the controller parameters that should be tuned can be greatly reduced. Theoretical analysis about the stability of the closed-loop system is manifested. In addition, simulations were conducted on a numerical discrete time system and an inverted pendulum system to validate the presented control strategy.