The double-holding water tank system is a common non-linear control system that plays a crucial role in process control in the chemical industry. It consists of two cylindrical glass containers: the preset tank and the main tank. The main challenge in controlling this system is adjusting the main control valve to ensure that the actual liquid level of the main tank tracks the desired liquid level. This paper explores the zeroing dynamics (ZD) method and its application in tracking control. A non-linear model is developed for the double-holding water tank system, and the ZD method is used to design an effective controller (called the ZD controller) for tracking control. Additionally, the robustness of the double-holding water tank system in the presence of time-varying perturbations is investigated. In order to substantiate the effectiveness and robustness of the ZD controller, simulation experiments on four different tracking trajectories corresponding to four different practical situations, as well as an extra simulation experiment considering time-varying perturbations, are conducted. Furthermore, a comparative simulation experiment based on the backstepping method is conducted. The presented results successfully illustrate the feasibility and effectiveness of the ZD method for the tracking control of double-holding water tank systems.

In the traditional iterative learning control (ILC) method, the operational time interval is conventionally fixed to facilitate a seamless learning process along the iteration axis. However, this condition may frequently be contravened in real-time applications owing to unknown uncertainties and unpredictable factors. In essence, replicating a control system at a consistent time interval proves challenging in practical scenarios. This paper proposes an adaptive iterative learning control (AILC) method for the multi-input–multi-output (MIMO) nonlinear system with nonuniform trial lengths and an invertible control gain matrix. Compared to the existing AILC research that features nonuniform trial lengths, the control gain matrix of the system in this paper is assumed to be invertible. Hence, the general requirement in the conventional AILC method that the control gain matrix of the system is positive-definite (or negative-definite) or even known is relaxed. Moreover, the tracking reference allows it to be iteration-varying. Finally, to prove the convergence of the system, the composite energy function is introduced and to verify the validity of the AILC method, a robot movement imitation with an uncalibrated camera system is used. The simulation results show that the actual output can track the desired reference trajectory well, and the tracking error converges to zero after 30 iterations.

Japan is located in Pacific volcanic seismic belt, and lies at the junction of the Pacific plate and the Eurasian plate. This makes Japan one of the most seismically active regions in the world. Earthquake prediction, and especially huge earthquake prediction for Japan is necessary to take disaster preparedness and mitigation measures. In this paper, addition-subtraction frequency (ASF) method with three inputs is presented for predicting a potential Mw8.1-or-above earthquake in Japan after year 2020. The date data of earthquakes which this paper uses are Japan's real seismic data in the past. Meanwhile, three forms of initial date data [i.e., m/d/y (month/day/year), m/y (month/year), and y (year)] are used as the inputs of numerical experiments. Thus, possible occurrence dates of Mw8.1-or-above earthquakes in Japan can be identified via ASF method. Finally, via consistency analysis of these possible dates, the date 4 May 2030 is the one with the highest possibility.

Although some existing studies have addressed event-triggered iterative learning control–related problems, most of them focus on one-dimensional systems or investigate control systems with the aid of certain two-dimensional analytical methods. This article explores the problem of event-triggered adaptive iterative learning control design for two-dimensional linear discrete-time systems described by the Fornasini–Marchesini model. First, an improved event-triggering condition that only requires the system state and tracking error is devised. Second, by introducing the event-triggered control into the iterative domain, an adaptive parameter law is designed. Then, a novel two-dimensional event-triggered adaptive iterative learning control scheme is developed, which can effectively reduce the updating number of control inputs, alleviate the computational burden on the controller, and save network communication resources. A rigorous theoretical analysis is conducted on the developed two-dimensional event-triggered adaptive iterative learning control scheme using a composite energy function, and the results show that the developed scheme can ensure the convergence of tracking errors. Finally, a simulation example is given to demonstrate the effectiveness of the proposed two-dimensional event-triggered adaptive iterative learning control scheme.