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Tracking control of Small Unmanned Ground Vehicles (SUGVs) is easily affected by the nonlinearity and time-varying characteristics. An improved predictive control scheme based on the multi-dimensional Taylor network (MTN) is proposed for tracking control of SUGVs. First, a MTN model is used as a predictive model to construct a SUGV model and back propagation (BP) is taken as its learning algorithm. Second, the predictive control law is designed and the traditional objective function is improved to obtain a predictive objective function with a differential term. The optimal control quantity is given in real time through iterative optimization. Meanwhile, the stability of the closed-loop system is proved by the Lyapunov stability theorem. Finally, a tracking control experiment on the SUGV model is used to verify the effectiveness of the proposed scheme. For comparison, traditional MTN and Radial Basis Function (RBF) predictive control schemes are introduced. Moreover, a noise disturbance is considered. Experimental results show that the proposed scheme is effective, which ensures that the vehicle can quickly and accurately track the desired yaw velocity signal with good real-time, robustness, and convergence performance, and is superior to other comparison schemes.

Predefined-time control has experienced substantial advancements in recent years. Nevertheless, the current technology has not achieved widespread adoption in nonlinear multi-agent systems (NMASs), and significant issues pertaining to the input quantization and actuator failures remain unaddressed. This paper investigates the problem of predefined-time consensus control for NMASs with input quantization and actuator faults. Notably, the study takes into account scenarios where each actuator may experience an infinite number of faults. In conjunction with practical predefined-time stability theory, an innovative predefined-time adaptive consensus control method has been developed within the framework of the backstepping method, incorporating the approximation technique of the multi-dimensional Taylor network (MTN). Additionally, by utilizing the characteristics of quantized nonlinear sectors and the structural model of actuator faults, novel adaptive estimation techniques are devised to handle the effects caused by actuator faults and quantized inputs. To further alleviate computational burdens and tackle the issue of computational explosion, a finite-time differentiator is employed to estimate the derivative of the virtual control. The proposed control scheme achieves the desired performance of predefined-time convergence. Rigorous theoretical analyses indicate that the proposed control scheme can drive consensus errors to converge within a small range within a predefined-time, and users have the flexibility to choose the settling time. Moreover, all signals in the closed-loop system remain bounded. Finally, simulation results are provided to validate the effectiveness of the proposed approach.

Lithium-ion batteries have become an important power source in low-carbon transportation energy, and the safe operation and remaining useful life prediction are of great significance. Aiming at the shortcomings of existing methods, such as low prediction accuracy and a short prediction period, this paper proposes a real-time update high-order extended Kalman filter method based on fixed-step life prediction for vehicle lithium batteries based on the principle of combining models and data. First, the state model describing the parameters in the dynamic energy attenuation model is established, and the energy attenuation model is regarded as the observation model of the system to meet the requirements of establishing the Kalman filter. Secondly, the multi-step prediction equation of the state model is established by iterative recursion. At the same time, the multi-step prediction equation between the existing energy output value and the future output value is established based on the multi-dimensional Taylor network (MTN). The multiplicative noise term introduced in the dynamic modeling process is regarded as the hidden variable of the system to meet the requirements of establishing the multi-step linear predictive Kalman filter. Finally, the effectiveness of the new method is verified by digital simulation examples.

Time series forecasting in power systems is crucial for power supply planning and exerts a direct impact on the electricity market. Accurate forecasting can effectively mitigate decision-making risks. This paper proposes a forecasting method based on a multi-dimensional Taylor network (MTN) and applies it to electricity price prediction. The time series is decomposed into one low-frequency signal and several high-frequency signals. The MTN model is constructed for each frequency sequence. The final forecast is obtained by aggregating the predictions from all frequency components. Using European electricity price data as a case study, experimental results demonstrate that the proposed method achieves high predictive accuracy.

This work investigates the problem of Multi-dimensional Taylor Network (MTN)-based fault-tolerant control (FTC) for single-input and single-output nonlinear systems in non-strict feedback form. A MTN-based FTC method is presented for nonlinear systems with actuator faults and unmodeled dynamics. The actuator faults are contains both the loss of effectiveness factor of the actuator and a time-varying bias signal. MTN is used to approximate the unknown nonlinear functions, while unmodeled dynamics and dynamical disturbances are handled with the help of dynamical signal functions. A systemically backstepping-based fault-tolerant control scheme is proposed based on Lyapunov stability theory and MTN approximation ability. The suggested technique ensures that all closed-loop system signals are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small region around the origin. To demonstrate the effectiveness of the proposed controller design, three examples, including a single-link robot manipulator, are presented.

This paper investigates an adaptive decentralized predefined performance control problem for a class of large-scale nonlinear systems with nonsymmetric input saturation by using multi-dimensional taylor network (MTN) approach. Firstly, the input saturation model is approximated by a smooth function with a bounded approximation error and unknown nonlinear functions are estimated by MTNs. Secondly, a decentralized tracking control algorithm is established by integrating the idea of prescribed performance control into backstepping recursive technique. Thirdly, by using the designed MTN-based adaptive decentralized controller, all the closed-loop signals are bounded and all the tracking errors satisfy the predefined transient and steady-state performance, respectively. Finally, the presented control method is effective by introducing three examples, and the simulation results verify that the correctness and reasonableness of the proposed control algorithm.

In this paper, the tracking control problem of the state constrained stochastic nonlinear systems with unknown control direction is studied, and a novel adaptive prescribed performance control (PPC) approach is developed with the help of the multi-dimensional Taylor network (MTN). Firstly, a performance function is introduced into the first step of backstepping to ensure transient performance under state constraints. Secondly, the tangent time-varying barrier Lyapunov functions (tan-TVBLFs) are constructed to prevent all states from violating the given time-varying boundary. Thirdly, the MTNs are employed to estimate the unknown nonlinearity in the process of controller design, and a new adaptive PPC strategy is designed. Then, the Lyapunov stability theorem is used to prove that the closed-loop system is semi-global uniformly ultimately bounded (SGUUB) in probability, and the tracking error can be kept in an adjustable small neighborhood of the origin. Finally, the effectiveness of the proposed scheme is verified by the simulation of a numerical example and an actual control system.

For the large-scale nonlinear systems subject to dynamic uncertainties, an adaptive multi-dimensional Taylor network (MTN)-based decentralized control strategy is proposed, which can effectively solve output tracking control problem of the systems. Firstly, a dynamic signal is introduced to cope with the problem of unknown nonlinear dynamic uncertainties. Secondly, in each step of the backstepping, only one MTN is used to approximate the combination of unknown nonlinear functions. Then, in the last step of the backstepping, a new adaptive control scheme is designed, which realizes the stability and boundedness of the controlled systems. It is worth noting that the large-scale nonlinear systems, the unknown dynamic uncertainties and the MTN appear in the same framework for the first time. Finally, three simulation examples are presented to verify the feasibility of the proposed control strategy.

Within the field of permanent magnet synchronous motor sensorless speed control systems, we present a novel scheme with a Multi-dimensional Taylor Network (MTN)-based nonlinear observer as the core, supplemented by two auxiliary MTN modules to realize closed-loop control: (1) MTN Model Identifier: Provides real-time PMSM nonlinear dynamic feedback for the observer; (2) MTN Adaptive Inverse Controller: Compensates for load disturbances using the observer’s estimated states. The study focuses on optimizing the MTN observer to address key limitations of existing methods (high computational complexity, lack of stability guarantees, and low estimation accuracy). Compared with the neural network observer, this MTN-based scheme stands out due to its straightforward structure and significantly reduced approximately 40% computational complexity. Specifically, the intricate calculations and high resource consumption typically associated with neural network observers are circumvented. Subsequently, by leveraging Lyapunov theory, an adaptive learning rule for the MTN weights is meticulously devised, which seamlessly bridges the theoretical proof of the nonlinear observer’s stability. Simulation results demonstrate that the proposed MTN observer achieves rapid convergence of speed and position estimation errors (with steady-state errors within ±0.5% of the rated speed and ±0.02 rad for rotor position) after a transient period of less than 0.2 s. Even when stator resistance is increased by tenfold to simulate parameter variations, the observer maintains high estimation accuracy, with speed and position errors increasing by no more than 1.2% and 0.05 rad, respectively, showcasing strong robustness. These results collectively confirm the efficacy and practical value of the proposed scheme in PMSM sensorless speed control.

Nonlinear systems are very common in real life, but because they are not superposed and homogeneous, there are many difficulties in controlling nonlinear systems. Therefore, an adaptive control method based on a multi-dimensional Taylor network (MTN) is proposed for a class of nonlinear systems with strict feedback so that the output of the system can track the given signal. In order to achieve the control effect, we define a new state variable and transform the strict feedback system. After transformation, the original feedback system has a standard form, and two parameters to be identified are obtained. Then, the state observer is designed, and the two parameters are identified via the approximation of the MTN. On this basis, the controller design and a system stability analysis are completed. The lemma is introduced, and the stability condition is established by using this low-pass filter to ensure that all closed-loop signals are semi-globally uniform and finally bounded and the output tracking error converges to the residual set near zero. Finally, a numerical simulation of a hydraulic system is carried out to verify the effectiveness of the proposed method. Under the three indexes, the proposed method has obvious advantages.