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This work focuses on developing a forecasting model for the nonlinear system with herding. Firstly, for clear presentation of the mechanism of herding behavior, a concept called intermittent positive feedback is defined. The mathematical expression of intermittent positive feedback is formulated in terms of dead-zone functions with the beginning and ending thresholds in the positive and negative directions. Then a dynamic surrogate based on the intermittent positive feedback multi-dimensional Taylor network is established, and a method for identifying its parameters is proposed. Multi-dimensional Taylor network module simulates the long-term trends of time series. Subsequently, an optimization model based on the alternating iteration of the parameters is developed to enhance the forecast accuracy of the intermittent positive feedback part. Simulation results demonstrate that the forecasting effect of the proposed modeling method is superior to that of conventional non-mechanism data-based surrogates for herding behavior. [ABSTRACT FROM AUTHOR]

In this paper, a recursive d -step-ahead predictive control scheme based on multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of multiple-input multiple-output (MIMO) nonlinear systems with input time-delay. The MTN predictive model is designed using a recursive approach to compensate the influence of time-delay, and an extended Kalman filter (EKF) is applied as its learning algorithm. An MTN controller is developed based on a proportional–integral–derivative (PID) controller where the closed-loop errors between the reference input and the system output are set as the MTN controller's inputs. Then, a back propagation (BP) algorithm, designed to update its weights according to errors caused by system uncertainty, is used as a learning algorithm for the MTN controller. Meanwhile, the convergence of the MTN predictive model and the stability of the closed-loop system are evaluated. Two numerical examples and a practical example – continuous stirred tank reactor (CSTR) process are presented to verify the superiority of the proposed scheme. The experimental results and the computational complexity analysis show that the proposed scheme is effective, promising its desirable robustness, anti-disturbance, tracking and real-time performance. [ABSTRACT FROM AUTHOR]

For stochastic nonlinear systems (SNSs) perturbed by compound uncertainties, the conventional model-based control approaches assume that the evolution behavior of uncertain variables is known. Unfortunately, such approaches are often conservative for most practical scenarios with the slow convergence speed and unsatisfactory anti-interference performance. For this sake, an adaptive control scheme based on deep deterministic policy gradient (DDPG) and multi-dimensional Taylor network (MTN) is proposed here to address the tracking problem for a category of SNSs subject to fast time-varying uncertainties, stochastic disturbance and unknown time-varying delays. The effect of time delay is embedded in the reproducing kernel Hilbert space through the error coordinate transformation. In the framework of DDPG, the MTN-based surrogate is utilized to construct the online network and target network via the temporal-difference method, which promises more desirable real-time performance due to its concise structure than conventional NN-based surrogates. In order to enhance the robustness of the system under fast time-varying uncertainties, a novel persistent excitation (PE) mechanism is designed to ensure that the control policy is appropriately rewarded or punished. Based on the PE condition, weights of MTNs converge exponentially and animate the system to evolve towards the target persistently. The tracking error and closed-loop state signals are proved theoretically to be uniformly ultimately bounded (UUB) via Lyapunov–Krasovskii functional. A numerical simulation from the process industry verifies the effectiveness of the proposed method. • An adaptive optimal control strategy based on DDPG is developed. • A novel persistent excitation (PE) mechanism is designed to incentivize the evolution. • PE-based evaluation ensures the fast maneuver encounters time-varying uncertainties. • MTNs are utilized as surrogates for better real-time performance. [ABSTRACT FROM AUTHOR]

An adaptive controller is developed that is based on the multidimensional Taylor network (MTN). This controller is used for multi-input and multi-output (MIMO) uncertain discrete-time nonlinear systems. This newly developed MTN is dissimilar with the neural network, in which only multiplication and addition are needed for this controller. Thus, real-time control is more easily to be achieved. The theoretical analysis shows that the output errors of the system are convergent and the output signals are semi-globally, uniformly and ultimately bounded. To illustrate the validity of MTN-based adaptive controller (MTNAC), a numerical example is given. The simulation data demonstrate that this MNTAC has better real-time performance and higher robustness compared with neural networks. • The MIMO uncertain nonlinear systems with couplings and different orders. • MTN controller with good tracking and disturbance suppressing. • MTN controller with simple structure, good real-time and easy implementation. • Semi-globally, uniformly and ultimately bounded, and converge to a compact set. • An adaptive adjustment algorithm is developed to solve the problem. • Numerical simulation and a controller of a two-stage manipulator verifying. [ABSTRACT FROM AUTHOR]

In this paper, an inverse control scheme based on the novel dynamic network (multi-dimensional Taylor network (MTN)) is proposed for the real-time tracking control of nonlinear time-varying systems with noise disturbances. Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling, the adaptive inverse controller for inverse modeling, and the adaptive nonlinear filter for eliminating the noise disturbances, whose weights are modified by the variable forgetting factor recursive least squares (VFF-RLS), back propagation through model (BPTM), normalized least mean square (NLMS) algorithms, respectively. To avoid "compromise", this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbances are implemented in two relatively independent processes. Furthermore, the weight-elimination algorithm is introduced for choice of effective regression items to avoid the dimension explosion, thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network. After a certain number of training, the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application. To ensure that MTN inverse control is strict in theory, the general conditions for the existence of single-input/single-output (SISO) nonlinear inverse systems are identified. Simulation of the MTN inverse control is conducted to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of multi-dimensional Taylor network (MTN) decentralised adaptive output-feedback tracking control is investigated for large-scale stochastic nonlinear systems. MTNs are used to approximate the unknown nonlinear functions, and a MTN state observer is designed for estimating the unmeasured states. Based on the designed MTN state observer, and by combining the backstepping technique with dynamic surface control (DSC), an adaptive MTN decentralised output-feedback tracking control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability, and the tracking errors converge to an arbitrarily small neighbourhood around the origin in the sense of mean quartic value. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and the simulation results demonstrate that the proposed method promises desirable real-time performance and tracking control. [ABSTRACT FROM AUTHOR]

MTN optimal control scheme of SISO nonlinear time-varying discrete-time systems based on multi-dimensional Taylor network (MTN) is proposed to achieve the real-time output tracking control for a given reference signal. Firstly, an ideal output signal is selected and Pontryagin minimum principle adopted to obtain the numerical solution of the optimal control law for the system relative to the ideal output signal, with the corresponding optimal output termed as desired output signal. Then, MTN optimal controller (MTNC) is generated automatically to fit the optimal control law, and the conjugate gradient (CG) method is employed to train the weight parameters of MTNC offline to acquire the initial weight parameters of MTNC for online training that guarantees the stability of closed-loop system. Finally, a four-term back propagation (BP) algorithm with a second order momentum term and error term is proposed to adjust the weight parameters of MTNC adaptively to implement the output tracking control of the systems in real time; the convergence conditions for the four-term BP algorithm are determined and proved. Simulation results show that the proposed MTN optimal control scheme is valid; the system's actual output response is capable of tracking the given reference signal in real time. [ABSTRACT FROM AUTHOR]

Summary This paper investigates the problem of adaptive multi‐dimensional Taylor network (MTN) decentralized tracking control for large‐scale stochastic nonlinear systems. Minimizing the influence of randomness and complex nonlinearity, which increases computational complexity, and improving the controller's real‐time performance for the stochastic nonlinear system are of great significance. With combining adaptive backstepping with dynamic surface control, a decentralized adaptive MTN tracking control approach is developed. In the controller design, MTNs are used to approximate nonlinearities, the backstepping technique is employed to construct the decentralized adaptive MTN controller, and the dynamic surface control technique is adopted to avoid the "explosion of computational complexity" in the backstepping design. It is proven that all the signals in the closed‐loop system remain bounded in probability, and the tracking errors converge to a small residual set around the origin in the sense of a mean quartic value. As the MTN contains only addition and multiplication, the proposed control method is more simplified and of good real‐time performance, compared with the existing control methods for large‐scale stochastic nonlinear systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this paper has good real‐time performance and control quality, and the dynamic performance of the closed‐loop system is satisfactory. [ABSTRACT FROM AUTHOR]