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Control of stochastic nonlinear systems turns out to be notoriously difficult when stochastic uncertainties and time‐varying delays occur simultaneously. This article presents a tractable adaptive control scheme for the stochastic nonlinear system with time‐varying delays. To mitigate the effects of stochastic uncertainties, an adaptive embedded cubature Kalman filter is developed to realize the robust estimation of the state. Unlike the conventional cubature Kalman filter with fixed construction, a semi‐definite programming is designed to adjust the weights of cubature points dynamically. Such programming guarantees the positive definiteness of the error covariance matrix, which enhances the reliability of the filtering procedure. Based on more accurate state estimations, the multidimensional Taylor network (MTN) is utilized to evaluate the dynamic performance under time‐varying delays and approximate the optimal policy in the deterministic policy gradient framework. Adaptive tracking control with high computational efficiency is achieved due to the concise topological structure of MTN. The exponential convergence of the state estimation error and the semi‐globally uniform ultimate boundness of the tracking error are verified theoretically. The effectiveness of the proposed method is confirmed by a numerical simulation based on a practical electric industrial system. [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]

In view of the difficulty of modelling time-varying nonlinear systems, a multidimensional Taylor network (MTN) model based on dynamic characteristic clustering is proposed to establish an online time series forecasting model. The construction method of a MTN, the definitions of the dynamic characteristics, and their similarity criteria are discussed. Specific steps of the MTN online model, based on dynamic clustering, are given. A practical example is presented to demonstrate how the proposed method works in a real application, and its effectiveness is verified. [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, an adaptive control approach based on the multi‐dimensional Taylor network (MTN) is proposed to control the non‐linear uncertain time‐varying systems with noise disturbances. MTNs are introduced to formulate adaptive filtering, non‐linear identification and optimal control. First, an MTN filter is developed to eliminate the control interference and measurement noise, so that the model output without stochastic disturbance can be obtained. Then, an MTN identifier (MTNI) is so designed as to be capable of dynamic mapping and require fewer weights than traditional neural networks. On the basis of the above, the MTN controller (MTNC) is developed to realise the precise tracking control of the system. The non‐linear uncertain time‐varying system is identified by MTNI, which then provides sensitivity information of the plant to MTNC to make it adaptive. Furthermore, the skeletonisation algorithm is adopted to remove redundant inputs and redundant regression items from MTNI and MTNC for concise MTNs. Successful convergence and faster learning are guaranteed using the Lyapunov theorem, and the optimal learning rates are identified. Simulation results demonstrate that the proposed approach features its accurate identification, excellent tracking and better anti‐interference capability for the adaptive real‐time control of uncertain, stochastic and time‐varying non‐linear systems. [ABSTRACT FROM AUTHOR]

Nonlinear time-varying systems without mechanism models are common in application. They cannot be controlled directly by the traditional control methods based on precise mathematical models. Intelligent control is unsuitable for real-time control due to its computation complexity. For that sake, a multidimensional Taylor network (MTN) based output tracking control scheme, which consists of two MTNs, one as an identifier and the other as a controller, is proposed for SISO nonlinear time-varying discrete-time systems with no mechanism models. A MTN identifier is constructed to build the offline model of the system, and a set of initial parameters for online learning of the identifier is obtained. Then, an ideal output signal is selected relative to the given reference signal. Based on the system identification model, Pontryagin minimum principle is introduced to obtain the numerical solution of the optimal control law for the system relative to the given ideal output signal, with the corresponding optimal output taken as the desired output signal. A MTN controller is generated automatically to fit the numerical solution of the optimal control law using the conjugate gradient (CG) method, and a set of initial parameters for online learning of the controller is obtained. An adaptive back propagation (BP) algorithm is developed to adjust the parameters of the identifier and controller in real time, and the convergence for the proposed learning algorithm is verified. Simulation results show that the proposed scheme is valid. [ABSTRACT FROM AUTHOR]