Adaptive tracking control for stochastic nonlinear systems with time-varying delays using multi-dimensional Taylor network.

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.

MTN output feedback tracking control for MIMO discrete-time uncertain nonlinear systems.

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.

Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems with time-varying delay.

Though many studies are focused on the stabilization of nonlinear systems with time-varying delay, they fail to involve the dynamic regulation without on-line optimization commonly. For this sake, feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem are employed here to verify that the multi-dimensional Taylor network (MTN) controller can stabilize the single input single output (SISO) nonlinear time-varying delay systems through dynamic regulation of the system output with no need for on-line optimization. Here, the design of the controller is transformed into a convex optimization problem, which is tackled by means of the appropriate optimization method. Like its PD-like controller peers, the MTN controller functions well in eliminating the dependence on the system model. The effectiveness of the proposed approach is demonstrated and confirmed via two examples.

An approach to estimating product design time based on fuzzy v-support vector machine.

This paper presents a new version of fuzzy support vector machine (FSVM) developed for product design time estimation. As there exist problems of finite samples and uncertain data in the estimation, the input and output variables are described as fuzzy numbers, with the metric on fuzzy number space defined. Then, the fuzzy v-support vector machine (Fv-SVM) is proposed on the basis of combining the fuzzy theory with the v-support vector machine, followed by the presentation of a time estimation method based on Fv-SVM and its relevant parameter-choosing algorithm. The results from the applications in injection mold design and software product design confirm the feasibility and validity of the estimation method. Compared with the fuzzy neural network (FNN) model, our Fv-SVM method requires fewer samples and enjoys higher estimating precision.