A 2-dimensional stochastic Burgers equation with dissipative term perturbed by Wiener noise is considered. The aim is to prove the well-posedness, existence, and uniqueness of invariant measure as well as strong law of large numbers and convergence to equilibrium.

The stability problem is investigated for a class of uncertain networks of neutral type with leakage, time-varying discrete, and distributed delays. Both the parameter uncertainty and the generalized activation functions are considered in this paper. New stability results are achieved by constructing an appropriate Lyapunov-Krasovskii functional and employing the free weighting matrices and the linear matrix inequality (LMI) method. Some numerical examples are given to show the effectiveness and less conservatism of the proposed results.

A new approach of real-time path planning based on belief space is proposed, which solves the problems of modeling the real-time detecting environment and optimizing in local path planning with the fusing factors. Initially, a double-safe-edges free space is defined for describing the sensor detecting characters, so as to transform the complex environment into some free areas, which can help the robots to reach any positions effectively and safely. Then, based on the uncertainty functions and the transferable belief model (TBM), the basic belief assignment (BBA) spaces of each factor are presented and fused in the path optimizing process. So an innovative approach for getting the optimized path has been realized with the fusing the BBA and the decision making by the probability distributing. Simulation results indicate that the new method is beneficial in terms of real-time local path planning.

The nonlinear model of main drive system in cold rolling process, which considers the influence with parameter uncertainties such as clearance and variable friction coefficient, as well as external disturbance by roll eccentricity and variation of strip material quality, is built. By transformation, the lower triangular structure form of main drive system is obtained. The backstepping algorithm based on signal compensation is proposed to design a linear time-invariant (LTI) robust controller, including a nominal controller and a robust compensator. A comparison with PI controller shows that the controller has better disturbance attenuation performance and tracking behaviors. Meanwhile, according to its LTI characteristic, the robust controller can be realized easily; therefore it is also appropriated to high speed dynamic rolling process.

A model predictive control (MPC) is proposed for the piecewise affine (PWA) systems with constrained input and time delay. The corresponding operating region of the considered systems in state space is described as ellipsoid which can be characterized by a set of vector inequalities. And the constrained control input of the considered systems is solved in terms of linear matrix inequalities (LMIs). An MPC controller is designed that will move the PWA system with time delay from the current operating point to the desired one. Multiple objective functions are used to relax the monotonically decreasing condition of the Lyapunov function when the control algorithm switches from a quasi-infinite horizon to an infinite horizon strategy. The simulation results verify the effectiveness of the proposed method. It is shown that, based on LMI constraints, it is easy to get the MPC for the PWA systems with time delay. Moreover, it is suitable for practical application.

Focusing on the analog circuit performance evaluation demand of fast time responding online, a novel evaluation strategy based on adaptive Least Squares Support Vector Regression (LSSVR) which employs multikernel RBF is proposed in this paper. The superiority of the multi-kernel RBF has more flexibility to the kernel function online such as the bandwidths tuning. And then the decision parameters of the kernel parameters determine the input signal to map to the feature space deduced that a well plant model by discarding redundant features. Experiment adopted the typical circuit Sallen-Key low pass filter to prove the proposed evaluation strategy via the eight performance indexes. Simulation results reveal that the testing speed together with the evaluation performance, especially the testing speed of the proposed, is superior to that of the traditional LSSVR and $\epsilon$-SVR, which is suitable for promotion online.

We consider the exponential stabilization for Timoshenko beam with distributed delay in the boundary control. Suppose that the controller outputs are of the form ${\alpha }_{\mathrm{1}}{u}_{\mathrm{1}}(t)+{\beta }_{\mathrm{1}}{u}_{\mathrm{1}}(t-\tau )+{\int }_{-\tau }^{\mathrm{0}}\mathrm{‍}{g}_{\mathrm{1}}(\eta )u_{\mathrm{1}}(t+\eta )d\eta$ and ${\alpha }_{\mathrm{2}}{u}_{\mathrm{2}}(t)+{\beta }_{\mathrm{2}}{u}_{\mathrm{2}}(t-\tau )+{\int }_{-\tau }^{\mathrm{0}}\mathrm{‍}{g}_{\mathrm{2}}(\eta )u_{\mathrm{2}}(t+\eta )d\eta$; where $u_{\mathrm{1}}(t)$ and $u_{\mathrm{2}}(t)$ are the inputs of boundary controllers. In the past, most stabilization results for wave equations and Euler-Bernoulli beam with delay are required ${\alpha }_i>{\beta }_i>\mathrm{0},i=\mathrm{1,2}$. In the present paper, we will give the exponential stabilization about Timoshenko beam with distributed delay and demand to satisfy the lesser conditions for ${\alpha }_i,{\beta }_i,i=\mathrm{1,2}$.

Due to the recent rapid growth of advanced sensing and production technologies, the monitoring and diagnosis of multivariate process operating performance have drawn increasing interest in process industries. The multivariate statistical process control (MSPC) chart is one of the most commonly used tools for detecting process faults. However, an out-of-control MSPC signal only indicates that process faults have intruded the underlying process. Identifying which of the monitored quality variables is responsible for the MSPC signal is fairly difficult. Pinpointing the responsible variable is vital for process improvement because it effectively determines the root causes of the process faults. Accordingly, this identification has become an important research issue concerning recent multivariate process applications. In contrast with the traditional single classifier approach, the present study proposes hybrid modeling schemes to address problems that involve a large number of quality variables in a multivariate normal process. The proposed scheme includes multivariate adaptive regression splines (MARS), logistic regression (LR), and artificial neural network (ANN). By applying MARS and LR techniques, we may obtain fewer but more significant quality variables, which can serve as inputs to the ANN classifier. The performance of our proposed approaches was evaluated by conducting a series of experiments.

We investigate the state-feedback stabilization problem for a class of stochastic feedforward nonlinear time-delay systems. By using the homogeneous domination approach and choosing an appropriate Lyapunov-Krasovskii functional, the delay-independent state-feedback controller is explicitly constructed such that the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the proposed design method.

A nonlinear model predictive control (MPC) is proposed for underactuated surface vessel (USV) with constrained invariant manifolds. Aimed at the special structure of USV, the invariant manifold under the given controller is constructed in terms of diffeomorphism and Lyapunov stability theory. Based on MPC, the states of the USV are steered into the constrained terminal invariant manifolds. After the terminal manifolds set is reached, a linear feedback control is used to stabilize the system. The simulation results verified the effectiveness of the proposed method. It is shown that, based on invariant manifolds constraints, it is easy to get the MPC for the USV and it is suitable for practical application.