Publications

A spectral-approximation-based intelligent modeling approach is proposed for the distributed thermal processing of the snap curing oven that is used in semiconductor packaging industry. The snap curing oven can be described by a nonlinear parabolic distributed parameter system (DPS) in the time-space domain. After finding a proper approximation of the complex boundary conditions of the system, the spectral methods can be applied to time-space separation and model reduction, and neural networks (NNs) can be used for state estimation and system identification. With the help of model reduction techniques, the dynamics of the curing process derived from physical laws can be described by a model of low-order nonlinear ordinary differential equations with a few uncertain parameters and unknown nonlinearities. A neural observer can then be designed to estimate the states of the ordinary differential equation model from measurements taken at specified locations in the field. Using the estimated states, a hybrid general regression NN is trained to be a nonlinear model of the curing process in state-space formulation, which is suitable for the further application of traditional control techniques. Real-time experiments on the snap curing oven show that the proposed modeling method is effective. This modeling methodology can be applied to a class of nonlinear DPSs in industrial thermal processing.

<abstract><p>The inverse Frobenius-Perron problem (IFPP) is a collective term for a family of problems that requires the construction of an ergodic dynamical system model with prescribed statistical characteristics. Solutions to this problem draw upon concepts from ergodic theory and are scattered throughout the literature across domains such as physics, engineering, biology and economics. This paper presents a survey of the original formulation of the IFPP, wherein the invariant probability density function of the system state is prescribed. The paper also reviews different strategies for solving this problem and demonstrates several of the techniques using examples. The purpose of this survey is to provide a unified source of information on the original formulation of the IFPP and its solutions, thereby improving accessibility to the associated modeling techniques and promoting their practical application. The paper is concluded by discussing possible avenues for future work.</p></abstract>

This paper is devoted to the study of the modified minimal variance control (MMVC) of discrete‐time first‐order linear critically stable stochastic systems with prospective strong intervention (PSI) and control input constraints. Due to different evolutionary characteristics of systems with PSI, that is, the two modes of tending to infinity and having bounded oscillations, the discrete‐time first‐order linear critically stable systems can be partitioned into two types regarding the signs of a key system parameter a . A necessary and sufficient condition for the state mean convergence of a system with a = 1 is derived and the corresponding design of MMVC is formulated. For the critical stable system with a =− 1, its oscillation amplitudes of state means can be effectively suppressed or the means can converge under control. Finally, the effectiveness and advantages of the proposed control strategies comparing with MVC are confirmed by numerical simulations.

This paper proposes a novel multiscroll chaotic system, which is different from Chua's circuit and all its variants in most aspects of the algebraic form, circuit design, and geometrical structure of the attractor. In particular, the multiscroll attractor of this new system is more complex than that of the generalized Chua's circuit when they both have the same number of scrolls. The dynamical behaviors of the new system are then analyzed, including the bifurcation diagram and the Lyapunov exponent spectra. Moreover, a module-based circuit diagram is designed for realizing various multiscroll attractors. Finally, experimental circuits are implemented with physical observations reported.

This paper studies consensus and quasi-consensus in multi-agent dynamical systems. A linear consensus protocol in the second-order dynamics is designed where both the current and delayed position information is utilized. Time delay, in a common perspective, can induce periodic oscillations or even chaos in dynamical systems. However, it is found in this paper that consensus and quasi-consensus in a multi-agent system cannot be reached without the delayed position information under the given protocol while they can be achieved with a relatively small time delay by appropriately choosing the coupling strengths. A necessary and sufficient condition for reaching consensus in multi-agent dynamical systems is established. It is shown that consensus and quasi-consensus can be achieved if and only if the time delay is bounded by some critical value which depends on the coupling strength and the largest eigenvalue of the Laplacian matrix of the network. The motivation for studying quasi-consensus is provided where the potential relationship between the second-order multi-agent system with delayed positive feedback and the first-order system with distributed-delay control input is discussed. Finally, simulation examples are given to illustrate the theoretical analysis.

The Laplacian eigenvalue spectrum of a complex network contains a great deal of information about the network topology and dynamics, particularly affecting the network synchronization process and performance. This article briefly reviews the recent progress in the studies of network synchronizability, regarding its spectral criteria and topological optimization, and explores the role of higher-order topologies in measuring the optimal synchronizability of large-scale complex networks.

<p>Recently, a necessary and sufficient condition for multivaluedness to be implicitly exhibited by counter-cascaded systems was presented. Subsequently, several systems that exhibit multivaluedness were reported. This brief interprets a general information transmission system as a counter-cascaded system with Shannon’s noisy-channel coding theorem providing the necessary and sufficient conditions for multivaluedness and is therefore a particular instance of the counter-cascaded network framework.</p>

This paper answers affirmatively Problem 32 posted in \cite{GMM2012}, proving that, for every stationary fuzzy metric space $(X, M, *)$, the function $M_y(x):=M(x,y)$ defined therein is $\mathbb{R}$-uniformly continuous for all $y\in X$, and furthermore proves that the function $M$ is $\mathbb{R}$-uniformly continuous.

This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernández et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

No abstract is provided for this article.