Nth-order fuzzy linear differential equations

In this paper a numerical method for solving nth-order linear differential equations with fuzzy initial conditions is considered. The idea is based on the collocation method. The existence theorem of the fuzzy solution is considered. This method is illustrated by solving several examples.     

Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme

This article describes a finite difference scheme which is linearly uncoupled in computation for a nonlinearly coupled Schrödinger system. This numerical scheme is proved to preserve the original conservative properties. Using the discrete energy analysis method, we also prove that the scheme is unconditionally stable and second-order convergent in discrete _L2$L_2$-norm based on some preliminary estimations. The results show that the new scheme is efficiency.     

Stability of linear multistep methods for delay integro-differential equations

This paper is concerned with the numerical solution of delay integro-differential equations. The adaptation of linear multistep methods is considered. The emphasis is on the linear stability of numerical methods. It is shown that every A-stable, strongly 0-stable linear multistep method of Pouzet type can preserve the delay-independent stability of the underlying linear systems. In addition, some delay-dependent stability conditions for the stability of numerical methods are also given.     

A novel fault-tolerant sensor system for sensor drift compensation

The conventional fault-tolerant sensor systems would fail when outputs from incorporated sensors are either noisy or drifting. This paper presents a novel real-time fault compensation method, which uses state estimation and compensation techniques, that the sensor system can perform robust measurements even when outputs from every incorporated sensor are noisy and drifting. In a simulation example, the proposed design can detect and correct the sensor errors (dc bias and drift) in real time. For the dc bias, the minimum detectable offset value is 0.1, which is the same as the standard deviation of the sensor noise. The compensated sensor output is biased at values smaller than 0.02. For the sensor drifts, the proposed method can compensate drifts for the change rate of drifts up to four times faster than that of the signal to be measured. The highest change rate of drifts, that can be compensated by this method, is determined by the standard deviation of the sensor noise.     

Stability and control of nonlinear systems described by retarded functional equations: a review of recent results

This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.     

Lyapunov-based boundary feedback control in multi-reach canals

This paper presents a Lyapunov-based approach to design the boundary feedback control for an openchannel network composed of a cascade of multi-reach canals, each described by a pair of Saint-Venant equations. The weighted sum of entropies of the multi-reaches is adopted to construct the Lyapunov function. The time derivative of the Lyapunov function is expressed by the water depth variations at the gate boundaries, based on which a class of boundary feedback controllers is presented to guarantee the local asymptotic closed-loop stability. The advantage of this approach is that only the water level depths at the gate boundaries are measured as the feedback. Supported by the National Natural Science Foundation of China (Grant Nos. 60504026, 60674041), and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z173)     

酒精五塔蒸馏工艺过程模拟

针对典型的酒精蒸馏五塔工艺流程及蒸馏过程各物流的组成、压力、温度等工艺条件,分析模拟计算的热力学方法和热力学数据,结果表明,本文所选用的热力学方法SRKM、IDEAL、NRTL及物流组分交互作用参数均适用于酒精蒸馏五塔工艺流程,各工艺物流的模拟数据与设计数据最大误差均小于4.5%,模拟值与设计值比较吻合,不超出设计误差(10%)的限度.     

Control of 1-D parabolic PDEs with Volterra nonlinearities, Part I: Design

Boundary control of nonlinear parabolic PDEs is an open problem with applications that include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present stabilizing control designs for a broad class of nonlinear parabolic PDEs in 1-D. Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and employs spatial Volterra series nonlinear operators both in the transformation to a stable linear PDE and in the feedback law. The control law design consists of solving a recursive sequence of linear hyperbolic PDEs for the gain kernels of the spatial Volterra nonlinear control operator. These PDEs evolve on domains T_n of increasing dimensions n+1 and with a domain shape in the form of a “hyper-pyramid”, 0≤ξ_n≤ξ_n−1?≤ξ₁≤x≤1. We illustrate our design method with several examples. One of the examples is analytical, while in the remaining two examples the controller is numerically approximated. For all the examples we include simulations, showing blow up in open loop, and stabilization for large initial conditions in closed loop. In a companion paper we give a theoretical study of the properties of the transformation, showing global convergence of the transformation and of the control law nonlinear Volterra operators, and explicitly constructing the inverse of the feedback linearizing Volterra transformation; this, in turn, allows us to prove L² and H¹ local exponential stability (with an estimate of the region of attraction where possible) and explicitly construct the exponentially decaying closed loop solutions.     

Controller synthesis with guaranteed closed-loop phase constraints

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval [−α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function.