Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle

In this paper, sampled-data based average-consensus control is considered for networks consisting of continuous-time first-order integrator agents in a noisy distributed communication environment. The impact of the sampling size and the number of network nodes on the system performances is analyzed. The control input of each agent can only use information measured at the sampling instants from its neighborhood rather than the complete continuous process, and the measurements of its neighbors’ states are corrupted by random noises. By probability limit theory and the property of graph Laplacian matrix, it is shown that for a connected network, the static mean square error between the individual state and the average of the initial states of all agents can be made arbitrarily small, provided the sampling size is sufficiently small. Furthermore, by properly choosing the consensus gains, almost sure consensus can be achieved. It is worth pointing out that an uncertainty principle of Gaussian networks is obtained, which implies that in the case of white Gaussian noises, no matter what the sampling size is, the product of the steady-state and transient performance indices is always equal to or larger than a constant depending on the noise intensity, network topology and the number of network nodes.     

The generalization of a class of impulse stochastic control models of a geometric Brownian motion

Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment. This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process. By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls. Meanwhile, we also analyze the structure of optimal controls carefully. Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent. Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent. In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense. Supported by the National Natural Science Foundation of China (Grant No. 19671004)     

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.     

A single layer zero skew clock routing in X architecture

With its advantages in wirelength reduction and routing flexibility compared with conventional Manhattan routing, X architecture has been proposed and applied to modern IC design. As a critical part in high-performance integrated circuits, clock network design meets great challenges due to feature size decrease and clock frequency increase. In order to eliminate the delay and attenuation of clock signal introduced by the vias, and to make it more tolerant to process variations, in this paper, we propose an algorithm of a single layer zero skew clock routing in X architecture (called Planar-CRX). Our Planar-CRX method integrates the extended deferred-merge embedding algorithm (DME-X, which extends the DME algorithm to X architecture) with modified Ohtsuki’s line-search algorithm to minimize the total wirelength and the bends. Compared with planar clock routing in the Manhattan plane, our method achieves a reduction of 6.81% in total wirelength on average and gets the resultant clock tree with fewer bends. Experimental results also indicate that our solution can be comparable with previous non-planar zero skew clock routing algorithm. Supported in part by the National Natural Science Foundation of China (Grant No. 60876026), and the Specialized Research Fund for the Doctoral Program of Higher Education (Crant No. 200800030026)     

Generating planar spiral by geometry driven subdivision scheme

Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry...     

Polarization discrimination between repeater false-target and radar target

High fidelity repeater false-target badly affects a radar system’s detecting, tracking, and data processing. It is an available approach of confronting false-target for radar that discriminates firstly and then eliminates. Whereas for the technique progress about the repeater false-target jam, it is more and more difficult to discriminate this jam in the time-domain, frequency-domain, or space-domain. The technique using polarization information to discriminate the target and false-target is discussed in th...     

Controllability of multi-agent systems based on agreement protocols

This paper investigates the controllability of multi-agent systems based on agreement protocols. First, for a group of single-integrator agents, the controllability is studied in a unified framework for both networks with leader-following structure and networks with undirected graph. Some new necessary/sufficient conditions for the controllability of networks of single-integrator agents are established. Second, we prove that, under the same topology and same prescribed leaders, a network of high-order dynamic agents is completely controllable if and only if so is a network of single-integrator agents. Third, how the selection of leaders and the coupling weights of graphs affect the controllability is analyzed. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.     

Texture synthesis via the matching compatibility between patches

A new patch-based texture synthesis method is presented in this paper. By the method, a set of patches that can be matched with a sampled patch for growing textures effectively, called the matching compatibility between patches, is generated first for each patch, and the set is further optimized by culling the patches that may cause synthesis conflicts. In this way, similarity measurement calculation for selecting suitable patches in texture synthesis can be greatly saved, and synthesis conflicts between neighbouring patches are substantially reduced. Furthermore, retrace computation is integrated in the synthesis process to improve the texture quality. As a result, the new method can produce high quality textures as texture optimization, the best method to date for producing good textures, and run in a time complexity linear to the size of the output texture. Experimental results show that the new method can interactively generate a large texture in 1024 × 1024 pixels, which is very difficult to achieve by existing methods. Supported by the National Basic Research Program of China (Grant No. 2009CB320802), the National Natural Science Foundation of China (Grant Nos. 60773026, 60833007), the National High-Tech Research & Development Program of China (Grant Nos. 2006AA01Z306, 2008AA01Z301), and the Research Grant of University of Macau     

Accurate evaluation of Green’s functions in a layered medium by SDP-FLAM

Based on local Taylor expansions on the complex plane, a method for fast locating all modes (FLAM) of spectral-domain Green’s Functions in a planar layered medium is developed in this paper. SDP-FLAM, a combination of FLAM with the steepest descent path algorithm (SDP), is employed to accurately evaluate the spatial-domain Green’s functions in a layered medium. According to the theory of complex analysis, the relationship among the poles, branch points and Riemann sheets is also analyzed rigorously. To inverse the Green’s functions from spectral to spatial domain, SDP-FLAM method and discrete complex image method (DCIM) are applied to the non-near field region and the near filed region, respectively. The significant advantage of SDP-FLAM lies in its capability of calculating Green’s functions in a layered medium of moderate thickness with loss or without loss. Some numerical examples are presented to validate SDP-FLAM method. Supported by the National Natural Science Foundation of China (Grant No. 60621002), and the State Key Development Program for Basic Research of China (Grant No. 2009CB320200)     

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)