Output Regulation for a Class of Infinite Dimensional Systems with an Unknown Exosystem

This paper is about solving the output regulation problem for a class of infinite dimensional systems with an unknown exosystem. First, under the unit relative degree assumption, the infinite dimensional system is decomposed into a cascaded one composed of a one‐dimensional system and an infinite dimensional system. Then, the problem is solved by combining an adaptive internal model and an adaptive control. The presented results are illustrated via a periodic tracking problem of a heat equation.     

Biologically Plausible Associative Memory: Continuous Unit Response + Stochastic Dynamics

A neural network model of associative memory is presented which unifies the two historically more relevant enhancements to the basic Little-Hopfield discrete model: the graded response units approach and the stochastic, Glauber-inspired model with a random field representing thermal fluctuations. This is done by casting the retrieval process of the model with graded response neurons, into the framework of a diffusive process governed by the Fokker-Plank equation, which leads to a Langevin system describing the process at a microscopic level, while the time evolution of the probability density function is governed by a multivariate Fokker Planck equation operating over the space of all possible activation patterns. The present unified approach has two notable features: (i) greater biological plausibility and (ii) ability to escape local minima of energy (associated with spurious memories), which makes it a potential tool for those complex optimization problems for which the previous models failed.     

Liveness Checking as Safety Checking for Infinite State Spaces

In previous work we have developed a syntactic reduction of repeated reachability to reachability for finite state systems. This may lead to simpler and more uniform proofs for model checking of liveness properties, help to find shortest counterexamples, and overcome limitations of closed-source model-checking tools. In this paper we show that a similar reduction can be applied to a number of infinite state systems, namely, (ω−)regular model checking, push-down systems, and timed automata.     

尺度空间的联想记忆网络在灰度图中的应用

形态联想记忆网络具有十分优越的抗膨胀噪声或者腐蚀噪声的能力,但抗混合噪声的能力很弱,而在实际中,随机噪声往往是混合型的,既有膨胀噪声又有腐蚀噪声.将形态学尺度空间和形态联想记忆网络相结合,得到了一种新的联想记忆网络,它也具有优越的抗膨胀噪声或者腐蚀噪声的能力,同时它对随机噪声有一定的鲁棒性.通过对含有随机噪声的灰度图像进行自联想记忆和识别处理实验,取得了较为理想的结果,验证了其具有良好的性能.     

A Continuous-Time Model of Autoassociative Neural Memories Utilizing the Noise-Subspace Dynamics

This paper presents a continuous-time model of Autoassociative Neural Memories (ANMs) which correspond to a modified version of pseudoinverse-type ANMs. This ANM model is derived from minimizing the energy function for a modular neural network. Through the eigendecomposition of the connection matrix, we show that the dynamical properties of the ANM are qualitatively different in the two state subspaces: a pattern-subspace and a noise-subspace. The proposed ANM has a distinctive feature in the noise-subspace dynamics. The size of basins of attraction can be varied by controlling the contribution of the noise-subspace dynamics to the whole network. The first simulation confirms this attractive feature. In the second simulation, we investigate the performance robustness of the ANM for several kinds of correlated pattern sets. These simulation results confirm the usefulness of the proposed ANM.     

Boundary and Distributed Control for a Nonlinear Three‐Dimensional Euler‐Bernoulli Beam Based On Infinite Dimensional Disturbance Observer

Control problems in spatially distributed systems are challenging because the disturbance is of infinite dimensions. To this end, this paper discusses an infinite dimensional disturbance observer design, which is illustrated based on a partial differential equation (PDE) model of a nonlinear three‐dimensional Euler‐Bernoulli beam. The basic idea of the observer design is to modify the estimations based on the difference between the estimated output and actual output. Moreover, an auxiliary parameter system is established to help with the analysis. Then a Lyapunov function candidate consisting of the energy of the system, the observer error and an auxiliary term is given. After a series of analyses of the function, distributed controllers and boundary controllers based on the proposed observer are given to restrain vibration. Finally, by numerical simulations, the convergence of the observer is demonstrated, and the efficacy of control performance is also shown.     

时滞杂交双向联想记忆神经网络的全局指数稳定性

在近十几年里，已提出了一类与双向联想记忆相联系的神经网络模型，这些模型推广了单层自联想Hebbian相关器为两层异联想模式匹配器，因而，这类网络在模式识别、信号与图像处理等领域中有广阔的应用前景．研究了带离散时滞杂交双向联想记忆神经网络的收敛特性，利用Halanay型不等式获得了网络全局指数稳定性的充分条件，所得结果是与时滞无关的；已证明利用Halanay型不等式获得的结果改进了由Lyapunov方法获得的结果，而且获得的结果容易判定，并且给出了一个数值例子以说明所得结论的正确性．     

Finite Memory Loading in Hairy Neurons

This paper presents a method to expand the basins of stable patterns in associative memory. It examines fully-connected associative memory geometrically and translate the learning process into an algebraic optimization procedure. It finds that locating all the patterns at certain stable corners of the neurons’ hypercube as far from the decision hyperplanes as possible can produce excellent error tolerance. It then devises a method based on this finding to develop the hyperplanes. This paper further shows that this method leads to the hairy model, or the deterministic analogue of the Gibb’s free energy model. Through simulations, it shows that this method gives better error tolerance than does the Hopfield model and the error-correction rule in both synchronous and asynchronous modes.     

Stability Analysis of Linear Shift‐Invariant Dynamics in Honeycomb Structure

This paper deals with the stability of linear shift‐invariant multidimensional dynamical systems defined on honeycomb structure. Two different honeycomb structures are discussed. The local dynamical states are assumed to be distributed to honeycomb cells in the first consideration, and they are assumed to be distributed to the nodes of honeycomb mesh in the second consideration. In each honeycomb structure, the fundamental linear shift‐invariant dynamics is introduced and then the stability criterion is presented.     

Existence and stability of limit cycles in control of anti-lock braking systems with two boundaries via perturbation theory

This paper presents a two-phase control logic for anti-lock braking systems (ABS). ABS are by now a standard component in every modern car, preventing the wheels from going into a lock situation where the wheels are fixed by the brake and the stopping distances are greatly prolonged. There are different approaches to such control logics. An ABS design proposed in recent literature controls the wheel's slip by creating stable limit cycles in the corresponding phase space. This design is modified via an analytical approach that is derived from perturbation theory. Simulation results document shorter braking distance compared to available tests in the literature.