Synchronization of chaotic attractors with different equilibrium points

This paper investigates the synchronization of coupled chaotic systems with many equilibrium points. By addition of an external switching piecewise-constant controller, the system changes to a new one with several independent chaotic attractors in the state space. Then, by addition of a nonlinear state feedback control, the chaos synchronization is presented. This method can be used in many couples of chaotic systems characterized by the same equilibrium point or by two different equilibrium points, even they are the same systems (Lorenz, Jerk, Van der Pol) or two chaotic systems with different structures (Lorenz modified).     

On the stability of the information state system

The purpose of this paper is to present some preliminary results on the stability of the information state system. The information state system underlies the (infinite dimensional) dynamics of an H_∞ controller for a nonlinear system. Thus it is important to understand its stability and the structure of its equilibrium points. We analyse the important case corresponding to the mixed sensitivity problem. We prove the existence of an equilibrium information state, convergence under very general conditions to such an equilibrium state p_e and uniqueness of this state (up to an irrelevant constant). In this case the equilibrium p_e is usually singular in the sense that it takes on the value − ∞ except on a low dimensional subset of its domain.This meshes with the article [9] which analysed the effect of using p_e to initialize the information state controller and gave explicit formulas which in many cases produce a dramatic reduction in the amount of computation required to implement the controller. What this article suggests is that indeed p_e is the only equilibrium initialization possible.     

Using Event-Based Method to Estimate Cybersecurity Equilibrium

Estimating the global state of a networked system is an important problem in many application domains.The classical approach to tackling this problem is the periodic(observation)method,which is inefficient because it often observes states at a very high frequency.This inefficiency has motivated the idea of event-based method,which leverages the evolution dynamics in question and makes observations only when some rules are triggered(i.e.,only when certain conditions hold).This paper initiates the investigation of using the event-based method to estimate the equilibrium in the new application domain of cybersecurity,where equilibrium is an important metric that has no closed-form solutions.More specifically,the paper presents an event-based method for estimating cybersecurity equilibrium in the preventive and reactive cyber defense dynamics,which has been proven globally convergent.The presented study proves that the estimated equilibrium from our trigger rule i)indeed converges to the equilibrium of the dynamics and ii)is Zeno-free,which assures the usefulness of the event-based method.Numerical examples show that the event-based method can reduce 98%of the observation cost incurred by the periodic method.In order to use the event-based method in practice,this paper investigates how to bridge the gap between i)the continuous state in the dynamics model,which is dubbed probability-state because it measures the probability that a node is in the secure or compromised state,and ii)the discrete state that is often encountered in practice,dubbed sample-state because it is sampled from some nodes.This bridge may be of independent value because probability-state models have been widely used to approximate exponentially-many discrete state systems.     

线性控制系统动平衡状态分析

针对含有输入的动力系统的一类平衡状态(不是针对自由系统的某一个平衡点)进行了讨论。这个平衡状态与输入有关,所以被称作动平衡状态。在某些特定条件下,可以得到动平衡状态的表达式。通过推导和证明,建立了在奇异和非奇异两种线性系统下动平衡状态的表达式,同时还提出了动平衡状态可控性的概念和存在的条件。     

Optimization of microorganisms growth processes

Microorganisms growth processes are encountered in many biotechnological applications. For an increased economic benefit, optimizing their productivity is of great interest. Often the growth is inhibited by the presence in excess of other components. Inhibition determines the occurrence of multiple equilibrium points, which makes the optimal steady state reachable only from a small region of the system state space. Thus dynamic control is needed to drive the system from an initial state (characterized by a low concentration of microorganisms) to the optimal steady state. The strategy presented in this paper relies on the solutions of two optimization problems: the problem of optimal operation for maximum productivity in steady state (steady state optimization) and the problem of the start-up to the optimal steady state (transient optimization). Steady state optimization means determining the optimal equilibrium point (the amount of microorganisms harvested is maximum). The transient optimization is solved using the maximum principle of Pontryagin.The proposed control law, which drives the bioreactor from an initial state to the optimal steady state while maximizing the productivity, consists of switching the manipulated variable (dilution rate) from the minimum to the maximum value and then to the optimal value at well defined instants. This control law substantially increases the stability region of the optimal equilibrium point. Aside its efficiency, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any microorganisms growth process which involves only one biochemical reaction. This means that the sequence of the control levels does not depend on the structure and parameters of the reaction kinetics, the values of the yield coefficients or the number of components in the bioreactor.     

横风下高速列车系统动力学的平衡状态法

基于车辆-轨道耦合动力学和空气动力学提出了一种快速计算横风下高速列车系统动力学行为的平衡状态方法.首先,忽略轨道不平顺并利用流固耦合联合仿真方法计算横风下高速列车的平衡状态;然后,将平衡状态下的气动力加载到车辆-轨道耦合动力学模型并计算高速列车动力学响应.利用建立的平衡状态方法,研究了列车在速度为13.8 m/s的横风下以350 km/h速度运行时的流固耦合动力学行为.比较了平衡状态方法和联合仿真方法两种方法下列车姿态、安全性和舒适性指标的差异,计算结果差别在3.26%以内.研究结果表明:平衡状态方法计算横风下高速列车流固耦合的效率更高.     

离散事件动态系统

离散事件动态系统理论的应用十分广泛.它在计算机网络、柔性生产系统等领域的研究 中起着非常重要的作用.它必将成为控制理论的一个重要分支.本文重点叙述了离散事件 动态系统的几种排队网络模型及其稳态状态分布,给出了用离散事件动态系统描述计算机网 络、柔性生产系统的例子.     

Influence of Consumer Preferences on the Equilibrium in an Open Economy

This investigation describes possible equilibrium states of an open economy under the presence of monopolies. Walrasian equilibrium is considered. Each subject of the economy is an insatiable consumer. The structure of consumption in the economy depends on volumes of production of goods. An algorithm is proposed to solve the problem of economic equilibrium. The presented constraints on model characteristics provide the existence of equilibrium in the economy. The possibility of staying the economy in an equilibrium state with specified intervals of values of selected characteristics is revealed. The achievement of a desirable equilibrium state is provided by the choice of levels of taxation of monopolies.     

Biped side step in the frontal plane

A three-link planar model of a biped is studied in the frontal plane. When this model is subjected to certain on-off constraints, the forces of constraint are derived as functions of the system state and the input, and can be shown in a simple block diagram. Linear state-variable feedback is designed to stabilize and decouple the system for small motions about an equilibrium state. The motion of this biped is implemented as a sequence of state transitions between stable equilibrium states. Ramp state and input references are used to guide the biped system from one equilibrium state to the next. Single-support postural stabilization and side step and return motions were investigated by computer simulation in order to evaluate the effectiveness of this control strategy.     

The Lagrange problem on an optimal column: old and new results

The paper is devoted to the optimization and post-buckling behavior of columns elastically supported at both ends. The unimodal solutions are analyzed, and it is shown that for nonzero support stiffnesses they are not optimal. The bimodal formulation of the problem is set up. By using analytical expressions for bimodal columns obtained earlier, the bimodal optimal solutions are integrated for different values of the support stiffnesses. With the assumption of geometrical nonlinearity, the post-buckling behavior of the bimodal optimal columns is studied. It is shown that the initial post-buckling behavior is governed by four supercritical solutions emanating from the trivial equilibrium state at the critical load. The stability of the new equilibrium states is investigated by using the second variation of the total potential energy. It is shown that only two post-buckling equilibrium states are stable while the other two are unstable, this conclusion being valid for all considered values of the support stiffnesses. An important limit case of a clamped–simply supported column that has caused debate in many publications is analyzed.     

Robust control of a class of under-actuated mechanical systems with model uncertainty

Robust control of under-actuated mechanical systems (UMSs) with model uncertainty is still a challenging problem. For UMSs, the model parametric uncertainties make it difficult to precisely calculate the isolated equilibrium point corresponding to a fixed input. Without an accurate destination state, many set-point control methods cannot eliminate the positioning errors. An improved sliding mode control (ISMC) method is proposed to solve the robust control problem for a class of UMSs with model uncertainty and input disturbance. A balance variable is introduced in the sliding surface design to compensate for the disturbance caused by the inaccurate destination state, and the ISMC method is proposed to make the system state reach the sliding surface in finite time. Linear matrix inequality approach and particle swarm optimisation algorithm are applied to design the sliding mode surface parameters. The simulation results on an UMS are presented to show the effectiveness of the proposed scheme.     

Asymptotic Behavior and Stability for Solutions of a Biochemical Reactor Distributed Parameter Model

This paper deals with the dynamical analysis of a tubular biochemical reactor. The existence of nonnegative state trajectories and the invariance of the set of all physically feasible state values under the dynamical equation as well as the convergence of the state trajectories to equilibrium profiles are proved. In addition, the existence of multiple equilibrium profiles is analyzed. It is proved that, under physically meaningful conditions, the system has two stable and one unstable equilibrium profiles.      

Supply chain network equilibrium with revenue sharing contract under demand disruptions

Contract is a common and effective mechanism for supply chain coordination, which has been studied extensively in recent years. For a supply chain network model, contracts can be used to coordinate it because it is too ideal to obtain the network equilibrium state in practical market competition. In order to achieve equilibrium, we introduce revenue sharing contract into a supply chain network equilibrium model with random demand in this paper. Then, we investigate the influence on this network equilibrium state from demand disruptions caused by unexpected emergencies. When demand disruptions happen, the supply chain network equilibrium state will be broken and change to a new one, so the decision makers need to adjust the contract parameters to achieve the new coordinated state through bargaining. Finally, a numerical example with a sudden demand increase as a result of emergent event is provided for illustrative purposes.     

A stabilization method for steady motions with zero roots in the closed system

Based on previous results, we consider stabilization problems for both non-asymptotic stability and asymptotic stability with respect to all variables for equilibrium positions and stationary motions of mechanical systems with redundant coordinates. The linear stabilizing control is defined by the solution of a linear–quadratic stabilization problem for an allocated linear controllable subsystem of as small dimension as possible. We find sufficient conditions under which a complete nonlinear system closed by this control is ensured asymptotic stability despite the presence of at least as many zero roots of the characteristic equation as the number of geometric relations. We prove a theorem on the stabilization of the control equilibrium applied only with respect to redundant coordinates and constructed from the estimate of the phase state vector obtained by a measurement of as small dimension as possible.     

The relationship between seismic frequency and magnitude as based on the Maximum Entropy Principle

Entropy is a state function. The entropy increase principle tells us that under isolated or adiathermal conditions, the spontaneous development of a system from a state of non-equilibrium to a state of equilibrium is a process of entropy increase, in which a state of equilibrium corresponds to a state of maximum entropy. When the system is in a state of equilibrium, it is also at its most chaotic and disordered. The occurrence of earthquakes can be classified as a random event and can be described using entropy. Earthquakes occur in the most disordered way, indicating that entropy has reached its maximum value, so we can use the Maximum Entropy Method to determine the distribution of earthquakes that occur within a certain area curing a particular period of time. Results show that the formula representing the relationship between seismic frequency and magnitude (based on data and experience) is in fact a negative exponential distribution under given restraints and supposing seismic entropy is set as the maximum value. Therefore, we can theoretically explain the origin of the relationship between seismic frequency and magnitude.     

Simulating a function of visual peripheral processes with an analogVLSI network

A two-dimensional analog VLSI network for implementing a function of motion perception during the peripheral process is described. The network contains many nodes, or processing elements (PEs), which operate concurrently in asynchronous fashion. Each PE performs an image-difference operation as well as thresholding to extract motion information on a pixel-by-pixel basis. Analog voltage, which interacts extremely quickly, implements all computations. An energy equilibrium state of the network provides stabilized analog voltage across the network. SPICE simulations and experiments using real images verify the results of the theoretical analysis     

基于在线开路电压估算的电池均衡指标研究

开路电压作为均衡指标可以准确反映电池组中单体的不一致性状态,如何在线实时获得开路电压是电池均衡研究的难点之一。使用BP神经网络结合当前工作状态下的电流、电压与荷电状态在线估算开路电压,并以此作为均衡指标在自主研制的BMS算法验证平台采用耗散型均衡方式实现电池放电阶段均衡。实验结果表明：在相同均衡策略下,在线估算的开路电压均衡指标与工作电压均衡指标相比,工作截止时的开路电压偏差近似为初始开路电压偏差的一半,因此能够准确地表征锂电池的不一致性。为电池组均衡指标的选择提供指导,促进电池组均衡技术的发展。     

四旋翼无人机飞行姿态模型参考自适应控制

四旋翼无人机具有机械结构简单、可垂直起降等优势,在各个领域都有极广泛的应用.经典控制算法如PID对无人机在受扰动或环境变化时的控制效果不理想,难以调节至平衡状态.论文对动力学建模加以适当简化,设计了自适应控制律,数值仿真实验结果表明,模型参考自适应控制能在很大范围内有效屏蔽干扰,验证该算法是有效的.     

The Classical Regulation Problem: Its Solution by Optimal Control Methods

The fundamental problem of the classical regulation theory in the class of bounded control is investigated. Optimal control methods are applied to design operation algorithms for regulators, which generate in real time feedback for transferring a system from the neighborhood of one equilibrium state (steady-state motion) to the neighborhood of another state with transition process of high quality and stabilize the system relative to the new equilibrium state. The results are illustrated by an example of regulation of a fourth-order dynamic system.     

On the selection of a tax strategy and on an equilibrium in an economy

Equilibrium conditions in an open economic system with monopolies are investigated. The model takes into account the presence of insatiable consumers among economy subjects. The influence of selection of a tax strategy on the realization of a certain equilibrium state of the economy is found out. The conditions of realization of an optimal equilibrium state are found. The model is applied to the analysis of the influence of monopolies on the Ukrainian economy.