轮腿式机器人倾覆稳定性分析与控制

对于运动在不平坦地形中的移动机器人而言,其倾覆稳定性非常关键．设计了一种结构对称的轮腿式机器人,它有4个独立的轮腿运动单元,能够变化多种构形．采用动态能量稳定锥方法和倾覆稳定性指数对机器人的稳定性进行综合评价,建立了一个模糊神经网络自适应控制系统．根据稳定性指数值,该系统可以实时改变机器人的构形和速度,保证其倾覆稳定性．正弦路面上的仿真结果表明,该系统所产生的动作实时性好、可靠性高,能够降低机器人自主越障过程中的危险．     

含离散和分布时变时延神经网络系统的指数稳定性

针对一类含有离散和分布时延神经网络,在神经激活函数较弱的约束条件下,通过定义一个更具一般性的Lyapunov泛函,使用凸组合技术,得到了新的基于线性矩阵不等式表示的指数稳定性判据.与现有结果相比,这些判据具有较小的保守性.仿真算例表明,得到的结果是有效的且保守性小.     

A piecewise analysis method to stability analysis of linear continuous/discrete systems with time‐varying delay

The delay‐dependent stability problem of linear continuous/discrete systems with time‐varying delay is investigated based on a piecewise analysis method (PAM). In the method, the variation interval of the time delay is firstly divided into several subintervals. By checking the variation of the Lyapunov functional in every subinterval, some new delay‐dependent stability criteria are derived. Several numerical examples show that our method can lead to much less conservative results than those in the existing references. Moreover, when the number of the divided subintervals increases, the corresponding criteria can provide an improvement on the results. Copyright © 2008 John Wiley & Sons, Ltd.     

A new adaptive backstepping Coulomb friction compensator for servo control systems

A new Coulomb friction compensator is proposed for servo control systems in this paper. The novelty of the new approach lies in its capability of assigning the eigenvalues of the resulting closed loop system while attacking the problem. First, based on the standard backstepping methodology, an implicit Lyapunov function, with part of the components being only symbolically constructed at the very beginning, is utilized. To increase the robustness of the system against disturbance and model inaccuracy, an integral term is employed in the design. Using part of the variable gradient method, we are able to turn the implicit Lyapunov function into an explicit one, which is positive definite, and whose time‐derivative is negative definite. Second, it will be shown that the resulting closed loop error system is a switched linear system with two possible active modes that share the same set of eigenvalues, which is at our disposal. Unlike the common adaptive control design methods, such as the Control Lyapunov Function approach, in which the gains are typically positive but otherwise arbitrary, and are hence difficult to choose and have a lack of connection with the system's performance, our new scheme imposes two further constraints on the gains. It turns out that we can then match these gains with the coefficients of the desired characteristic equation of the closed loop system. In this respect, the gains are linked to the system's overall performance, which is a new and very appealing feature for such a scheme. Finally, a procedure of constructing a common Lyapunov function is provided to prove exponential stability of the aforementioned switched linear system. In addition, using the invariance principle, we will show the convergence of the estimated Coulomb friction coefficient to its real value. Numerical simulations are given to validate the effectiveness of the design and its robustness against friction time‐variations. Compared to existing results, the proposed scheme is much simpler, hence, much more advantageous computationally. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.     

Control of frictional dynamics of a one-dimensional particle array

Control of frictional forces is required in many applications of tribology. While the problem is approached by chemical means traditionally, a recent approach was proposed to control the system mechanically to tune frictional responses. We design feedback control laws for a one-dimensional particle array sliding on a surface subject to friction. The Frenkel-Kontorova model describing the dynamics is a nonlinear interconnected system and the accessible control elements are average quantities only. We prove local stability of equilibrium points of the un-controlled system in the presence of linear and nonlinear particle interactions, respectively. We then formulate a tracking control problem, whose control objective is for the average system to reach a designated targeted velocity using accessible elements. Sufficient stabilization conditions are explicitly derived for the closed-loop error systems using the Lyapunov theory based methods. Simulation results show satisfactory performances. The results can be applied to other physical systems whose dynamics is described by the Frenkel-Kontorova model.     

模拟时滞化学反应系统中的DK-Leap算法

最近发展的可精确模拟时滞化学反应系统的动力学状态的时滞随机模拟算法(delay stochastic simulation algorithm,DSSA)的模拟效率很低。本文提出了一个模拟时滞化学反应系统的加速DK-Leap(Delay K-Leap)算法。DK-Leap算法首先确定满足Leap条件的总反应次数K,然后利用得到τ的概率密度函数随机确定时间区间[t,t τ)。由于每个反应通道的反应次数由K确定,该算法可得到较好的模拟精度。数值试验表明DK-Leap算法在模拟时滞化学反应系统时能取得很好的性能。     

Adaptive prescribed time control for quadrotor formation with stochastic links failure

The formation control for multiple quadrotors subject to maintaining the formation configuration and collision avoidance in the situation of stochastic links failure is investigated in this paper. First, the distributed formation controller is designed, the position controller is developed to manage the desired formation of position, and the attitude controller is developed to control the translation and rotation movements of the quadrotor. Then, in order to avoid the collisions between multiple quadrotors and the obstacles, a potential energy function method is introduced into the quadrotor formation control combined with the nest adaptive control. Inspired by the design of event trigger controller, a communication compensation controller is designed to ensure the stability of quadrotor formation under the condition of random communication interruption and recovery. Moreover, a prescribed time function is designed, which means the convergence time of the formation system can be set in advance. The prescribed time stability of the formation control system is proved by Lyapunov theory. Finally, the simulation results verify the effectiveness and superiority of this method.     

Confidence regions of two-stage stochastic linear complementarity problems

Two-stage stochastic linear complementarity problems (TSLCP) model a large class of equilibrium problems subject to data uncertainty, and are closely related to two-stage stochastic optimization problems. The sample average approximation (SAA) method is one of the basic approaches for solving TSLCP and the consistency of the SAA solutions has been well studied. This paper focuses on building confidence regions of the solution to TSLCP when SAA is implemented. We first establish the error-bound condition of TSLCP and then build the asymptotic and nonasymptotic confidence regions of the solutions to TSLCP by error-bound approach, which is to combine the error-bound condition with central limit theory, empirical likelihood theory, and large deviation theory.