不同时间尺度的慢变量引起的簇放电研究

本文基于两个重要的慢负反馈机制给出了一个组合型的胰腺β-细胞模型.在这个模型中,不同簇放电模式对快、中、慢的振荡周期具有鲁棒性,这样可以通过快振荡周期簇放电模式的快慢动力学分析得到所有簇放电的动力学机理和拓扑类型.对于快振荡周期的簇放电,较慢的慢变量α几乎为常数,较快的慢变量Cer对快子系统没有影响,因此只要考虑慢变量...     

Analysis of singular systems using orthogonal functions

The use of orthogonal functions to analyze singular systems is investigated. It is shown that the differential-algebraic system equation may be converted to an algebraic generalized Lyapunov equation that can be solved for the coefficients ofx(t)in terms of the orthogonal basis functions. This generalized Lyapunov equation may be considered as a "discrete" equation on the slow subspace of the system, and as a "continuous" equation on its fast subspace. Necessary and sufficient conditions for the existence of a unique solution are given in terms of the relative spectrum of the system. A generalized Bartels/Stewart algorithm based on theQZalgorithm is presented for its efficient solution. Relations are drawn with the invariant subspaces of the system.     

System decomposition technique for spray modelling in CFD codes

A new decomposition technique for a system of ordinary differential equations is suggested, based on the geometrical version of the integral manifold method. This is based on comparing the values of the right hand sides of these equations, leading to the separation of the equations into ‘fast’ and ‘slow’ variables. The hierarchy of the decomposition is allowed to vary with time. Equations for fast variables are solved by a stiff ODE system solver with the slow variables taken at the beginning of the time step. The solution of the equations for the slow variables is presented in a simplified form, assuming linearised variation of these variables for the known time evolution of the fast variables. This can be considered as the first order approximation for the fast manifold. This technique is applied to analyse the explosion of a polydisperse spray of diesel fuel. Clear advantages are demonstrated from the point of view of accuracy and CPU efficiency when compared with the conventional approach widely used in CFD codes. The difference between the solution of the full system of equations and the solution of the decomposed system of equations is shown to be negligibly small for practical applications. It is shown that in some cases the system of fast equations is reduced to a single equation.     

Robust sampled-data H/sub /spl infin// control of linear singularly perturbed systems

State-feedback H/sub /spl infin// control problem for linear singularly perturbed systems with norm-bounded uncertainties is studied. The fast variables are sampled with fast rates, while for the slow variables both cases of slow and of fast sampling are considered. The recent "input delay" approach to sampled-data control is applied, where the closed-loop system is represented as a continuous one with time-varying input delay. Linear matrix inequalities (LMIs) for solution of H/sub /spl infin// control problem are derived via input-output approach to stability and L/sub 2/-gain analysis of time-delay systems. A numerical example illustrates the efficiency of the method.     

Sliding Mode Control and State Estimation for a Class of Nonlinear Singularly Perturbed Systems

This paper is concerned with the design of a controller-observer scheme for the exponential stabilization of a class of singularly perturbed nonlinear systems. The controller design uses a sliding mode technique and is divided in two phases: slow feedback control and fast feedback control so that a final composite control is obtained. Assuming that only the fast state is available and the system's output is a function of the slow state, an observer design is presented. A stability analysis is also made to provide sufficient conditions for the ultimate boundedness of the full order closed-loop system when the slow state is estimated by means of the observer. An application to the model of a permanent magnet stepper motor is given to show the controller-observer methodology and stability analysis.     

Decentralized control for two time-scale discrete-time systems

Output feedback design of discrete-time decentralized systems with slow and fast modes is considered. Conditions for the complete separation of slow and fast subsystems are given. The slow and fast subsystem outputs, which are obtained by applying the slow and fast subcontrollers to the corresponding subsystems, will be shown to approximate those of the original system. Also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.     

Team-optimal closed-loop Stackelberg strategies for systems with slow and fast modest†

This paper discusses team-optimal closed-loop Stackelberg strategies for systems with slow and fast modes. It is established that the cost functions of the players in the pure slow and the full-order games have the same value in the limit as the small singular perturbation parameters tends to zero. It is shown that if the leader bases the design of his approximate strategy on the slow subsystem, while the follower bases his design on the full-order system, then the resulting solution is ill-posed. Moreover, if the fast information is incorporated in the approximate strategy of the leader, then it is shown that the singular perturbation technique of constructing approximate strategies by composing the slow and fast strategies is ill-posed and cannot be used in this problem. A new design methodology to construct approximate Stackelberg strategies by solving reduced-order problems, which have the same information structure as the full-order one, is presented. It is shown that the conditions for existenco and uniqueness of the solution of the full-order problem can be established through those conditions of the reduced-order problems. Finally, it is proved that the approximate strategies, besides being team near-optimal, possess the asymptotic Stackelberg property.     

The observer-based controller design of discrete-time singularly perturbed systems

A class of linear shift-invariant discrete-time singularly perturbed systems with inaccessible states is considered. A design technique is formulated by which the stabilizing controller can be formed through the controllers of the slow and fast subsystems. Sufficient conditions for stability of the closed-loop system under this composite controller are given.     

Design of linear time-invariant controllers for multirate systems

In this paper we discuss a frequency domain approach to model multirate single-input single-output (SISO) systems which facilitates design of linear time-invariant (LTI) controllers operating at the fast rate. To illustrate the approach we consider a dual-rate system with slow output measurements and fast control actions. We obtain necessary and sufficient conditions for the existence of stabilizing linear time-invariant (LTI) controllers for which model matching is also achieved at the fast rate with a desired single-rate system. Moreover, a solution to the problem of parameterizing the set of such LTI controllers is also given.     

Nonclassical relaxation oscillations in neurodynamics

A modification of the well-known FitzHugh–Nagumo model from neuroscience has been proposed. This model is a singularly perturbed system of ordinary differential equations with a fast variable and a slow variable. The existence and stability of a nonclassical relaxation cycle in this system have been studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function. A one-dimensional circle of unidirectionally coupled neurons has been considered. The existence of an arbitrarily large number of traveling waves for this chain has been shown. In order to illustrate the increase in the number of stable traveling waves, numerical methods were involved.     

Delay-dependent resilient-robust stabilisation of uncertain networked control systems with variable sampling intervals

This work is concerned with the robust resilient control problem for uncertain networked control systems (NCSs) with variable sampling intervals, variant-induced delays and possible data dropouts, which is seldom considered in current literature. It is mainly based on the continuous time-varying-delay system approach. Followed by the nominal case, delay-dependent resilient robust stabilising conditions for the closed-loop NCS against controller gain variations are derived by employing a novel Lyapunov–Krasovskii functional which makes good use of the information of both lower and upper bounds on the varying input delay, and the upper bound on the variable sampling interval as well. A feasible solution of the obtained criterion formulated as linear matrix inequalities can be gotten. A tighter bounding technique is presented for acquiring the time derivative of the functional so as to utilise many more useful elements, meanwhile neither slack variable nor correlated augmented item is introduced to reduce overall computational burden. Two examples are given to show the effectiveness of the proposed method.     

Adaptive composite suboptimal control for linear singularly perturbed systems with unknown slow dynamics

In this article, using singular perturbation theory and adaptive dynamic programming (ADP) approach, an adaptive composite suboptimal control method is proposed for linear singularly perturbed systems (SPSs) with unknown slow dynamics. First, the system is decomposed into fast‐ and slow‐subsystems and the original optimal control problem is reduced to two subproblems in different time‐scales. Afterward, the fast subproblem is solved based on the known model of the fast‐subsystem and a fast optimal control law is designed by solving the algebraic Riccati equation corresponding to the fast‐subsystem. Then, the slow subproblem is reformulated by introducing a system transformation for the slow‐subsystem. An online learning algorithm is proposed to design a slow optimal control law by using the information of the original system state in the framework of ADP. As a result, the obtained fast and slow optimal control laws constitute the adaptive composite suboptimal control law for the original SPSs. Furthermore, convergence of the learning algorithm, suboptimality of the adaptive composite suboptimal control law and stability of the whole closed‐loop system are analyzed by singular perturbation theory. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed methods.     

Servo-systems with discrete-variable structure control

This paper is concerned with the computer-based variable structure control of servo-systems. A discrete-variable structure control is presented and a condition is given for stability. The strategy ensures that sliding mode can be obtained exponentially fast to keep the system robust. Simulation results show the effectiveness of the proposed technique.     

A singular perturbation canonical form of invertible systems: determination of multivariate root-loci

A new canonical form of multivariable invertible systems is given. This form is suitable for the singular perturbation analysis of such singular problems as multi-variable asymptotic root-loci under high-gain feedback, cheap control, state variable estimation with weak measurement noise, etc. Appropriate selection and decomposition of state variables into slow and fast changing groups is a key feature that loads to well-defined singular perturbation models. The selection of state variables is accomplished without explicitly calculating any eigenvalues of the given system but by knowing the direct relationship of the output and its differential coefficients with the input. The use of the canonical form to characterize the multivariable root-loci under high-gain feedback is demonstrated.     

再入飞行器姿控系统的准连续高阶滑模设计

针对存在参数不确定性和外扰的飞行器再入姿态控制问题,提出一种基于准连续高阶滑模的控制方案.首先基于奇异摄动理论将姿态控制系统分为快、慢两回路;随后在慢回路滑模控制系统设计中利用范数型切换函数代替符号函数以使虚拟控制量平滑连续;在快回路设计中,基于积分型快速终端滑模、反馈控制和准连续高阶滑模控制理论设计快回路控制系统.理论分析和仿真结果均表明,该控制方案在增强系统鲁棒性的同时能够有效削弱系统抖振.     

Variable Time Impulse System Optimization with Continuous Control and Impulse Control

Optimal control of a variable time impulse system is considered in this study. Besides impulse control, the system is assumed to operate with continuous control also. Necessary conditions for the optimization of such system are derived using the calculus of variations. A reinforcement based solution technique called a single network adaptive critic (SNAC) method is developed in this paper to obtain an optimal solution. Details of the SNAC‐based algorithm are presented. Simulation examples are also presented for illustrative purposes.     

具连续分布时滞的抛物型系统的变结构控制

基于比较原理,利用推广的向量Hanalay微分不等式,Dini导数,结合Green公式及不等式分析技术,研究一类具分布时滞的抛物型控制系统的变结构控制问题．首先对所导出的滑动模运动方程,在仅要求系数矩阵是个M-矩阵的条件下,获得了滑动模运动方程全局指数稳定性的充分条件,建立了滑动模运动方程全局指数稳定性定理．其次,设计了仅由状态函数描述的变结构控制器,给出了运动轨线到达滑动模态区的时间的估计．     

Fast Riccati equation solutions: Partitioned algorithms

In this paper, using the ‘partitioning’ approach to estimation, exceptionally robust and fast computational algorithms for the effective solution of continuous Riccati equations are presented. The algorithms have essentially a decomposed or ‘partitioned’ structure which is both theoretically interesting as well as computationally attractive. Specifically, the ‘partitioned’ solution is given exactly in terms of a set of elemental solutions which are both simple as well as completely decoupled from each other, and as such computable in either a parallel or serial processing mode. Moreover, the overall solution is given by a simple recursive operation of the elemental solution. Extensive computer simulation has shown that the ‘partitioned’ algorithm is numerically very effective and robust, especially in the case of ill-conditioned Riccati solutions, e.g. for ill-conditioned initial conditions, or for stiff system matrices. Further, the ‘partitioned’ algorithm is very fast, ranging up to several orders of magnitude faster than the corresponding Runge-Kutta algorithm.