A result on the hyperstability of a class of hybrid dynamic systems

This paper presents a hyperstability theorem for a class of hybrid dynamic systems composed of coupled differential and difference equations subject to (possibly) time-varying nonlinearities satisfying a Popov-type inequality. The nonlinear controller generates the plant input at all times from its sampled values by defining an extended discrete system. The hyperstability results are obtained from this discrete system of special type whose state consists of the sampled continuous substate and the digital substate of the given hybrid system. Some corollaries and related physical interpretations are also given     

Synthesis of discrete model reference adaptive systems

The synthesis of discrete model reference adaptive systems is discussed from the hyperstability point of view. The results included here are an extension of previous results obtained by the author for the continuous case [1].     

基于Popov超稳定性理论的模糊自适应控制器设计方法

对一类常见的非线性系统,利用Popov超稳定性理论得到一种模糊自适应控制方 案,该方案在模型匹配的条件下能保证闭环系统的(渐近)稳定性.当模型匹配条件不满足时, 通过引入一个辅助控制量使系统仍保持稳定.因此,文中提出的方法普遍适用于一类非线性 离散或连续控制系统的设计.     

Hyperstability of linear time-varying discrete systems

The hyperstability of a class of linear time-varying discrete systems is studied. Sufficient conditions for hyperstability and for stability in the sense of Lyapunov are obtained.     

线性不确定系统鲁棒滤波器设计

分别研究了一类线性不确定连续和离散系统的鲁棒保成本滤波器的设计问题.采用保 成本滤波器(guaranteed cost filter)的设计思想,用线性矩阵不等式的形式给出鲁棒保成本滤波 器存在的简便检验条件,由LMI的解直接得到滤波器各参数的值.对鲁棒保成本滤波器存在的 系统,进一步优化成本矩阵,获得了最优鲁棒保成本滤波器.最后给出一个仿真实例,结果验证 了方法的有效性.     

Robust stabilization of nonlinear stochastic 2‐D systems: LaSalle‐type theorem approach

LaSalle theorem (also known as the LaSalle invariance principle) plays an essential role in the systems and control theory. Recently, it has been extensively studied and developed for various types of one‐dimensional (1‐D) systems including deterministic and stochastic 1‐D systems in discrete‐ and continuous‐time domains. For two‐dimensional (2‐D) systems, such studies have received considerably less attention. In this article, based on discrete martingale theory, a LaSalle‐type theorem is first developed for a class of discrete‐time nonlinear stochastic 2‐D systems described by a Roesser model. The proposed result can be regarded as an extension of stochastic Lyapunov‐like theorem, which guarantees the convergence almost surely of system state trajectories. Extensions to the problem of optimal guaranteed cost control of nonlinear stochastic 2‐D systems are also presented. The proposed schemes are then utilized to derive tractable synthesis conditions of a suboptimal state‐feedback controller for uncertain 2‐D systems with multiplicative stochastic noises. The effectiveness of the obtained results is illustrated by given numerical examples and simulations.     

On the synthesis of adaptive tests for nondeterministic finite state machines

The paper suggests a method for synthesis of adaptive tests with guaranteed coverage for checking functioning of discrete systems whose behavior is described by nondeterministic finite state machines. In contrast to other known methods, we do not represent the complete test as a tree but list test cases one by one and check functioning of the finite state machine on each test case. The complete test detects all defective systems that are r-distinguishable from the reference system. Besides, the test detects other defective systems containing traces that are not present in the specification; but detection of all such systems that are r-compatible with the specification is not guaranteed.     

A modified extended Kalman filter for linear discrete-time systems with unknown parameters

This technical communique presents a modified extended Kalman filter for estimating the states and unknown parameters in discrete-time, multi-input multi-output linear systems. The hyperstability of the filter is guaranteed by introducing a compensator into the estimation mechanism. It is proved that the estimates for the states and unknown parameters converge to the exact values if some conditions are assumed to the estimation mechanism. A numerical example shows that the proposed filter is much more effective than the extended Kalman filter in the estimation of unknown parameters.     

基于二维混合模型的改进型重复控制系统保性能设计方法

针对一类具有参数不确定性的线性系统, 基于连续/离散二维混合模型进行改进型重复控制系统的保性能设计. 首先给出一种具有反馈作用的改进型重复控制系统结构, 通过独立地考虑重复控制系统的连续控制行为与离散学习行为, 建立重复控制系统的连续/离散二维混合模型, 并将重复控制的设计问题转化为一类连续/离散二维系统的状态反馈控制问题. 然后, 应用二维Lyapunov泛函导出保性能改进型重复控制器存在的充分条件, 进而证明该条件等价于一个线性矩阵不等式可解性问题. 最后通过求解对应的凸优化问题, 给出了最优保性能控制器的具体形式. 数值仿真验证了所提出方法的有效性.     

一类不确定脉冲型混杂系统的保代价控制

针对混合代价函数,研究了参数不确定脉冲型混杂系统的保代价控制问题,给出了混杂状态反馈保代价控制律的设计方法,由此得到的控制律既能使系统闭环鲁棒渐近稳定,又可使系统的闭环混合代价指标在对象参数摄动的范围内不超过确定的上界.本文提出的控制律不仅包含连续时间动态,也包含离散事件动态,而且其离散事件动态行为不需要与被控系统的离散事件动态行为一致,因此设计时不要求被控系统的每个连续时间子系统都具有可控性.仿真结果表明所提设计方法是可行有效的.     

A variational integrators approach to second order modeling and identification of linear mechanical systems

The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in general are not guaranteed under general discretization procedures. We discuss a simple class of variational integrators for linear second order mechanical systems and propose a constrained identification technique which employs simple linear transformation formulas to recover the continuous time parameters of the system from the discrete-time identified model. We test this approach on a simulated eight degrees of freedom system and show that the new procedure leads to an accurate identification of the continuous-time parameters of second-order mechanical systems starting from discrete measured data.     

一类不确定离散时间系统的积分滑模控制

针对一类同时存在匹配和非匹配不确定性的离散时间系统,提出一种基于幂次函数的离散积分滑模控制方法.理论分析表明,所提出的方法可以消除离散积分滑模控制系统的抖振,而且能够保证对系统的匹配和非匹配不确定性具有强鲁棒性.在系统不确定性的界未知的情况下,通过引入一步延时干扰估计完成了控制器的设计,并给出了闭环系统稳定性证明.仿真结果验证了所提出方法的有效性.     

Hyperstability and average hyperstability conditions for a broad class of gaussian stochastic systems

The author investigates the hyperstability problem for a broad class of single-control stochastic systems which may be considered as disturbed models of given deterministic systems. The stochasticity comes from the control, which is disturbed by an additive Gaussian noise with its own gain. Hyperstability conditions are given when the noise has a time-independent variance. When this variance depends explicitly upon the time, we define the time-average hyperstability, and conditions for average hyperstability are given. Similar problems are solved for multicontrol Gaussian systems. Illustrative examples show how one can derive from these results a broad class of absolute stability conditions.     

Augmented finite transition systems as abstractions for control synthesis

This work is motivated by the problem of synthesizing switching protocols for continuous switched systems described by differential or difference equations, in a way that guarantees that the resulting closed-loop trajectories satisfy certain high-level specifications expressed in linear temporal logic. We introduce augmented finite transition systems as an abstract representation of the continuous dynamics; the augmentation consists in encodings of liveness properties that can be used to enforce progress in accordance with the underlying continuous dynamics. Abstraction and refinement relations that induce a preorder on this class of finite transition systems are established, and, by construction, this preorder respects the feasibility (i.e., realizability) of the synthesis problem. Hence, existence of a discrete strategy for one of these abstract finite transition systems guarantees the existence of a switching protocol for the continuous system that enforces the specification for all resulting trajectories. We show how abstractions and refinements can be computed for different classes of continuous systems through an incremental synthesis procedure that starts with a coarse abstraction and gradually refines it according to the established preorder relations. Finally, the incremental synthesis procedure is tailored to a class of temporal logic formulas by utilizing specific fixed point structures to enable localized updates in the refinement steps. The procedure is not guaranteed to terminate in general but we illustrate its practical applicability on numerical examples.     

脉冲控制下多智能体系统的保性能双向编队控制

研究混杂脉冲控制下二阶非线性多智能体系统的双向编队控制问题,以及保性能双向编队控制问题.根据领导智能体、目标编队以及邻居智能体的状态对每个智能体设计双向编队控制的状态反馈控制器及脉冲控制器.基于双向编队的目标,定义适当的误差系统,将双向编队问题转化为误差系统的稳定性问题.利用平均脉冲强度以及平均脉冲区间的定义,给出在混...     

Linear quadratic networked control of uncertain polytopic systems

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous‐time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete‐time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete‐time domain assures a guaranteed quadratic cost to the closed‐loop continuous‐time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm‐bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete‐time domain, a digital robust state feedback control law that stabilizes the original continuous‐time system assuring an upper bound to the quadratic cost of the closed‐loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

离散广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是广义大系统理论的基本问题之一,对其稳定性的研究要比状态空间大系统复杂得多,因为广义大系统不仅需要考虑稳定性,而且还要考虑正则性和因果性(离散广义系统)及脉冲自由(连续广义系统).本文在所有孤立子系统都是正则的且具有因果关系的条件下,利用Lyapunov方程,应用Lyapunov函数方法,研究了广义离散线性大系统和广义离散非线性大系统的稳定性和不稳定性问题,给出了离散广义大系统稳定性和不稳定性判定定理,得到了离散广义大系统的关联稳定参数域和不稳定域.     

Optimization of nuclear fuel reloading by the homogenization method

In this paper we apply the homogenization method to the optimization of the position of fuel assemblies in a nuclear reactor core. For this type of problem the state equation is a system of diffusion equations for the neutron flux. Homogenization theory allows us to relax a truly discrete optimization problem into a continuous and well-posed optimization problem. The latter one is solved by using classical methods of optimal control. A discrete admissible distribution of assemblies is recovered by a numerical penalization technique. The main advantage of homogenization is that the resulting reloading pattern is guaranteed to be near optimal whatever the initial guess.     

A new form of stable adaptive observer

A new form of adaptive observer which is guaranteed to be globally stable via hyperstability theories is presented. Its main advantage over existing designs is that asymptotic unbiased estimates are obtained in the presence of output noise. Experimental results are given to demonstrate the performance of this observer.