Optimal interval controller design for uncertain systems

The interval controller design is a hot issue for uncertain systems, whereas how to design an optimal interval controller under the premise of ensuring system stability is a difficult problem that needs further study. This paper mainly aims at the single input single output uncertain system to propose an optimal interval controller based on the Kharitonov theorem and an interval optimization algorithm, which can guarantee the stability and optimization of a closed-loop interval system. According to the Kharitonov theorem, the optimal interval controller design can be transformed into an optimal controller synthesis issue of multiple vertex objects. An interval particle swarm optimization (IPSO) algorithm is then used to optimize the quadratic performance index with interval variables for each vertex object to obtain the solution domains of the controller parameters, and the vertex method is utilized to prevent interval width expansion or divergence in the iteration. Finally, the intersections of the solution domains for all vertex objects are obtained as the optimal interval solution of interval controller parameters. In addition, the stability verification approach of the closed-loop system and the empirical rule to select the interval particle width are given. Simulation results for typical examples demonstrate that the designed interval controller not only performs optimally but also can robustly stabilize the interval system.     

Formation control for multi‐agent systems through an iterative learning design approach

This paper deals with formation control problems for multi‐agent systems by using iterative learning control (ILC) design approaches. Distributed formation ILC algorithms are presented to enable all agents in directed graphs to achieve the desired relative formations perfectly over a finite‐time interval. It is shown that not only asymptotic stability but also monotonic convergence of multi‐agent formation ILC can be accomplished, and the convergence conditions in terms of linear matrix inequalities can be simultaneously established. The derived results are also applicable to multi‐agent systems that are subject to stochastic disturbances and model uncertainties. Furthermore, the feasibility of convergence conditions and the effect of communication delays are discussed for the proposed multi‐agent formation ILC algorithms. Simulation results are given for uncertain multi‐agent systems to verify the theoretical study. Copyright © 2012 John Wiley & Sons, Ltd.     

Robustness of sampled-data control systems having parametricuncertainty: a conic sector approach

The robustness of sampled-data control systems when the open-loop system is modeled by a family of plants having affine or interval uncertainty structure is considered. Using the conic sector approach as adapted to sampled-data systems, the authors give a sufficient condition for robust stability that depends only on edge parameters in the case of affine uncertainty and on vertex parameters when interval uncertainty is assumed     

含多状态时滞的连续时间迭代学习控制系统稳定性分析

探讨了含多状态时滞连续时间迭代学习控制系统的稳定性分析问题, 尤其是当系统参数带有多面体不确定性时的鲁棒稳定性分析问题. 通过引入一个扩展算子, 利用迭代学习控制中的二维分析方法给出了时滞系统整个学习动态过程的连续离散Roesser系统描述. 基于所得的Roesser系统, 首先利用二维系统理论给出了保证迭代学习控制系统渐近稳定的充要条件, 然后结合鲁棒H∞控制理论提出了以线性矩阵不等式形式描述的充分条件来保证迭代学习控制系统的单调收敛性. 结果表明, 通过求解线性矩阵不等式确定的学习增益可以使控制输入误差随着迭代次数的增加单调收敛于零. 仿真结果表明, 通过增加满足一组线性矩阵不等式条件的P型学习增益能够使得一个鲁棒渐近稳定的迭代学习控制方案变为鲁棒单调收敛的, 同时还可以大大提高收敛速率.     

区间分数阶系统的鲁棒稳定性判别准则:0 < α < 1

针对同元阶次在0和1之间的区间分数阶系统,提出了类似Kharitonov定理的鲁棒稳定性判别准则. 研究了区间分数阶系统分母的主分支函数值集不包含原点所需满足的条件.根据除零原理, 给出了区间分数阶系统鲁棒稳定的顶点和棱边条件. 定义了由分母函数系数构成的矩阵,通过检验矩阵是否在负实轴上存在特征值来检验棱边条件. 最后,通过对两个数值算例的分析说明了这种方法的有效性.     

Robust stability region of fractional order PIλ controller for fractional order interval plant

In this article, by using the fractional order PI^λ controller, we propose a simple and effective method to compute the robust stability region for the fractional order linear time-invariant plant with interval type uncertainties in both fractional orders and relevant coefficients. The presented method is based on decomposing the fractional order interval plant into several vertex plants using the lower and upper bounds of the fractional orders and relevant coefficients and then constructing the characteristic quasi-polynomial of each vertex plant, in which the value set of vertex characteristic quasi-polynomial in the complex plane is a polygon. The D-decomposition method is used to characterise the stability boundaries of each vertex characteristic quasi-polynomial in the space of controller parameters, which can obtain the stability region by varying λ orders in the range (0,?2). These regions of each vertex plant are computed by using three stability boundaries: real root boundary (RRB), complex root boundary (CRB) and infinite root boundary (IRB). The method gives the explicit formulae corresponding to these boundaries in terms of fractional order PI^λ controller parameters. Thus, the robust stability region for fractional order interval plant can be obtained by intersecting stability region of each vertex plant. The robustness of stability region is tested by the value set approach and zero exclusion principle. Our presented technique does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. It also offers several advantages over existing results obtained in this direction. The method in this article is useful for analysing and designing the fractional order PI^λ controller for the fractional order interval plant. An example is given to illustrate this method.     

Stability of first and high order iterative learning control with data dropouts

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plants are subject to output measurement data dropouts. It is assumed that data dropout occurs during the data transfers from the plant to the ILC controller, resulting in what is called intermittent ILC. Using the super-vector approach for ILC, the expectation of output error is used to develop conditions for stability of the first order ILC and high order ILC processes. Through the theoretical analysis, it is shown that the convergence of the intermittent ILC is guaranteed although some measurements are missing. The analysis is also supported by numerical examples.     

受扰动2-D线性时变系统的迭代学习控制

利用2-D系统理论的Roesser模型,给出了受扰动的线性时变离散系统迭代学习控制(ILC)问题的一种解决方法.对系统所受的已知扰动,给出其学习律参数的选取范围以及仅经一次迭代就能实现输出完全跟踪期望轨迹的参数选取方法;对系统所受的未知扰动,首先对SISO系统提出其学习律存在的条件及参数选取方法,进而推广到MIMO系统中,提出MIMO系统学习律的参数选取方法.最后给出两个数值例子进一步说明所得结果的有效性.     

Vertex results for uncertain systems

In the spirit of Kharitonov, the robust stability of feedback systems under both structured and unstructured perturbations is discussed. Extreme point results are obtained. The stability margin of an interval system family is achieved at pre-specified twelve vertex systems