Robust Adaptive Model Tracking for Distributed Parameter Control of Linear Infinite-dimensional Systems in Hilbert Space

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinitedimensional Hilbert space. The result will not require the use of the standard Barbalat0s lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.      

Approximation algorithm for an infinite-dimensional operator equation XL−BX=C

We study an infinite-dimensional operator equation XL–BX=C in a separable Hilbert space. The equation arises in the stabilization study of general linear parabolic systems, where the operatorsL, B, and C are coefficient operators describing a feedback control system. The solution to the stabilization naturally leads to an approximation problem of the operator equation. In this paper we propose a concrete algorithm for the approximation with the prescribed convergence rate when the closed operatorL is self-adjoint or more generally a spectral operator with compact resolvent.The original version of the paper was written while the author was with the Department of Mathematics, Faculty of Engineering, Kumamoto University, Kumamoto 860, Japan.     

Iterative methods for solving extended general mixed variational inequalities

In this paper, we introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.     

New triangular operator generators for fuzzy systems

Triangular operators (t-operators) form an integral part in the design and analysis of fuzzy systems. Simple monotonic, continuous, nonconditional functions are used in an operator generator to generate t-operators. Depending on the operator generator and the function that it uses, it becomes easier to characterize and classify the families of t-operators. In this paper, the author proposes two operator generators that will extend the domain of triangular operators in the realm of fuzzy set theory. The conventional operator generators generate a t-norm and a t-conorm by using a decreasing function and an increasing function, respectively. In contrast, in this study, increasing functions generate t-norms, while decreasing functions generate t-conorms, respectively     

Weak admissibility does not imply admissibility for analytic semigroups

Two conjectures on admissible control operators by George Weiss are disproved in this paper. One conjecture says that an operator B defined on an infinite-dimensional Hilbert space U is an admissible control operator if for every element uU the vector Bu defines an admissible control operator. The other conjecture says that B is an admissible control operator if a certain resolvent estimate is satisfied. The examples given in this paper show that even for analytic semigroups the conjectures do not hold. In the last section we construct a semigroup example showing that the first estimate in the Hille–Yosida theorem is not sufficient to conclude boundedness of the semigroup.     

Existence and Controllability Results for a New Class of Impulsive Stochastic Partial Integro‐Differential Inclusions with State‐Dependent Delay

In this paper, we study a new class of impulsive stochastic partial integro‐differential inclusions with state‐dependent delay in separable Hilbert spaces. Firstly, by using stochastic analysis theory, analytic resolvent operators, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of mild and extremal mild solutions for these systems in the α‐norm. Secondly, we establish the controllability of the controlled stochastic partial integro‐differential inclusions with not instantaneous impulses. The results are obtained under the mixed Lipschitz and Carathéodory conditions. Finally, an example is provided to show the application of our results.     

广义不确定系统的无脉冲鲁棒性和大范围脉冲鲁棒控制

本文研究了广义不确定系统在两种参数摄动（ 结构参数摄动和非结构参数摄动）下的无脉冲鲁棒性问题,给出了系统无脉冲鲁棒性的充分 判据.在此基础上,进一步研究了广义不确定系统在结构参数摄动下的大范围脉冲鲁棒控制 问题,在理想系统满足一定条件和系统的结构参数摄动的摄动界任意给定的情况下,提出了 该类控制器的具体设计步骤.最后,通过一个例子说明结论的可行性.     

A Faà di Bruno Hopf algebra for a group of Fliess operators with applications to feedback

A Faà di Bruno type Hopf algebra is developed for a group of integral operators known as Fliess operators, where operator composition is the group product. Such operators are normally written in terms of generating series over a noncommutative alphabet. Using a general series expansion for the antipode, an explicit formula for the generating series of the compositional inverse operator is derived. The result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product, that is, the generating series for the Fliess operator representation of the closed-loop system written in terms of the generating series of the Fliess operator component systems. This formula is employed to provide a proof that local convergence is preserved under feedback.     

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     

Generalized intuitionistic fuzzy soft power aggregation operator based on t-norm and their application in multicriteria decision-making

The aim of this paper is to develop some new power aggregation operators for intuitionistic fuzzy (IF) soft numbers. The aggregation operators are named as IF soft power averaging (IFSPA) operator, weighted IFSPA (WIFSPA) operator, ordered WIFSPA operator, IF soft power geometric (IFSPG) operator, and weighted and ordered weighted IFSPG aggregation operators. The salient features of these operators are discussed in detail. Further, these operators are extended to its generalized version and called generalized IFSPA or geometric aggregation operators. Then, we utilized these operators to develop an approach to solve the decision-making problem under IF soft set environment and demonstrated with an illustrative example. A comparative analysis of existing approaches has been done for showing the validity of the proposed work.     

From a theoretical model to a predictive simulation model of operator interaction with support systems: designing experiments to build the numerical simulation

In this paper, we will discuss a methodology developed and applied in the European ITERATE project with the objective of designing experiments that will provide data to seed the numerical model of operator behaviour in different surface transport modes: road vehicles, rail transport and ships. The experiments aim to investigate how new technologies support different types of operators in different contexts. A structured approach was adopted. Firstly, an initial selection of the systems to be investigated was made, describing the support they provide for operators. Hypotheses were formulated on the effects of operator parameters on the interaction with the systems. A final selection of systems for the experiments was made, focusing on systems providing support for collision avoidance and speed management. The operator parameters (culture, attitude and personality, experience, driver state (such as fatigue) and the demands of the task) were operationalised and piloted. The next step was the development of scenarios to be implemented in a driving simulator. In the last step, the final experiments were designed and detailed.     

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

In this paper, we investigate a new class of fractional impulsive stochastic partial integro‐differential equations with infinite delay in Hilbert spaces. By using the stochastic analysis theory, fractional calculus, analytic α‐resolvent operator and the fixed point technique combined with fractional powers of closed operators, we firstly give the existence of of mild solutions and optimal mild solutions for the these equations. Next, the controllability of the controlled fractional impulsive stochastic partial integro‐differential systems with not instantaneous impulses is presented. Finally, examples are also given to illustrate our results.     

A fuzzy self-tuning parallel genetic algorithm for optimization

The genetic algorithm (GA) is now a very popular tool for solving optimization problems. Each operator has its special approach route to a solution. For example, a GA using crossover as its major operator arrives at solutions depending on its initial conditions. In other words, a GA with multiple operators should be more robust in global search. However, a multiple operator GA needs a large population size thus taking a huge time for evaluation. We therefore apply fuzzy reasoning to give effective operators more opportunity to search while keeping the overall population size constant. We propose a fuzzy self-tuning parallel genetic algorithm (FPGA) for optimization problems. In our test case FPGA there are four operators—crossover, mutation, sub-exchange, and sub-copy. These operators are modified using the eugenic concept under the assumption that the individuals with higher fitness values have a higher probability of breeding new better individuals. All operators are executed in each generation through parallel processing, but the populations of these operators are decided by fuzzy reasoning. The fuzzy reasoning senses the contributions of these operators, and then decides their population sizes. The contribution of each operator is defined as an accumulative increment of fitness value due to each operator's success in searching. We make the assumption that the operators that give higher contribution are more suitable for the typical optimization problem. The fuzzy reasoning is built under this concept and adjusts the population sizes in each generation. As a test case, a FPGA is applied to the optimization of the fuzzy rule set for a model reference adaptive control system. The simulation results show that the FPGA is better at finding optimal solutions than a traditional GA.     

Robustness analysis of nonlinear feedback systems: an input-outputapproach

This paper presents an approach to robustness analysis for nonlinear feedback systems. We pursue a notion of model uncertainty based on the closeness of input-output trajectories which is not tied to a particular uncertainty representation, such as additive, parametric, structured, etc. The basic viewpoint is to regard systems as operators on signal spaces. We present two versions of a global theory where stability is captured by induced norms or by gain functions. We also develop local approaches (over bounded signal sets) and give a treatment for systems with potential for finite-time escape. We compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations, e.g., small-time delays. We also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations. The paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection     

卷积形态滤波与图像去噪

本文提出的卷积形态变换是一种新的形态变换形式,具有线性卷积的结构和形态变换的性质。这种新的形态变换以乘性结构元素为特征,它不同于具有加性结构元素的普通形态变换,对于它们的性质和结构的研究也是本文的主要工作之一。另一方面的工作是针对卷积形态核提出了一种结构化的自动生成算法。研究表明,卷积形态滤波与卷积积分变换一样,对于图像具有去噪和平滑作用,且在实验效果上具有较通常的形态滤波和线性卷积变换更优的去噪和平滑功能。     

Factorization and the Nehari theorem in time-varying systems

The Nehari Theorem and related results on operator interpolation play an important role in modern system theory. These results are embedded in a function-theoretic conceptual framework and therefore restricted to LTI systems. We give a state space oriented extension of the Nehari Theorem to a time-varying system-theoretic setting. In that setting the theorem addresses the issue of measuring the distance between a noncausal bounded I/O operator and the family of causal I/O operators in stable linear systems. The analysis is based on the recent time-domain LQ optimization approach to robust control. The discussion includes a geometrical analysis of stable and antistable invariant subspaces, a short study of certain types of co-prime factorizations of I/O operators in time-varying systems, and a parametrization of all suboptimal solutions.The research was supported in part by the National Science Foundation under Grant ECS 9108927 and by the U.S. Army Research Office under Contract DAALO3 92 G 0015.The research was supported by NSERC, Canada.     

毕达哥拉斯犹豫模糊集成算子及其决策应用

针对毕达哥拉斯犹豫模糊多属性决策中,集成算子的重要作用以及集成算子不完善的情况,较为系统地研究了毕达哥拉斯犹豫模糊集成算子。为此,在毕达哥拉斯模糊数的运算和运算法则基础上,定义了毕达哥拉斯犹豫模糊有序加权平均算子（PHFOWA）、广义有序加权平均算子（GPHFOWA）和混合平均算子（PHFHA）,以及毕达哥拉斯犹豫模糊有序加权几何平均算子（PHFOWG）、广义有序加权几何平均算子（GPHFOWG）和混合几何平均算子（PHFHG）,并结合数学归纳法,分别给出了它们的计算公式,讨论了它们的有界性、单调性和置换不变性等性质。建立了基于毕达哥拉斯犹豫模糊集成算子的多属性决策方法,并应用算例和相关方法比较说明了决策方法的可行性与有效性。     

New approach to time-domain analysis for stability robustness of dynamic systems

This paper presents a new approach to the analysis of the stability robustness of dynamic systems in state-space models. By continuously perturbing the state matrix, instead of solving the Lyapunov equation, an elegant stability robustness fundamental is derived. Subsequently, the allowable norm bound of the error matrix can be obtained under weakly structured perturbations, and the magnitude bound on individual elements of the error matrix can be obtained under highly structured perturbations. The merits of the theorems and corollary developed are demonstrated by two examples where the results achieved are much better than those already published in the literature. The concept that the perturbed state matrix would depend on the operating frequencies is also introduced.     

具Cauchy-Ventcel边界的阻尼波方程的对数衰减性

本文研究有界区域上具Cauchy-Ventcel边界条件的波动方程的解的衰减性质。在不要求耗散区域满足几何控制条件的情形下,我们得到了波方程的对数衰减结果。 主要结果的证明依赖于具Cauchy-Ventcel边界条件的椭圆方程的插值不等式以及关于该椭圆方程的预解式估计。为得到期望的插值不等式, 我们采用的工具是整体Carleman估计。     

Robust stability of perturbed switching systems by matrix measure

The robust stability of switching systems is a very difficult problem because of the difficulty in separating the perturbations of the models and the reset maps. In this paper, we apply matrix measure to separate the perturbations of the models and the reset maps. Then the conditions for robust stability of perturbed switching systems with structured perturbations can be readily derived. Sufficient conditions for robust stability of switching systems are proposed, and bounds for structured perturbations based on nonnegative matrices that still ensure stability are derived.