Structural invertibility of transfer functions

In this note, we study certain properties of a transfer function in terms of the structure of the state-space representation (A, B, C). Specifically, the rank of the transfer function and the degree of a decoupled system (which can be obtained by applying a left decoupler) are characterized in terms of the structure of (A, B, C).     

On the invertibility of linear systems

Sain and Massey [1] have obtained necessary and sufficient conditions for the invertibility of continuous and discrete time linear systems and have also found bounds for what they termed the "inherent integration" (continuous time) or the "inherent delay" (discrete time) of an invertible linear system. In this note, we tighten these bounds by modifying an argument used to prove the Sain-Massey result.     

On the invertibility of linear multivariable systems

Some results concerning invertibility of a class of linear, time-invariant systems are presented. It is shown that by an appropriate factorization of the transfer matrix of such a system, the problem of cheeking its invertibility can be reduced to that of checking the invertibility of a lower-order system. A sufficient condition for invertibility is also obtained.     

Constructing finite automata with invertibility by transformation method

Ra,Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields.In a previous paper,the authors generalized Ra,Rb transformations to deal with nonlinear memory finite automata,and gave sufficient conditions for weak inverse and for weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automata satisfying one of these sufficient conditions were also given.This paper extends the concepts,methods and results to general finite automata,in which states consist of finite input history,finite output history and finite “inner state“ history.     

The steady-state invertibility and feedforward control of linear time-invariant systems

The notion of steady-state invertibility of a system is introduced, which is concerned about the problem of being able to find an input so that the output of a stable system is asymptotically equal to a specified output of a certain class of functions. Necessary and sufficient conditions are found for a linear time-invariant system to be steady-state invertible. Application of these results is then made to find necessary and sufficient conditions for a feedforward controller to exist for a general linear time-invariant system, so that asymptotic tracking, in the presence of a general class of measurable disturbances occurs. Explicit feedforward controllers which will accomplish this are obtained. Properties of the steady-state invertibility condition are then obtained; in particular, it is shown that a system is "almost always" steady-state invertible if the number of plant inputs is not less than the number of outputs; if the number of plant inputs is less than the number of outputs, then a system is "almost never" steady-state invertible. It is then shown that a system which is minimum phase and which has at least the same number of inputs as outputs is always steady-state invertible.     

用贝叶斯网络进行因果分析

因果分析是贝叶斯网络的一个重要应用领域。因果分析不同于相关分析,无论对数据分析、扰动分析还是预测都是十分重要的。贝叶斯网络虽然有一定的因果语义(我们常常用变量的因果关系构造贝叶斯网络结构),但贝叶斯网络是条件独立性的表示,因此我们不能不加限定地用贝叶斯网络进行因果分析。贝叶斯     

Temporal Causal Abduction

The paper is devoted to presentation of the idea of Temporal Causal Networks (TCN). Temporal Causal Networks constitute a tool for representing and dealing with causal dependencies propagation over time. A temporal causal network is a causal network incorporating explicit representation of time during which its symptoms/nodes are valid, not valid, or unknown. The atemporal causal structure is basically an AND/OR/NOT causal graph, i.e. a causal graph incorporating basic logical connectives for the representation of different types of causal dependencies. The presented approach uses a specific time constraints propagation algorithm to determine possible system behavior in time. The main application includes simulation, monitoring and elements of diagnostic reasoning for dynamic systems with explicit time representation.     

Causal dynamic inference

We suggest a general logical framework for causal dynamic reasoning. As a first step, we introduce a uniform structural formalism and assign it two kinds of semantics, abstract dynamic models and relational models. The corresponding completeness results are proved. As a second step, we extend the structural formalism to a two-sorted state-transition calculus, and prove its completeness with respect to the associated relational semantics.     

Action-Based Causal Reasoning

In this paper we present a causal theory based on aninterventionist conception of causality, i.e., a preference toselect causes among a set of actions which an agent has the abilityto perform or not to perform (free will). The most interestingproposals encountered in the literature, in nonmonotonic reasoning,all revolve around the ordered notion of similarity, abnormality,preference etc... but do not provide a full-fledgedsolution to the problem of the concrete definition of this order. Inour approach we relate the notion of action to norms (what isnormally the case when an action is undertaken, what is normally theoutcome of that action) and considering reasonable assumptions, weshow the existence and uniqueness of the set of voluntary causes foran observed effect (explanation problem). Moreover, the approach advocated in this paper handles ramifications correctly.     

A note on the invertibility of nonlinear input-output differential systems

A new conceptual framework employing differential algebra is proposed for solving the long-standing problem of inverting nonlinear input-output differential systems. Simple characterizations of left and right invertibility are given which rest upon an invariant integer which, for constant linear systems, turns out to be the rank of the transfer matrix.     

一种基于因果强度的局部因果结构主动学习方法

因果结构学习是贝叶斯网络学习中一种重要的结构学习方法,因果关系揭示了系统要素作用的本质。由于 仅利用观测数据很难准确地发现变量间的因果关系,且通常人们仅关心网络中关于某一变量的局部因果关系,因此针 对难以从观测数据中仅获取所感兴趣的变量的局部因果结构的问题,提出了一种局部结构学习方法,即一种基于因果 强度的局部因果结构主动学习方法(CSI-I_CS工力。CSI一工CSI方法融合了马尔可夫毯的结构划分能力和扰动学习的因 果发现能力,并且引入了因果强度进行扰动结点的选择。利用HITON MI3算法寻找目标结点的马尔可夫毯,生成关 于目标结点的局部模型;然后,利用不对称信息墒对局部模型中的每一结点进行因果强度分析,选取因果强度值较大 的结点进行扰动,生成扰动数据;进而,联合扰动数据和观测数据利用准确方法(exact method)学习边的后验概率,从 而获得一个关于目标结点的局部因果网络。利用结构信息嫡对CSI-LCSL方法的学习结果进行评估。在标准网络上 的实验结果证实了CSI一LCSI、算法的有效性。     

Animating Causal Overlays

Most approaches to representing causality, such as the common causal graph, require a separate and static view, but in many cases it is useful to add the dimension of causality to the context of an existing visualization. Building on research from perceptual psychology that shows the perception of causality is a low‐level visual event derived from certain types of motion, we are investigating how to add animated causal representations, called visual causal vectors, onto other visualizations. We refer to these as causal overlays. Our initial experimental results show this approach has great potential but that extra cues are needed to elicit the perception of causality when the motions are overlaid on other graphical objects. In this paper we describe the approach and report on a study that examined two issues of this technique: how to accurately convey the causal flow and how to represent the strength of the causal effect.     

Left invertibility of discrete systems with finite inputs and quantised output

The aim of this article is to address left invertibility for dynamical systems with inputs and outputs in discrete sets. We study systems which evolve in discrete time within a continuous state-space. Quantised outputs are generated by the system according to a given partition of the state-space, while inputs are arbitrary sequences of symbols in a finite alphabet, which are associated to specific actions on the system. Our main results are obtained under some contractivity hypotheses. The problem of left invertibility, i.e. recovering an unknown input sequence from the knowledge of the corresponding output string, is addressed using the theory of iterated function systems (IFS), a tool developed for the study of fractals. We show how the IFS naturally associated to a system and the geometric properties of its attractor are linked to the invertibility property of the system. Our main result is a necessary and sufficient condition for left invertibility and uniform left invertibility for joint contractive systems. In addition, an algorithm is proposed to recover inputs from output strings. A few examples are presented to illustrate the application of the proposed method.     

The invertibility of the XOR of rotations of a binary word

We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen [Cryptographic hash functions, PhD thesis, Technical University of Denmark, 28 November 2008]. Our proof may be new.)     

Computational versus Causal Complexity

The main claim of this paper is that notions of implementation based on an isomorphic correspondence between physical and computational states are not tenable. Rather, ``implementation' has to be based on the notion of ``bisimulation' in order to be able to block unwanted implementation results and incorporate intuitions from computational practice. A formal definition of implementation is suggested, which satisfies theoretical and practical requirements and may also be used to make the functionalist notion of ``physical realization' precise. The upshot of this new definition of implementation is that implementation cannot distinguish isomorphic bisimilar from non-isomporphic bisimilar systems anymore, thus driving a wedge between the notions of causal and computational complexity. While computationalism does not seem to be affected by this result, the consequences for functionalism are not clear and need further investigations.     

Causal Message Sequence Charts

Scenario languages based on Message Sequence Charts (MSCs) have been widely studied in the last decade. The high expressive power of MSCs renders many basic problems concerning these languages undecidable. However, several of these problems are decidable for languages that possess a behavioral property called “existentially bounded”. Unfortunately, collections of scenarios outside this class are frequently exhibited by systems such as sliding window protocols. We propose here an extension of MSCs called causal Message Sequence Charts and a natural mechanism for defining languages of causal MSCs called causal HMSCs (CaHMSCs). These languages preserve decidable properties without requiring existential bounds. Further, they can model collections of scenarios generated by sliding window protocols. We establish here the basic theory of CaHMSCs as well as the expressive power and complexity of decision procedures for various subclasses of CaHMSCs. We also illustrate the modeling power of our formalism with the help of a realistic example based on the TCP sliding window feature.     

Causal models for diagnostic reasoning

Theories of qualitative physics are crucial in developing knowledge-based systems in engineering. Basic models for diagnostic reasoning are based on causal connections between the system parameters. In this paper a knowledge representation and problem solving technique is presented as a ground-laying step. The technique is based on the concepts introduced by Iwasaki and Simon⁹ and employs the methods of analysis from the field of control engineering. The causal analysis of systems with feedback is done by using knowledge about their block diagrams. A constraint representing the feed-forward path is modified in order to eliminate the feedback parameter. This approach supports the confluence heuristic in de Kleer and Brown's qualitative physics⁴. Causal dependencies that partially describe the behaviour of a system are used to generate a search space for faulty components. This approach is based on reasoning about counterfactuals using modal categorizations, as proposed by Nicolas Rescher and Herbert Simon¹². The scope of application of this method in real-time monitoring and diagnosis of large industrial processes is discussed.     

基于互信息的直接因果搜索算法

因果关系挖掘是数据挖掘领域一个新的研究方向,具有很大的实用意义,但理论建模的困难阻碍了它的发展。20世纪90年代,在因果建模研究成果的基础上,国外开始针对此方向进行研究,目前已得到了一些理论算法。该文针对已有算法鲁棒性、实用性差,不适合大规模数据挖掘应用的缺点,提出了一种基于互信息的因果数据挖掘算法———直接因果搜索算法;仿真试验表明,该算法能很好地搜索出目标变量的直接因果,与其他算法相比,对于数据、门限的变化更具鲁棒性。