Behavioral Systems Theory Research Articles

A common heritage of behaviour systems

Abstract Behaviour systems theory had its beginnings with Nikolaas Tinbergen’s “hierarchical systems”, an aspect of his thinking and writing that he conspicuously left out of his very memorable 1963 manifesto. This starting point has since been developed within psychology, where it has provided numerous advances. Tinbergen’s aspiration for behaviour systems had been principled integration of ethology with physiology, but the bridge among sciences it ultimately provided led to psychology. To an ethology audience, this paper attempts to reintroduce behaviour systems as a part of Tinbergen’s legacy to make accessible the theoretical developments of behaviour systems theory that have occurred outside of ethology over the last several decades. To a psychology audience, the paper serves as a reminder of the ethological origins of behaviour systems. Both sciences and their integration stand to benefit from recognising this point of common heritage.

Modellingand supervisory control of hybrid dynamical systems via fuzzy l-complete approximation approach

This paper proposes a fuzzy l-complete approximation technique based on Willems’ behavioural systems theory for a class of hybrid system with symbolic inputs and quantized measurements. The discrete controller (or supervisor) is designed based on the abstracted (or approximated) system and high-level specifications. Furthermore, we show that the set of external behaviour (i.e., state set) of the fuzzy l-complete approximation based on the notion of ‘guardian states’ contains or at least equal to the behaviour set generated by traditional l-complete discrete abstraction. Finally, several simulation examples are presented to show the effectiveness of the proposed method for supervisory control of a special class of hybrid systems.

First things first: anger management group work in a mainstream high school setting

In an attempt to support the emotional development and behavioural choices of young students in grades 7–10, a six session therapeutic group programme was devised – culminating in a written manual to enable future replication of the programme. This pilot programme was introduced as a once-weekly, morning session aimed at prioritising a student’s need for emotional regulation in an attempt to support academic learning outcomes. Specifically, the group programme provided a five-stage understanding of the cycle of anger, with an additional session allocated for case studies and review. This article seeks to describe the pilot intervention – specifically the therapeutic content – such that it can be replicated elsewhere. Informed by cognitive behavioural therapy, attachment theory and systems theory, the programme sought to respond to the similar needs of multiple students within a time efficient and age-appropriate format.

The Past Is Present: Representations of Parents, Friends, and Romantic Partners Predict Subsequent Romantic Representations.

This study examined how representations of parent-child relationships, friendships, and past romantic relationships are related to subsequent romantic representations. Two-hundred 10th graders (100 female; Mage =15.87years) from diverse neighborhoods in a Western U.S. city were administered questionnaires and were interviewed to assess avoidant and anxious representations of their relationships with parents, friends, and romantic partners. Participants then completed similar questionnaires and interviews about their romantic representations six more times over the next 7.5years. Growth curve analyses revealed that representations of relationships with parents, friends, and romantic partners each uniquely predicted subsequent romantic representations across development. Consistent with attachment and behavioral systems theory, representations of romantic relationships are revised by representations and experiences in other relationships.

Aggression Protects Against the Onset of Major Depressive Episodes in Individuals With Bipolar Spectrum Disorder

A growing body of research suggests that bipolar spectrum disorders (BSDs) are associated with high aggression. However, little research has prospectively examined how aggression may affect time to onset of hypomanic/manic versus major depressive episodes. In a longitudinal study, we tested the hypothesis that aggression would prospectively predict a shorter time to the onset of hypomanic/manic episodes and a longer time to the onset of major depressive episodes, based on the behavioral approach system theory of BSDs. Young adults (N = 120) diagnosed with cyclothymia, bipolar II disorder, or bipolar disorder not otherwise specified were followed every 4 months for an average of 3.55 years. Participants completed measures of depressive and manic symptoms, family history of mood disorder, impulsivity, and aggression at baseline and were followed prospectively with semistructured diagnostic interview assessments of hypomanic/manic and major depressive episodes and treatment seeking for mood problems. Cox proportional hazard regression analyses indicated that overall, physical, and verbal aggression predicted a longer time to major depressive episode onset, even after controlling for baseline depressive and manic symptoms, family history of mood disorder, treatment seeking for mood problems, and impulsivity. Aggression, however, did not significantly predict time to onset of hypomanic/manic episodes, controlling for the same covariates. The findings suggest that approach-related behaviors may be utilized to delay the onset of major depressive episodes among people with BSDs.

Behavioral controllability and coprimeness for pseudorational transfer functions

Controllability plays various crucial roles in behavioral system theory. While there exist several characterizations of this notion, in terms of the Bézout identity, image representation, direct sum decomposition, etc., its overall picture for infinite-dimensional systems still remains rather incomplete, in spite of various existing attempts. This article gives an extension of such results in a well-behaved class of infinite-dimensional systems, called pseudorational. A proper choice of an algebra makes the treatment more transparent. We establish equivalent conditions for controllability in terms of the Bézout identity, relationships with notions such as image representation and direct sum decompositions.

Synthesis and application of a real‐time model‐free behavioral controller with bumpless switching mechanism

SummaryThe aims of this paper are twofold. Firstly, we present a model‐free algorithm for synthesizing an online controller. Secondly, this algorithm also addresses the issue of switching this controller in a closed loop with a bumpless interconnection mechanism. The novelty of this algorithm lies in the fact that we do not use any a priori knowledge of the model of the plant in real time. We use the mathematical framework of behavioral system theory to demonstrate the online controller synthesis and its implementation mechanism. The effectiveness of the proposed algorithm is demonstrated on the experimental three‐tank system. Copyright © 2015 John Wiley & Sons, Ltd.

Towards Kron reduction of generalized electrical networks

Kron reduction is used to simplify the analysis of multi-machine power systems under certain steady state assumptions that underly the usage of phasors. Using ideas from behavioral system theory, in this paper we show how to perform Kron reduction for a class of electrical networks, called homogeneous electrical networks, without steady state assumptions. The reduced models can thus be used to analyze the transient as well as the steady state behavior of these electrical networks.

Asynchronous [formula omitted]-complete approximations

This paper extends the l-complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous l-complete approximation, an asynchronous version of the well-known concepts of state property, memory span and l-completeness is introduced, extending the behavioral systems theory in a consistent way.

A hierarchical and modular control architecture for sequential behaviours

This paper develops a hierarchical and modular control architecture for so called sequential behaviours, i.e. for plant dynamics and specifications that are represented as formal languages of infinite-length words. Our main result is the elaboration of structural properties that allow for abstraction based controller design and that are preserved under closed-loop composition. Thus, we propose to alternate controller design, closed-loop composition and abstraction in order to construct a hierarchical control system in a bottom-up fashion. When the overall plant is composed from a number of components, our approach naturally extends to the alternation of controller design, closed-loop composition, abstraction and component composition. Technically, our results are based on the notion of input-output systems known from behavioural systems theory, with a particular focus on liveness properties represented as sequential behaviours that are not necessarily topologically closed.

Legitimising risk taking: articulating dangerous behaviour on the road

Using a deliberative approach 228 members of the public from four locations in the United Kingdom took part in six focus groups that met on three occasions. Applying a model based on two interlocking sets of theories (Ajzen's Theory of Planned Behaviour and Bronfenbrenner's Ecological Systems Theory) in the analysis of participants' responses, the paper explores the social and environmental systems that an individual interacts with in the articulation of risky behaviours on the road. Participants discussed how taking risks changed over their lifecourse and how they became safer with age. Social norms and perceived behavioural control influence road user safety behaviour through the exchanging of attitudes, and younger drivers especially are more likely to embrace the symbolic role of the car. The paper concludes that the nature of identity and culture within risk taking is important when designing interventions on the ground.

Duality in the behavioral systems theory

In this note, Willems’ behavioral framework is slightly generalized in order to define the dual of a linear system and make the concepts of controllability and observability dual to each other.

A subspace approach to linear dynamical systems

In this paper we present an approach to linear dynamical systems which combines the positive features of two well known formulations, namely, standard state space theory (see for e.g., Wonham, 1978 [9]) and behavioural systems theory (see Polderman and Willems, 1997 [4]). Our development is also ‘geometric’ in the tradition of Wonham and others. But, instead of using explicit linear maps, we work with linear relations implicitly which amounts to working with subspaces. One of our primary motivations is computational efficiency—all our computations can be performed on the system as it is without elimination of variables and further (unlike the ‘behaviourists’ who manipulate matrices with polynomial entries) we work only with real matrices.Using our formulation we derive the standard vector space results on controlled and conditioned invariant subspaces of linear dynamical systems. Duality, which is a distinctive feature of state space theory but not of the behavioural view point, comes out naturally in our approach too through the use of the adjoint. We illustrate our ideas for an important class of dynamical systems viz., electrical networks.The theory proposed in this paper gives a unified description of both the standard linear dynamical systems and the linear singular systems (or the linear descriptor systems) (see for e.g., F. Gantmacher 1959 [1] and Lewis, 1986 [2]). Therefore, the algorithms described for the invariant spaces in this paper are also applicable to linear singular systems.

Behavioural Inhibition System (BIS) sensitivity differentiates EEG theta responses during goal conflict in a continuous monitoring task

Previous research has revealed that EEG theta oscillations are affected during goal conflict processing. This is consistent with the behavioural inhibition system (BIS) theory of anxiety (Gray & McNaughton, 2000). However, studies have not attempted to relate these BIS-related theta effects to BIS personality measures. Confirmation of such an association would provide further support for BIS theory, especially as it relates to trait differences. EEG was measured (32 electrodes) from extreme groups (low/high trait BIS) engaged in a target detection task. Goal conflicts were introduced throughout the task. Results show that the two groups did not differ in behavioural performance. The major EEG result was that a stepwise discriminant analysis indicated discrimination by 6 variables derived from coherence and power, with 5 of the 6 in the theta range as predicted by BIS theory and one in the beta range. Also, across the whole sample, EEG theta coherence increased at a variety of regions during primary goal conflict and showed a general increase during response execution; EEG theta power, in contrast, was primarily reactive to response execution. This is the first study to reveal a three-way relationship between the induction of goal conflict, the induction of theta power and coherence, and differentiation by psychometrically-defined low/high BIS status.

UNA TEORÍA CONDUCTUAL DE SISTEMAS DEL DESARROLLO

Behavioral Systems Theory <881) is the confluence of principies from behavior analysis and dynamical systems theory applied to human development. BSI takes a natural science approach to the study of the changas in bahavior/anvironment relationships ovar tha lifespan. ln BSI, simple mechanisms produce complex developmantal outcomas. Iba parallelism between natural seiection and learning ¡5 emphasized and the importance of principIes of operant Iearning in development is stressed. Development is considerad to be multidirectional, multiply determinad and multileveled. Among the BSI principies described are reciprocai daterminism, nonlinearity, coalescent organization, leading parts, control parameters, and attractor states. Ihe role of contingencias in organizing patterns of behavior is presentad. Weight is placed on davelopment as skills learning.

Technical Committee on Behavioral Systems and Control Theory [Technical Committee Activities

Technical Committee on Behavioral Systems and Control Theory [Technical Committee Activities

Exact linear modeling with polynomial coefficients

Given a finite set of polynomial, multivariate, and vector-valued functions, we show that their span can be written as the solution set of a linear system of partial differential equations (PDE) with polynomial coefficients. We present two different but equivalent ways to construct a PDE system whose solution set is precisely the span of the given trajectories. One is based on commutative algebra and the other one works directly in the Weyl algebra, thus requiring the use of tools from non-commutative computer algebra. In behavioral systems theory, the resulting model for the data is known as the most powerful unfalsified model (MPUM) within the class of linear systems with kernel representations over the Weyl algebra, i.e., the ring of differential operators with polynomial coefficients.

Why social scientists don't like Darwin and what can be done about it

The paper identifies three reasons why social scientists have not readily accepted a Darwinian perspective: first, in the relative importance they attribute to variability in social and cultural systems; second, in their conception of social evolution; third, in their emphasis on the emergent properties of social interaction. I locate the social sciences’ position in the late nineteenth century debate between Durkheim and Tarde, but point out that Durkheim is wrongly accused of presenting the human mind as a ‘blank slate’. Durkheim and Tarde took different lessons from Darwin's Origin of Species. The concept of co-evolution, as applied in behavioural ecology and complex systems theory, promises to bring the social and evolutionary sciences closer together. Our species has evolved a complex capacity for sustaining social relations, and outbreaks of violence must be explained not only in terms of evolved psychological dispositions, but also put in their social context. The diffusion of innovations in a farming economy must likewise be explained as a response to changes in the economic environment for which the farmers themselves are partly responsible through their engagement with the market economy. Cross-cultural applications of game theory indicate a fruitful way forward.

Trait BIS predicts alpha asymmetry and P300 in a Go/No‐Go task

Inspired by the revised Behavioural Inhibition System (BIS) theory the present study probed the association between individual differences in Trait BIS and electroencephalogram indicators of conflict processing/inhibition. Sixty‐nine male participants either high or low in Trait BIS completed a Go/No‐Go task while the electroencephalogram was recorded. As expected, Trait BIS was associated with the No‐Go‐anteriorisation of the P300 event‐related potential (i.e. an index of response inhibition presumably generated in the dorsal anterior cingulate—an area implicated in conflict processing) and with No‐ Go‐related changes towards left frontal alpha activity (i.e. presumably more activity in right prefrontal cortex—an area implicated in response inhibition). These findings support the role of conflict processing attributed to BIS functioning in the revised theory. Copyright © 2009 John Wiley & Sons, Ltd.

Behavioral Systems Theory: A Survey

Behavioral Systems Theory: A SurveyWe survey the so-called behavioral approach to systems and control theory, which was founded by J. C. Willems and his school. The central idea of behavioral systems theory is to put the focus on the set of trajectories of a dynamical system rather than on a specific set of equations modelling the underlying phenomenon. Moreover, all signal components are treated on an equal footing at first, and their partition into inputs and outputs is derived from the system law, in a way that admits several valid cause-effect interpretations, in general.