A Behavioral Approach to the Control of Discrete Linear Repetitive Processes

This paper formulates the theory of linear discrete time repetitive processes in the setting of behavioral systems theory. A behavioral, latent variable model for repetitive processes is developed and for the physically defined inputs and outputs as manifest variables, a kernel representation of their behavior is determined. Conditions for external stability and controllability of the behavior are then obtained. A sufficient condition for stabilizability is also developed for the behavior and it is shown under a mild restriction that, whenever the repetitive system is stabilizable, a regular constant output feedback stabilizing controller exists. Next a notion of eigenvalues is defined for the repetitive process under an action of a closed loop controller. It is then shown how under controllability of the original repetitive process, an arbitrary assignment of eigenvalues for the closed loop response can be achieved by a constant gain output feedback controller under the above restriction. These results on the existence of constant gain output feedback controllers are among the most striking properties enjoyed by repetitive systems, discovered in this paper. Results of this paper utilize the behavioral model of the repetitive process which is an analogue of the 1D equivalent model of the dynamics studied in earlier work on repetitive processes

On control laws for discrete linear repetitive processes with dynamic boundary conditions

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations in the sequence of pass profiles produced which increase in amplitude in the pass-to-pass direction and cannot be controlled by application of standard control laws. Here we give new results on the design of physically based control laws for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control

Poles and zeros – examples of the behavioral approach applied to discrete linear repetitive processes

In this paper the behavorial approach is applied to discrete linear repetitive processes, which are class of 2D systems of both systems theoretic and applications interest. The main results are on poles and zeros for these processes, which have exponential trajectory interpretations

Decoupling and iterative approaches to the control of discrete linear repetitive processes

This paper reports new results on the analysis and control of discrete linear repetitive processes which are a distinct class of 2D discrete linear systems of both systems theoretic and applications interest. In particular, we first propose an extension to the basic state-space model to include a coupling term previously neglected but which arises in some applications and then proceed to show how computationally efficient control laws can be designed for this new model

<i>H</i>₂ and mixed <i>H</i>₂/<i>H</i>_∞ Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation

Control and Filtering for Discrete Linear Repetitive Processes with H infty and ell 2--ell infty Performance

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass to pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws for the sub-class of so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. The main contribution is to show how control law design can be undertaken within the framework of a general robust filtering problem with guaranteed levels of performance. In particular, we develop algorithms for the design of an H? and $\ell_{2}–\ell_{\infty}$ dynamic output feedback controller and filter which guarantees that the resulting controlled (filtering error) process, respectively, is stable along the pass and has prescribed disturbance attenuation performance as measured by $H_{\infty}$ and $\ell_{2}$–$\ell_{\infty}$ norms

Allergic fetal priming leads to developmental, behavioral and neurobiological changes in mice.

The state of the mother's immune system during pregnancy has an important role in fetal development and disruptions in the balance of this system are associated with a range of neurologic, neuropsychiatric and neurodevelopmental disorders. Epidemiological and clinical reports reveal various clues that suggest a possible association between developmental neuropsychiatric disorders and family history of immune system dysfunction. Over the past three decades, analogous increases have been reported in both the incidence of neurodevelopmental disorders and immune-related disorders, particularly allergy and asthma, raising the question of whether allergic asthma and characteristics of various neurodevelopmental disorders share common causal links. We used a mouse model of maternal allergic asthma to test this novel hypothesis that early fetal priming with an allergenic exposure during gestation produces behavioral deficits in offspring. Mothers were primed with an exposure to ovalbumin (OVA) before pregnancy, then exposed to either aerosolized OVA or vehicle during gestation. Both male and female mice born to mothers exposed to aerosolized OVA during gestation exhibited altered developmental trajectories in weight and length, decreased sociability and increased marble-burying behavior. Moreover, offspring of OVA-exposed mothers were observed to have increased serotonin transporter protein levels in the cortex. These data demonstrate that behavioral and neurobiological effects can be elicited following early fetal priming with maternal allergic asthma and provide support that maternal allergic asthma may, in some cases, be a contributing factor to neurodevelopmental disorders

Dance and emotion in posterior parietal cortex: a low-frequency rTMS study

Background: The neural bases of emotion are most often studied using short non-natural stimuli and assessed using correlational methods. Here we use a brain perturbation approach to make causal inferences between brain activity and emotional reaction to a long segment of dance. &lt;p&gt;Objective/Hypothesis: We aimed to apply offline rTMS over the brain regions involved in subjective emotional ratings to explore whether this could change the appreciation of a dance performance.&lt;/p&gt; &lt;p&gt;Methods: We first used functional magnetic resonance imaging (fMRI) to identify regions correlated with fluctuating emotional rating during a 4-minutes dance performance, looking at both positive and negative correlation. Identified regions were further characterized using meta-data interrogation. Low frequency repetitive TMS was applied over the most important node in a different group of participants prior to them rating the same dance performance as in the fMRI session.&lt;/p&gt; &lt;p&gt;Results: FMRI revealed a negative correlation between subjective emotional judgment and activity in the right posterior parietal cortex. This region is commonly involved in cognitive tasks and not in emotional task. Parietal rTMS had no effect on the general affective response, but it significantly (p&lt;0.05 using exact t-statistics) enhanced the rating of the moment eliciting the highest positive judgments.&lt;/p&gt; &lt;p&gt;Conclusion: These results establish a direct link between posterior parietal cortex activity and emotional reaction to dance. They can be interpreted in the framework of competition between resources allocated to emotion and resources allocated to cognitive functions. They highlight potential use of brain stimulation in neuro-æsthetic investigations.&lt;/p&gt

Steady-State movement related potentials for brain–computer interfacing

An approach for brain-computer interfacing (BCI) by analysis of steady-state movement related potentials (ssMRPs) produced during rhythmic finger movements is proposed in this paper. The neurological background of ssMRPs is briefly reviewed. Averaged ssMRPs represent the development of a lateralized rhythmic potential, and the energy of the EEG signals at the finger tapping frequency can be used for single-trial ssMRP classification. The proposed ssMRP-based BCI approach is tested using the classic Fisher's linear discriminant classifier. Moreover, the influence of the current source density transform on the performance of BCI system is investigated. The averaged correct classification rates (CCRs) as well as averaged information transfer rates (ITRs) for different sliding time windows are reported. Reliable single-trial classification rates of 88%-100% accuracy are achievable at relatively high ITRs. Furthermore, we have been able to achieve CCRs of up to 93% in classification of the ssMRPs recorded during imagined rhythmic finger movements. The merit of this approach is in the application of rhythmic cues for BCI, the relatively simple recording setup, and straightforward computations that make the real-time implementations plausible