On the Control of Distributed Parameter Systems using a Multidimensional Systems Setting

The unique characteristic of a repetitive process is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration with resetting before the start of the each new one. 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 leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations which increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by standard linear systems approach and instead they must be treated as a multidimensional system, i.e. information propagation in more than one independent direction. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control systems design algorithms are developed for a model where a plane, or rectangle, of information is propagated in the passto- pass direction. The possible use of these in the control of distributed parameter systems is then described using a fourthorder wavefront equation

Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest whose dynamics evolve over a subset of the positive quadrant in the 2D plane. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Stability along the pass demands a bounded-input bounded-output property over the complete positive quadrant of the 2D plane and this is a very strong requirement, especially in terms of control law design. A more feasible alternative for some cases is strong practical stability, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality (LMI) based tests, which then extend to allow control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that extend to allow control law design in the presence of uncertainty in process model

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

The effects of repetitive electric cardiac stimulation in dogs with normal hearts, complete heart block and experimental cardiac arrest

Direct cardiac stimulation was conducted in the open chest. In normal animals, auricular stimulation at frequencies faster than the spontaneous rate caused little change in vascular pressures or cardiac output. Comparable ventricular stimulation in the same animals caused falls in cardiac output and blood pressure, with elevations in venous pressure. In contrast, ventricular stimulation in animals with complete heart block caused elevations in cardiac output and blood pressure, and declines in venous pressure. A study was also made of repetitive stimulation in experimental cardiac arrest. Occasionally pacemaking was of value in the resuscitation, but in most cases effective contractions could not be induced with stimulation

Basic gestures as spatiotemporal reference frames for repetitive dance/music patterns in samba and charleston

THE GOAL OF THE PRESENT STUDY IS TO GAIN BETTER insight into how dancers establish, through dancing, a spatiotemporal reference frame in synchrony with musical cues. With the aim of achieving this, repetitive dance patterns of samba and Charleston were recorded using a three-dimensional motion capture system. Geometric patterns then were extracted from each joint of the dancer's body. The method uses a body-centered reference frame and decomposes the movement into non-orthogonal periodicities that match periods of the musical meter. Musical cues (such as meter and loudness) as well as action-based cues (such as velocity) can be projected onto the patterns, thus providing spatiotemporal reference frames, or 'basic gestures,' for action-perception couplings. Conceptually speaking, the spatiotemporal reference frames control minimum effort points in action-perception couplings. They reside as memory patterns in the mental and/or motor domains, ready to be dynamically transformed in dance movements. The present study raises a number of hypotheses related to spatial cognition that may serve as guiding principles for future dance/music studies

LMI based Stability and Stabilization of Second-order Linear Repetitive Processes

This paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the secondorder dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in the original model

Testing rTMS-Induced Neuroplasticity: A Single Case Study of Focal Hand Dystonia

Focal hand dystonia in musicians is a neurological motor disorder in which aberrant plasticity is caused by excessive repetitive use. This work's purposes were to induce plasticity changes in a dystonic musician through five daily thirty-minute sessions of 1\u2009Hz repetitive transcranial magnetic stimulation (rTMS) applied to the left M1 by using neuronavigated stimulation and to reliably measure the effect of these changes. To this aim, the relationship between neuroplasticity changes and motor recovery was investigated using fine-grained kinematic analysis. Our results suggest a statistically significant improvement in motor coordination both in a task resembling the dystonic-inducing symptoms and in a reach-to-grasp task. This single case study supports the safe and effective use of noninvasive brain stimulation in neurologic patients and highlights the importance of evaluating outcomes in measurable ways. This issue is a key aspect to focus on to classify the clinical expression of dystonia. These preliminary results promote the adoption of kinematic analysis as a valuable diagnostic tool