# Poster session and reception

Tuesday, May 8, 2018 - 4:30pm - 6:00pm

Lind 400

**Heart Rhythm Control Using Novel Anti-Arrhythmic Pacing Protocol**

Alena Talkachova (University of Minnesota, Twin Cities)

Introduction. Periodic pacing of the heart is incorporated in various medical devices and is clinically used to treat cardiovascular diseases. The widely accepted periodic pacing algorithm, however, suffers drawbacks and inherently has pro-arrhythmic properties. Cardiac alternans, a beat-to-beat alternation in action potential duration (APD), is a precursor to fatal arrhythmias. During periodic pacing, changes in diastolic interval (DI) depend on subsequent changes in APD, thus enhancing cardiac instabilities through ‘feedback’ mechanism. Recently, an anti-arrhythmic Constant DI pacing protocol was proposed and shown to be effective in suppressing alternans in 0D and 1D in-silico studies. However, experimental validation of Constant DI in the heart has been unsuccessful due to the spatio-temporal complexity of 2D cardiac tissue and the technical challenges in its real-time implementation.

Purpose. Here, we developed a novel closed loop system to detect T-waves from real-time ECG data, enabling successful implementation of Constant DI, and performed high-resolution optical mapping experiments on isolated whole rabbit hearts to validate its anti-arrhythmic effects. The results were compared with: (1) Periodic pacing and (2) pacing with heart rate variability (HRV) introduced by using either Gaussian or Physiological patterns.

Results. First, we successfully implemented an algorithm for real-time detection of T-waves and validated its efficacy in controlling the DI on a beat-to-beat basis in the heart. Second, Constant DI pacing prevented the occurrence of alternans in the heart, in comparison to traditional Periodic pacing (5% vs 100%, p less than 0.05), thus providing an anti-arrhythmic effect. Constant DI pacing was associated with an increase in APD and decreases the maximum slope of APD restitution curve (Smax) while not affecting spatial heterogeneity of APD (µ) in comparison to Periodic pacing. On the other hand, feedback modulation using HRV pacing, which was modeled with either Gaussian or in-vivo Physiological patterns, promoted the formation of alternans and VF in the heart, thus enhancing arrhythmogenecity. HRV pacing was associated with both increased Smax and m, and earlier occurrence of alternans, in comparison to Periodic pacing, thus providing clear pro-arrhythmic effects.

Conclusion. We present a successful validation, using whole heart optical mapping experiments, of a novel anti-arrhythmic Constant DI pacing protocol that can be implemented in real time for the beat-to beat control of cardiac rhythm.**Control of Connected and Automated Vehicles with Communication Erasure Channels**

Thu Nguyen (Wayne State University)

Connected and automated vehicles require integrated design of communications and control to achieve coordination of highway vehicles. Random features of wireless communications result in uncertainties in networked systems and impact control performance. Here we model switching network topologies by Markov chains and examine the impact of communication erasure channels on vehicle platoon formation and robustness under a weighted and constrained consensus framework. By comparing convergence properties of networked control algorithms under different communication channel features, we characterize some intrinsic relationships between packet delivery ratio and convergence rate. Simulation case studies are performed to verify the theoretical findings.**Hybrid Competitive Lotka-Volterra Ecosystems: Countable Switching States and Two-time-scale Models**

Trang Bui (Wayne State University)

The work is concerned with competitive Lotka- Volterra model with Markov switching. Our main effort is to reduce the computational complexity. A novelty of the contribution is that the Markov chain has a countable state space. Another distinct feature is that two-time-scale systems are considered. The two-time scale feature is highlighted by introducing a small parameter into the generator of the Markov chain. When the small parameter goes to 0, there is a limit system or reduced system. It is established in this work that if the reduced system possesses certain properties such as permanence, extinction, recurrence etc, then the original complex system also has the same properties when the parameter is sufficiently small. These results are obtained by using the perturbed Lyapunove function methods.**H2-Filtering for discrete-time hidden Markov jump systems: A detector-based approach**

Oswaldo Costa (University of São Paulo (USP))

We consider the H2 filtering for discrete-time Markov jump linear systems assuming that the Markov chain cannot be measured. Instead the only information available to the filter comes from a detector in the spirit of the so-called hidden Markov models (HMM). The motivation for this approach is twofold: on the one hand, the most important cases regarding the availability of the Markov chain are generalized, such as the complete observation and the mode-independent cases; on the other hand the detector approach has a strong appeal to practical fields of research such as the active fault-tolerant control systems (AFTCS), where the measured variable could be regarded as a failure detector. We propose a sufficient condition based on the linear matrix inequality (LMI) formulation such that the H2 norm with respect to the estimation error is bounded. A numerical example is given in order to illustrate our results.**Unified Simulation for Nonlinear PDEs by Interpolatory HDG Methods**

Yangwen Zhang (Missouri University of Science and Technology)

We propose a new Interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method to unify simulation the nonlinear PDEs. This method has many postive features; First, we can avoid the numerical quadrature typically required for the assembly of the global matrix at each iteration. Second, we have simple explicit expressions for the nonlinear term and Jacobian matrix, which leads to a simple unified implementation for a variety of nonlinear PDEs. Third, the convergence rate is not reduced.**Finite Time Stabilization of Linear Systems with Unknown Dynamics**

Mohamad Kazem Shirani Faradonbeh (University of Florida)

Stabilization of dynamical systems is an important problem in control theory. For this purpose, the dynamics of the system need to be certainly known to the operator, which is infeasible in many applications. In fact, a control policy can destabilize the system of uncertain dynamics; i.e. drive its state to infinity. Further, finding an optimal policy might need the dynamics matrices to be precisely identified. Such an identification is challenging because of the unstable behavior of the system before the accomplishment of the stabilization procedure. Although a few asymptotic studies are available in the literature, there is hardly any result regarding the stabilization in finite time. In this work, we propose an algorithm to find a stabilization set in finite time. The results rely on the application of random linear feedbacks, as well as the identification of unstable systems.