Border Collision Bifurcation Control of Cardiac Alternans

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period doubling border collision bifurcation. No smooth period doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in control laws that quench the bifurcation and hence result in alternan suppression

Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems

Feedback controls that stabilize border collision bifurcations are designed for piecewise smooth systems undergoing border collision bifurcations. The paper begins with a summary of the main results on border collision bifurcations, and proceeds to a study of stabilization of these bifurcations for one-dimensional systems using both static and dynamic feedback. The feedback can be applied on one side of the border, or on both sides. To achieve robustness to uncertainty in the border itself, a simultaneous stabilization problem is stated and solved. In this problem, the same control is applied on both sides of the border. Dynamic feedback employing washout filters to maintain fixed points is shown to lead to stabilizability for a greater range of systems than static feedback. The results are obtained with a focus on systems in normal form

Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems

Feedback control of piecewise smooth discrete-time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasistatically varied. The goal of the control effort in this work is to modify the bifurcation so that the bifurcated steady state is locally attracting and locally unique. To achieve this, Lyapunov-based techniques are used. A sufficient condition for nonbifurcation with persistent stability in piecewise smooth maps of dimension $n$ that depend on a parameter is derived. The derived condition is in terms of linear matrix inequalities. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce desirable behavior

GPS Based Autonomous Navigation Study for the Lunar Gateway

This paper describes and predicts the performance of a conceptual autonomous GPS-based navigation system for NASA's planned lunar Gateway. This system is based on the flight-proven Magnetospheric Multiscale (MMS) GPS navigation system, augmented with an earth-pointed high-gain antenna and with an option for an atomic clock. High-fidelity simulations, calibrated against MMS flight data and making use of GPS transmitter patterns from the GPS Antenna Characterization Experiment (ACE) project are developed for operation of the system in the Gateway Near-Rectilinear Halo Orbit (NRHO). The results indicate that GPS can provide an autonomous, realtime navigation capability with comparable, or superior, performance to traditional Deep Space Network approach with eight hours of tracking per day

A Novel RF Architecture for Simultaneous Communication, Navigation, and Remote Sensing with Software-Defined Radio

The rapid growth of SmallSat and CubeSat missions at NASA has necessitated a re-evaluation of communication and remote-sensing architectures. Novel designs for CubeSat-sized single-board computers can now include larger Field-Programmable Gate Arrays (FPGAs) and faster System-on-Chip (SoCs) devices. These components substantially improve onboard processing capabilities so that varying subsystems no longer require an independent processor. By replacing individual Radio Frequency (RF) systems with a single software-defined radio (SDR) and processor, mission designers have greater control over reliability, performance, and efficiency. The presented architecture combines individual processing systems into a single design and establishes a modular SDR architecture capable of both remote-sensing and communication applications. This new approach based on a multi-input multi-output (MIMO) SDR features a scalable architecture optimized for Size, Weight, Power, and Cost (SWaP-C), with sufficient noise performance and phase-coherence to enable both remote-sensing and navigation applications, while providing a communication solution for simultaneous S-band and X-band transmission. This SDR design is developed around the NASA CubeSat Card Standard (CS2) that provides the required modularity through simplified backplane and interchangeable options for multiple radiation-hardened/tolerant processors. This architecture provides missions with a single platform for high-rate communication and a future platform to develop cognitive radio systems

Feedback Control of Border Collision Bifurcations in Two-Dimensional Discrete-Time Systems

The feedback control of border collision bifurcations is consideredfor two-dimensional discrete-time systems. These are bifurcations that can occur when a fixed point of a piecewise smooth system crosses the border between two regions of smooth operation. The goal of the control effort is to modify the bifurcation so that the bifurcated steady state is locally unique and locally attracting. In this way, the system's local behavior is ensured to remain stable and close to the original operating condition. This is in the same spirit as local bifurcation control results for smooth systems, although the presence of a border complicates the bifurcation picture considerably. Indeed, a full classification of border collision bifurcations isn't available, so this paper focuses on the more desirable (from a dynamical behavior viewpoint) cases for which the theory is complete. The needed results from the analysis of border collision bifurcations are succinctly summarized. The control design is found to lead to systems of linear inequalities. Any feedback gains that satisfy these inequalities is then guaranteed to solve the bifurcation control problem. The results are applied to an example to illustrate the ideas

Instability Monitoring and Control of Power Systems

Today's electric power systems are often subject to stress by heavy loading conditions, resulting in operation with a small margin of stability. This has led to research on estimating the distance to instability. Most of these research efforts are solely model-based. In this work, a signal-based approach for real-time detection of impending instability is considered. The main idea pursued here involves using a small additive white Gaussian noise as a probe signal and monitoring the spectral density of one or more measured states for certain signatures of impending instability. Input-to-state participation factors are introduced as a tool to aid in selection of locations for probe inputs and outputs to be monitored. Since these participation factors are model-based, the chapter combines signal-based and model-based ideas toward achieving a robust methodology for instability monitoring

New Results on Modal Participation Factors: Revealing a Previously Unknown Dichotomy

The final version of this paper appeared in IEEE Transactions on Automatic Control, Volume 54, Issue 7, July 2009, pp. 1439-1449.This paper presents a new fundamental approach to modal participation analysis of linear time-invariant systems, leading to new insights and new formulas for modal participation factors. Modal participation factors were introduced over a quarter century ago as a way of measuring the relative participation of modes in states, and of states in modes, for linear time-invariant systems. Participation factors have proved their usefulness in the field of electric power systems and in other applications. However, in the current understanding, it is routinely taken for granted that the measure of participation of modes in states is identical to that for participation of states in modes. Here, a new analysis using averaging over an uncertain set of system initial conditions yields the conclusion that these quantities(participation of modes in states and participation of states in modes) should not be viewed as interchangeable. In fact, it is proposed that a new definition and calculation} replace the existing ones for state in mode participation factors, while the previously existing participation factors definition and formula should be retained but viewed only as mode in state participation factors. Examples are used throughout the paper to illustrate the issues addressed and results obtained.National Science Foundation, Office of Naval Research

GPS Based Autonomous Navigation Study for the Lunar Gateway

No abstract availabl

Washout Filters in Feedback Control: Benefits, Limitations and Extensions

Advantages and limitations of washout filters in feedback control of both continuous-time and discrete-time systems are discussed and generalizations that alleviate the limitations are presented. Some previously unpublished results in the Ph.D. dissertation of one of the authors (Lee, 1991) are presented in the context of their relation to the generalized results and to recent publications on delayed feedback control. We show that delayed feedback control (for discrete-time systems) extensively used in control of chaos is a special case of washout filter-aided feedback. Moreover, the limitations of delayed feedback control can be overcome by the use of washout filter-aided feedback, which gives rise to the possibility of stabilizing a much larger class of systems