A graph theoretic approach to input-to-state stability of switched systems

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS. We allow non-ISS systems in the family and our analysis involves graph-theoretic arguments. A weighted digraph is associated to the switched system, and a switching signal is expressed as an infinite walk on this digraph, both in a natural way. Our class of stabilizing switching signals (infinite walks) is periodic in nature and affords simple algorithmic construction.Comment: 14 pages, 1 figur

Multi-agent persistent monitoring of a finite set of targets

The general problem of multi-agent persistent monitoring finds applications in a variety of domains ranging from meter to kilometer-scale systems, such as surveillance or environmental monitoring, down to nano-scale systems such as tracking biological macromolecules for studying basic biology and disease. The problem can be cast as moving the agents between targets, acquiring information from or in some fashion controlling the states of the targets. Under this formulation, at least two questions need to be addressed. The first is the design of motion trajectories for the agents as they move among the spatially distributed targets and jointly optimize a given cost function that describes some desired application. The second is the design of the controller that an agent will use at a target to steer the target's state as desired. The first question can be viewed in at least two ways: first, as an optimal control problem with the domain of the targets described as a continuous space, and second as a discrete scheduling task. In this work we focus on the second approach, which formulates the target dynamics as a hybrid automaton, and the geometry of the targets as a graph. We show how to find solutions by translating the scheduling problem into a search for the optimal route. With a route specifying the visiting sequence in place, we derive the optimal time the agent spends at each target analytically. The second question, namely that of steering the target's state, can be formulated from the perspective of the target, rather than the agent. The mobile nature of the agents leads to intermittencontrol, such that the controller is assumed to be disconnected when no agent is at the target. The design of the visiting schedule of agents to one target can affect the reachability (controllability) of this target's control system and the design of any specific controller. Existing test techniques for reachability are combined with the idea of lifting to provide conditions on systems such that reachability is maintained in the presence of periodic disconnections from the controller. While considering an intermittently connected control with constraints on the control authority and in the presence of a disturbance, the concept of 'degree of controllability' is introduced. The degree is measured by a region of states that can be brought back to the origin in a given finite time. The size of this region is estimated to evaluate the performance of a given sequence

Actuation Mechanism for a Switch-Mode Continuously Variable Transmission

With greater energy storage and power density than electric or hydraulic systems, a flywheel kinetic energy recovery system may be a solution for increasing efficiency in passenger vehicles. A Switch Mode Continuously Variable Transmission connects a high-speed flywheel to the drivetrain with a high-speed clutch. The goal of this project was to control the clutch’s high-speed duty cycle with improved efficiency, wear, and reliability than previous systems. The design uses an eccentric cam to drive a set of linear cams at high speed to engage the clutch. Each translating roller follower has an internal spring system to output the desired clamping force. Duty cycle is varied by changing the position of the eccentric camshaft. The device shows significant improvement over previous work

The Role Of N-Terminal Acidic Inserts On The Dynamics Of The Tau Protein.

Alzheimer’s disease (AD), the most prevalent neurodegenerative disease, is characterized in part by disruptions in axonal transport. Axonal transport is a process by which motor proteins carry organelles and other cargo made in the neuronal cell body along microtubule tracks to distal regions of the axon. The microtubule-associated protein (MAP) Tau plays a crucial role in regulating axonal transport, and is implicated in the development of AD and other types of dementia collectively known as Tauopathies. Tau is a neuronal-specific MAP that has six isoforms alternatively spliced from a single gene. These isoforms differ by the presence of zero, one, or two N-terminal acidic inserts and three or four C-terminal microtubule binding repeats. Tau is also known to be an intrinsically disordered protein that undergoes a dynamic equilibrium between static and diffusive states on the microtubule surface. The dynamics of Tau are important in the regulation of motor protein mediated axonal transport in neurons. Isoform-specific differences in the dynamic behavior of Tau on the microtubule surface, however, are not yet fully understood. Diffusive Tau is thought to be stabilized by electrostatic interactions between its N- and C-termini while static Tau is proposed to be extended with its C-terminal repeats contacting the microtubule and the N-terminus projected away from the microtubule surface. Thus, the N-terminal inserts may help regulate Tau’s dynamic behavior and function during axonal transport. In this study, the dynamics of two different isoforms of Tau, both with three-microtubule binding repeats but a different number of N-terminal acidic inserts, were assessed using single molecule imaging techniques and novel data analysis methods

“Field Weakening Operation of AC Machines for Traction Drive Applications.”

The rising cost of gasoline and environmental concerns have heightened the interest in electric/hybrid-electric vehicles. In passenger vehicles an electric traction motor drive must achieve a constant power speed range (CPSR) of about 4 to 1. This modest requirement can generally be met by using most of the common types of electric motors. Heavy electric vehicles, such as tanks, buses and off-road equipment can require a CPSR of 10 to 1 and sometimes much more. Meeting the CPSR requirement for heavy electric vehicles is a significant challenge. This research addresses the CPSR capability and control requirements of two candidates for high CPSR traction drives: the permanent magnet synchronous motor (PMSM) and the switched reluctance motor (SRM). It is shown that a PMSM with sufficiently large winding inductance has an infinite CPSR capability, and can be controlled using a simple speed control loop that does not require measurement of motor phase currents. Analytical and experimental results confirm that the conventional phase advancement method charges motor winding with required current to produce the rated power for the speed range where the back-EMF normally prevents the generation of the rated power. A key result is that for the PMSM, the motor current at high speed approaches the machine rating independent of the power produced. This results in poor partial load efficiency. The SRM is also shown to have infinite CPSR capability when continuous conduction is permitted during high speed operation. Traditional high speed control is of discontinuous type. It has been shown that this discontinuous conduction itself is the limiter of CPSR. Mathematical formulas have been developed relating the average current, average power, and peak current required producing the desired (rated) power to machine design parameters and control variables. Control of the SRM in the continuous conduction mode is shown to be simple; however, it does require measurement of motor current. For the SRM the motor current at high speed is proportional to the power produced which maintains drive efficiency even at light load conditions