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Nordkvist N.,Leeward Community College | Crouch P.E.,University of Hawaii at Manoa | Bloch A.M.,University of Michigan | Sanyal A.K.,New Mexico State University
Proceedings of the IEEE Conference on Decision and Control | Year: 2011

In this paper we define a class of optimal control problems which we denote "embedded optimal control problems". These are not true optimal control problems since the control system is not locally controllable on the manifold on which it is defined. Despite this, they allow for a well defined associated optimal control problem which does not admit abnormal extremals. We apply Pontryagin's maximum principle to the embedded optimal control problem to derive the generating differential equations for the normal and abnormal extremals. We show that the normal extremal generating equations in a sense contain the extremal generating equations for the associated optimal control problem. We show that this is not the case for the abnormal extremal generating equations. This has applications to the study of the optimal control of systems constrained to a given submanifold of a configuration space, for example the sphere or hypersphere. We apply the theory to three examples in order to illustrate its applicability and to show how it relates to well known results. © 2011 IEEE.

Aeby G.S.,Hawaii Institute of Marine Biology | Aeby G.S.,University of Hawaii at Manoa | Callahan S.,Hawaii Institute of Marine Biology | Callahan S.,University of Hawaii at Manoa | And 10 more authors.
Diseases of Aquatic Organisms | Year: 2016

In March 2010 and January 2012, we documented 2 widespread and severe coral disease outbreaks on reefs throughout Kāne'ohe Bay, Hawai'i (USA). The disease, acute Montipora white syndrome (aMWS), manifested as acute and progressive tissue loss on the common reef coral M. capitata. Rapid visual surveys in 2010 revealed 338 aMWS-affected M. capitata colonies with a disease abundance of (mean ± SE) 0.02 ± 0.01 affected colonies per m of reef surveyed. In 2012, disease abundance was significantly higher (1232 aMWS-affected colonies) with 0.06 ± 0.02 affected colonies m-1 . Prior surveys found few acute tissue loss lesions in M. capitata in Kāne'ohe Bay; thus, the high number of infected colonies found during these outbreaks would classify this as an emerging disease. Disease abundance was highest in the semi-enclosed region of south Kāne'ohe Bay, which has a history of nutrient and sediment impacts from terrestrial runoff and stream discharge. In 2010, tagged colonies showed an average tissue loss of 24% after 1 mo, and 92% of the colonies continued to lose tissue in the subsequent month but at a slower rate (chronic tissue loss). The host-specific nature of this disease (affecting only M. capitata) and the apparent spread of lesions between M. capitata colonies in the field suggest a potential transmissible agent. The synchronous appearance of affected colonies on multiple reefs across Kāne'ohe Bay suggests a common underlying factor. Both outbreaks occurred during the colder, rainy winter months, and thus it is likely that some parameter(s) associated with winter environmental conditions are linked to the emergence of disease outbreaks on these reefs. © The authors 2016. Open Access under Creative Commons by Attribution Licence. Use, distribution and reproduction are unrestricted. Authors and original publication must be credited.

Bloch A.M.,University of Michigan | Crouch P.E.,University of Hawaii at Manoa | Nordkvist N.,Leeward Community College
Journal of Geometric Mechanics | Year: 2013

In this paper we define "embedded optimal control problems" which prescribe parametrized families of well defined associated optimal control problems. We show that the extremal generating Hamiltonian equations for an embedded optimal control problem and any associated optimal control problem are simply related by a projection. Furthermore normal extremals project to normal extremals and similarly for abnormal extremals. An interesting class of embedded optimal control problems consists of Clebsch optimal control problems. We provide necessary conditions for a Clebsch optimal control problem to describe a variational problem and thereby a mechanical system. There may be many advantages to analyzing an embedded optimal control problem instead of a particular associated optimal control problem, for example the former being defined on a linear space and the latter on a nonlinear space. The continuous analysis is paralleled by a similar discrete analysis. We define a discrete embedded/Clebsch optimal control problem along with associated discrete optimal control problems and we show results that are analogous to the continuous results. We apply the theory, both in the continuous and the discrete setting, to two example systems: mechanical systems on matrix Lie groups and mechanical systems on n-spheres. © American Institute of Mathematical Sciences.

Xu J.,University of Hawaii at Manoa | Gao X.,University of Hawaii at Manoa | Padasdao B.E.,Leeward Community College | Boric-Lubecke O.,University of Hawaii at Manoa
Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS | Year: 2015

Doppler radar physiological sensing has been studied for non-contact detection of vital signs including respiratory and heartbeat rates. This paper presents the first micrometer resolution Wi-Fi band Doppler radar for sub-millimeter physiological displacement measurement. A continuous-wave Doppler radar working at 2.4GHz is used for the measurement. It is intended for estimating small displacements on the body surface resulting from physiological activity. A mechanical mover was used as target, and programmed to conduct sinusoidal motions to simulate pulse motions. Measured displacements were compared with a reference system, which indicates a superior performance in accuracy for having absolute errors less than 10μm, and relative errors below 4%. It indicates the feasibility of highly accurate non-contact monitoring of physiological movements using Doppler radar. © 2015 IEEE.

Sanyal A.K.,New Mexico State University | Nordkvist N.,Leeward Community College
Journal of Guidance, Control, and Dynamics | Year: 2012

A state estimation scheme that does not depend on the statistical distribution of bounded measurement noise is presented. This scheme is used to provide state estimates for feedback in an attitude tracking control scheme that exhibits almost global asymptotically stable tracking of a desired attitude trajectory with perfect state measurements. The control and estimation schemes use the global, unique representation of rigid body attitude provided by rotation matrices. Attitude and angular velocity state estimate updates are obtained from discrete multirate measurements using a deterministic filtering scheme. Propagation of discrete state estimates is carried out with a Lie group variational integrator, which preserves the orthogonality of rotation matrices during numerical propagation without reprojection. This integrator is also used to numerically simulate the feedback system. The performance of this attitude tracking control scheme is then compared with that of a recently reported quaternion observer-based continuous feedback attitude tracking scheme. This quaternion-based attitude tracking scheme is shown to exhibit unstable, unwinding behavior. Numerical simulation results for both these feedback tracking schemes are obtained for a satellite in circular Earth orbit tracking an oscillating angular velocity spin maneuver. These numerical results are then compared for control effort and time taken for the tracking errors to converge to the desired trajectory. © 2011 by Amit K. Sanyal.

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