Individual Enforcement of Canada\u27s Environmental Protection Laws: The Weak-spirited Need Not Try

It is no secret that public awareness and concern for environmental protection in Canada has increased significantly in recent years. Legislators have addressed these concerns by implementing new laws to regulate the various practices that impact negatively on the environment. With statutes in hand, environmentally conscious individuals are beginning to intervene personally to monitor compliance and ensure enforcement of these new laws

Crew appliance concepts. Volume 4, appendix C: Modular space station appliances supporting engineering data

Data collected for the appliances considered for the space station are presented along with plotted and tabulated trade study results for each appliance. The food management, and personal hygiene data are applicable to a six-man mission of 180-days

Study of outgassing and decomposition of Space Shuttle heat protection tiles, fillers and adhesive

A purge and trap technique which was employed to collect and separate the chemicals desorbing from the space shuttle heat protection tiles is described. The instrumentation included a mass spectrometer and gas chromatograph

Crew appliance concepts. Volume 2, appendix B: Shuttle orbiter appliances supporting engineering data

Technical data collected for the food management and personal hygiene appliances considered for the shuttle orbiter are presented as well as plotted and tabulated trade study results for each appliance. Food storage, food operation, galley cleanup, waste collection/transfer, body cleansing, and personal grooming were analyzed

Crew appliance study

Viable crew appliance concepts were identified by means of a thorough literature search. Studies were made of the food management, personal hygiene, housekeeping, and off-duty habitability functions to determine which concepts best satisfy the Space Shuttle Orbiter and Modular Space Station mission requirements. Models of selected appliance concepts not currently included in the generalized environmental-thermal control and life support systems computer program were developed and validated. Development plans of selected concepts were generated for future reference. A shuttle freezer conceptual design was developed and a test support activity was provided for regenerative environmental control life support subsystems

Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves observable functions of the state-space of a dynamical system [Koopman 1931, PNAS]. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems [Williams et al. 2015, JNLS]. Choosing nonlinear observable functions to form an invariant subspace where it is possible to obtain linear models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis using a new algorithm to determine terms in a dynamical system by sparse regression of the data in a nonlinear function space [Brunton et al. 2015, arxiv]; we show how this algorithm is related to DMD. Finally, we demonstrate how to design optimal control laws for nonlinear systems using techniques from linear optimal control on Koopman invariant subspaces.Comment: 20 pages, 5 figures, 2 code