Linearly Solvable Stochastic Control Lyapunov Functions

This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation to a linear partial differential equation for a class of problems with a particular constraint on the stochastic forcing. This linear partial differential equation can then be relaxed to a linear differential inclusion, allowing for relaxed solutions to be generated using sum of squares programming. The resulting relaxed solutions are in fact viscosity super/subsolutions, and by the maximum principle are pointwise upper and lower bounds to the underlying value function, even for coarse polynomial approximations. Furthermore, the pointwise upper bound is shown to be a stochastic control Lyapunov function, yielding a method for generating nonlinear controllers with pointwise bounded distance from the optimal cost when using the optimal controller. These approximate solutions may be computed with non-increasing error via a hierarchy of semidefinite optimization problems. Finally, this paper develops a-priori bounds on trajectory suboptimality when using these approximate value functions, as well as demonstrates that these methods, and bounds, can be applied to a more general class of nonlinear systems not obeying the constraint on stochastic forcing. Simulated examples illustrate the methodology.Comment: Published in SIAM Journal of Control and Optimizatio

Development and validation of the crew-station system-integration research facility

The various issues associated with the use of integrated flight management systems in aircraft were discussed. To address these issues a fixed base integrated flight research (IFR) simulation of a helicopter was developed to support experiments that contribute to the understanding of design criteria for rotorcraft cockpits incorporating advanced integrated flight management systems. A validation experiment was conducted that demonstrates the main features of the facility and the capability to conduct crew/system integration research

Spatial mapping of ordered and disordered domains of GaInP by near-field scanning optical microscopy and scanning capacitance microscopy

Journal ArticleImaging of topography, locally induced photoluminescence and Fermi-level pinning in adjacent ordered and disordered domains on a cleaved GaInP sample is performed using a near-field scanning optical microscope and scanning capacitance microscope at room temperature in air. Highly localized photoluminescence spectra obtained by the near-field scanning optical microscope on these domains show spectral peaks at 680 nm (ordered) and 648 nm (disordered) GaInP. The near-field scanning optical microscope and scanning capacitance microscope data confirm previously published data, indicating that the electronic surface structure of ordered GaInP is significantly different from that of disordered GaInP. Both approaches indicate that the Fermi-level at the surface of ordered GaInP is pinned, while the Fermi-level at the surface of disordered GaInP is not pinned. The size, structure, and position of the ordered and disordered domains observed by the near-field scanning optical microscope and scanning capacitance microscope agree with those obtained by cathodoluminescence and Kelvin probe force microscop

Flow patterns through vascular graft models with and without cuffs

The shape of a bypass graft plays an important role on its efficacy. Here, we investigated flow through two vascular graft designs±with and without cuff at the anastomosis. We conducted Digital Particle Image Velocimetry (DPIV) measurements to obtain the flow field information through these vascular grafts. Two pulsatile flow waveforms corresponding to cardiac cycles during the rest and the excitation states, with 10% and without retrograde flow out the proximal end of the native artery were examined. In the absence of retrograde flow, the straight end-to-side graft showed recirculation and stagnation regions that lasted throughout the full cardiac cycle with the stagnation region more pronounced in the excitation state. The contoured end-to-side graft had stagnation region that lasted only for a portion of the cardiac cycle and was less pronounced. With 10% retrograde flow, extended stagnation regions under both rest and excitation states for both bypass grafts were eliminated. Our results show that bypass graft designers need to consider both the type of flow waveform and presence of retrograde flow when sculpting an optimal bypass graft geometry

Use of vibratory shear enhanced processing to treat magnetic ion exchange concentrate: A techno-economic analysis

Disposal of waste generated by inland water treatment technologies is highly expensive. The introduction of vibratory shear enhanced processing (VSEP) to treat waste produced from magnetic ion exchange (MIEX) shows benefits in terms of performance and economics. A small VSEP unit fitted with a nanofiltration (NF) membrane is capable of treating up to 15. kL of MIEX waste per day, is able remove more than 97% of dissolved organic compounds as well as recover over 80% of waste in the form of permeate. The reuse of permeate to makeup brine has seen significant reductions in salt consumption and waste disposal at Wanneroo Groundwater Treatment Plant (GWTP). During the first year of VSEP operation, salt consumption reduced by 42% and waste disposal was projected to reduce by 23.9%. Further improvements in both cost categories were observed in the second year of operation and considering the same trend is followed, the payback period of the project will occur between the 6th and 7th year of operation for discounted analysis and has a positive net present value

Suboptimal stabilizing controllers for linearly solvable system

This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is transformed into a linear partial differential equation for a class of systems with a particular constraint on the stochastic disturbance. It is shown that this linear partial differential equation can be relaxed to a linear differential inclusion, allowing for approximating polynomial solutions to be generated using sum of squares programming. It is shown that the resulting solutions are stochastic control Lyapunov functions with a number of compelling properties. In particular, a-priori bounds on trajectory suboptimality are shown for these approximate value functions. The result is a technique whereby approximate solutions may be computed with non-increasing error via a hierarchy of semidefinite optimization problems

Efficiency of Fixed-Width Transect and Line-Transect-based Distance Sampling to Survey Red Junglefowl (Gallus gallus spadiceus) in Peninsular Malaysia

Reliable survey method is very important to estimate wildlife population. In this study, fixed-width strip- and line-transect samplings were simultaneously used to yield population estimates on oil palm plantation. The latter was found to be more accurate but less precise than the former based on the Per cent Relative Bias (hereafter PRB). Using the strip-transect, an overall density and abundance were estimated at 0.3237 birds/ha and 3 018 ± 273 birds (CV = 9.05%), respectively. An unbiased overall density generated by line-transect, D ± S.E. = 0.500 ± 0.069 birds/ha (95% CI: 0.38137 - 0.65521) and estimated total abundance, N ± S.E. was 4 661 ± 644 birds (95% CI: 3 556 - 6 109; CV = 13.81%) for the entire 9 323.53 ha study area. The former and latter method gave relative and absolute estimates, respectively