This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states.A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during prediction by parametrizing the control law as an affine function of the disturbances. Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization. The joint state chance constraints are conservatively approximated as a collection of individual chance constraints that are subsequently relaxed via the Cantelli-Chebyshev inequality. Feasibility of the SOCP is guaranteed by softening the approximated chance constraints using the exact penalty function method. Closed-loop stability in a stochastic sense is established by establishing that the states satisfy a geometric drift condition outside of a compact set such that their variance is bounded at all times. The SMPC approach is demonstrated using a continuous acetone-butanol-ethanol fermentation process, which is used for production of high-value-added drop-in biofuels.

We report the frictional performance and long-term tribological stability of various alkyl silane monolayer films on silicon by using pin-on-disk tribometry at ambient conditions. We show that the durability of monolayers derived from n-alkyltrichlorosilanes on silicon increases exponentially with the chain length of the silane precursor, which we relate to the cohesive energy of these monolayers through molecular dynamics simulations. X-ray photoelectron spectroscopy (XPS) was used to show that tribological damage consisted of the loss of molecular components that could be partially replaced upon exposure to a solution containing perfluorinated silane precursors. For monolayers derived from n-octadecyltrichlorosilane, a critical load was identified to be approximately 250 mN (200 MPa), above which failure of films occurred within 100 cycles of testing. Monolayers with hydroxyl surfaces exhibited reduced stabilities due to stronger tip-surface interactions. Monolayers with the capability for cross-linking exhibited much greater stabilities than monolayers where cross-linking was limited or prevented. Collectively, these results demonstrate that the mechanical durability of monolayers when subjected to a tribological load is greatly enhanced by maximizing dispersional interactions and cross-linking and minimizing tip-surface interactions.

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Stochastic uncertainties in complex dynamical systems lead to variability of system states, which can in turn degrade the closed-loop performance. This paper presents a stochastic model predictive control approach for a class of nonlinear systems with unbounded stochastic uncertainties. The control approach aims to shape probability density function of the stochastic states, while satisfying input and joint state chance constraints. Closed-loop stability is ensured by designing a stability constraint in terms of a stochastic control Lyapunov function, which explicitly characterizes stability in a probabilistic sense. The Fokker-Planck equation is used for describing the dynamic evolution of the states' probability density functions. Complete characterization of probability density functions using the Fokker-Planck equation allows for shaping the states' density functions as well as direct computation of joint state chance constraints. The closed-loop performance of the stochastic control approach is demonstrated using a continuous stirred-tank reactor.

Acetone-butanol-ethanol (ABE) fermentation by clostridia has shown promise for industrial-scale production of biobutanol. However, the continuous ABE fermentation suffers from low product yield, titer, and productivity. Systems analysis of the continuous ABE fermentation will offer insights into its metabolic pathway as well as into optimal fermentation design and operation. For the ABE fermentation in continuous Clostridium acetobutylicum culture, this paper presents a kinetic model that includes the effects of key metabolic intermediates and enzymes as well as culture pH, product inhibition, and glucose inhibition. The kinetic model is used for elucidating the behavior of the ABE fermentation under the conditions that are most relevant to continuous cultures. To this end, dynamic sensitivity analysis is performed to systematically investigate the effects of culture conditions, reaction kinetics, and enzymes on the dynamics of the ABE production pathway. The analysis provides guidance for future metabolic engineering and fermentation optimization studies.