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A multimodel scheduling approach is proposed for controlling strongly nonlinear processes. A global controller is built from a weighted combination of local linear controller outputs with the weights being functions of a defined closed-loop gap metric. The control algorithm is hybrid in that the global controller continuously weights the outputs of the local controllers whereas the weights are updated at constant time intervals. The proposed strategy is then implemented on two simulated processes, one of which exhibits output multiplicity and the other exhibits input multiplicity.

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of alpha-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Calpha coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of alpha-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of alpha-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins.

Discontinuous molecular dynamics (DMD) simulation and thermodynamic perturbation theory (TPT) have been used to study thermodynamic properties for organic compounds. The aim is to infer transferable intermolecular potential models based on correlating the vapor pressure and liquid density. The combination of DMD/TPT generates a straightforward global optimization problem for the attractive potential, instead of facing an iterative optimization−simulation type problem. This global optimization problem is then formulated as a black-box optimization problem and solved using a combination of random recursive search (RRS) and Levenberg−Marquardt (LM) optimization. RRS is suitable for black-box optimization problems since its algorithm is robust to the effect of random noises in the objective function and is advantageous in optimizing the objective function with negligible parameters. LM is efficient local to an optimum with a smooth response surface. The local response surface is shown to be smooth but very flat along valleys with a high degree of coupling between the potential parameters. The algorithm is demonstrated with discretized versions of the Lennard-Jones (LJ) potential and a linear step potential using a database of 231 hydrocarbons, alcohols, aldehydes, amines, amides, esters, ethers, ketones, phenols, sulfides, and thiols. A correspondence is established between the discretized LJ potential and the TraPPE model, demonstrating the manner of improving density estimates and a way of expediting improvement of continuous transferable potentials.

The dynamics of alpha-amylase inhibitor tendamistat around its native state is investigated using time series analysis of the principal components of the C(alpha) atomic displacements obtained from molecular dynamics trajectories. Collective motion along a principal component is modeled as a homogeneous nonstationary process, which is the result of the damped oscillations in local minima superimposed on a random walk. The motion in local minima is described by a stationary autoregressive moving average model, consisting of the frequency, damping factor, moving average parameters and random shock terms. Frequencies for the first 50 principal components are found to be in the 3-25 cm(-1) range, which are well correlated with the principal component indices and also with atomistic normal mode analysis results. Damping factors, though their correlation is less pronounced, decrease as principal component indices increase, indicating that low frequency motions are less affected by friction. The existence of a positive moving average parameter indicates that the stochastic force term is likely to disturb the mode in opposite directions for two successive sampling times, showing the modes tendency to stay close to minimum. All these four parameters affect the mean square fluctuations of a principal mode within a single minimum. The inter-minima transitions are described by a random walk model, which is driven by a random shock term considerably smaller than that for the intra-minimum motion. The principal modes are classified into three subspaces based on their dynamics: essential, semiconstrained, and constrained, at least in partial consistency with previous studies. The Gaussian-type distributions of the intermediate modes, called "semiconstrained" modes, are explained by asserting that this random walk behavior is not completely free but between energy barriers.