The model parameters can then be fit so that they recreate the estimated derivates as accurately as possible, rather than recreating the observed trajectory as accurately as possible.
The paper provides an optimal control algorithm, with the ℓ2-induced norm as the performance measure, for such a hybrid model, which ensures that the system tracks the desired trajectory as accurately as possible despite various disturbances and uncertainties.
After circumnavigating an obstacle, wild-type hyphae reverted to their original growth trajectory as soon as possible (Fig. 4A; Movie S3).
It allows simulating with a good accuracy chemical or biochemical systems of reactions generating statistically correct trajectories as possible solutions of a stochastic equation.
The requirements are formulated, which have to be met by the present-day models aimed at predicting the SEP fluxes in the spacecraft trajectories as accurately as possible.
Testing the order and extent of trait divergence during the evolution of a clade helps to understand the relative importance of separate morphological and climatic trajectories, as well as the possible drivers of species diversification.
As a starting point for the analysis of such missions, the objectives of this study are to identify target asteroids and evaluate possible transfer trajectories as well as the associated launch windows.
However, while restrictive mutations block many of the possible evolutionary trajectories, as has been previously emphasized, permissive mutations simultaneously open up new pathways, avoiding 'evolutionary dead-ends' and contributing to the diversity of enzyme homologs found in nature.
Finally, we showed how these results can be extended to fitness valleys with more intermediates, and to fitness landscapes with many possible evolutionary trajectories, as is the case in most naturally occurring populations.
In the proposed strategy, the state variables of the model are reset periodically along with predictive control action such that the process follows the reference trajectory as closely as possible.
