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Abstract Neural networks have been widely applied in system dynamics modeling. One particular type of networks, hybrid neural networks, combines a neural network model with a physical model, which can increase rate of convergence in training. However, most existing hybrid neural network methods require an explicit physical model constructed, which sometimes might not be feasible in practice or could weaken the capability of capturing complex and hidden physical phenomena. In this paper, we propose a novel approach to construct a hybrid neural network. The new method incorporates the physical information to the structure of network construction, but does not need an explicit physical model constructed. The method is then applied to modeling of bit-rock interaction in the down-hole drilling system as a case study, to demonstrate its effectiveness in modeling complex process and efficiency of convergence in training. 

The need for less fuel consumption and the trend of higher level of autonomy together urge the power optimization in multihybrid autonomous vehicles. Both the multivehicle coordination control and the hybrid powertrain energy management should be optimized to maximize fuel savings. In this paper, we intend to have a computationally efficient framework to optimize them individually and then evaluate the overall control performance. The optimization is conducted in series. First is at the multivehicle system's level where the distributed locally optimal solution is given for vehicles with nonlinear dynamics. Second, the powertrain management optimization is conducted at the hybrid powertrain level. We provide an analytical formulation of the powertrain optimization for each hybrid vehicle by using Pontryagin's minimum principle (PMP). By approximating the optimal instantaneous fuel consumption rate as a polynomial of the engine speed, we can formulate the optimization problem into a set of algebraic equations, which enables the computationally efficient real-time implementation. To justify the applicability of the methodology in real-time, we give directions on numerical iterative solutions for these algebraic equations. The analysis on the stability of the method is shown through statistical analysis. Finally, further simulations are given to confirm the efficacy and the robustness of the proposed optimal approach. An off-road example is given in the simulation, although the framework developed can be applied to on-road scenario as well.