Efficient Neural Network Modeling for Flight and Space Dynamics Simulation

Algorithm 1

NN algorithm for modeling nonlinear systems.

(1) Starting with the nonlinear model in the form of

𝑥̇(𝑡)=𝑓(𝑥,𝑢,𝑡),

where x are states vector and u is input vector.

(2) Linearize the nonlinear model around an operating point and represent it in state space form as follows:

𝑥̇(𝑡)=𝐴𝑥+𝐵𝑢,

where A, B are the system and input matrices, respectively.

(3) Discretize the continuous linearized system using finite difference, the equations will be

𝑥̇_𝑖+1=(𝐴+𝐼Δ𝑡)𝑥_𝑖+𝐵Δ𝑡𝑢_𝑖,

where I is the identity matrix and Δt is the time step.

(4) Build an analytic NN to replicate the linear model using the proposed linear system given in section two and Figure 2.

(5) Train the linear analytic NN with the nonlinear model data and with initial weights and biases taken from the linear analytic

NN.

(6) If the final NN model is not satisfactory, then increment model size by adding another linear model at different operating

point, repeat steps 2 to 5, and concatenate the two models to get a better approximation. The number of final concatenated

models depends on the required accuracy and the acceptable execution time.

(7) Stop