A formal verification method of Laplace transform based on Coq
A technology of Laplace transform and formal verification, applied in the field of formal verification, can solve problems such as inability to accurately verify Laplace transform, and achieve the effect of avoiding errors
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[0066] The invention can be used to verify the derivation process of the short-period motion transfer function model transfer function matrix in the flight control system. The following are the equations of motion for the aircraft:
[0067]
[0068] make
[0069] Among them, A and B are second-order real matrices, and X and U are two-dimensional function vectors. The above equation of motion is equivalently described as:
[0070]
[0071] The key step in deriving the transfer matrix is to perform Laplace transform on both ends of the motion equation under the zero initial condition, apply the properties of Laplace transform, and deduce X(s)=(SI-A)BU(s), as follows In Coq, the above kinematic equation is introduced as a hypothesis, which is the starting point of the proof work.
[0072] Hypothesis e: derive_RV2 X = RF2_plus(RF2_cmul A X)(RF2_cmul B U).
[0073] Transfer matrix inference result: X(s)=(SI-A)BU(s)
[0074] Theorem result: verify_pre X U s ->
[007...
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