A Two-Step Global Maximum Error Controller-Based TPWL MOR with POD Basis Vectors and Its Applications to MEMS

Algorithm 1

Original TPWL-GMEC method.

(1) Given a training input ;

(2) Simulate the nonlinear system (1) and store the states at all time steps

;

(3) Choose the initial state as the first LP , and set ;

(4) Update and built the current TPWL model;

(5) Simulate the current TPWL model to get the responses ;

(6) Find out the maximum error state :

Set and , where the root mean square error

(RMSE) is defined by

for  

Compute ;

if    then  , ;

end for

(7) if   and has not been selected as a LP

then  select the LP , set ;

(8) if   is increased in step () and ( is the maximum allowable LP number)

then go to step ().

(9) Return the selected LPs and end the loop.