Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`NonlinearSystems`
NLobservability  |
| {nO,transformation,resultsystem}=NLobservability[nlsystem,x0] computes the the dimension of the possibly locally observable part of the nonlinear system: nlsystem x0 nlsystem nlsystem x0 x0 | |
Examples
(1)
Basic Examples
(1)
In[1]:=
nlsystem={{x1,x2,x3},{u1},{y1},{FormulaToFunction[{x1,x2,x3,u1},{x2+u1,-x2+x1*u1,x3}],FormulaToFunction[{x1,x2,x3,u1},{x1^2}]},{1},{1},{1},{},{1},{}}
Out[1]=
{{x1,x2,x3},{u1},{y1},{Function[{x1,x2,x3,u1},{u1+x2,u1x1-x2,x3}],Function[{x1,x2,x3,u1},{}]},{1},{1},{1},{},{1},{}}
2
x1
In[2]:=
 | NLsystemcheck |
Out[2]=
True
In[3]:=
| NLobservability |
State transformation is xnew = transformation[xold] and transformation is a pure function; One may attach the inverse transformation as the third element in type, which must also be a pure function.
Out[3]=
2,{2x1,2x2,x3},{x11,x21,x31},{u1},{y1},Function{x11,x21,x31,u1},2u1+,2-,x31,Function{x11,x21,x31,u1},,{1},{1},{1},{},{1},{}
x21
2
u1x11
2
x21
2
2
x11
4
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""