Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearQuadraticControl`
LQRcontrol  |
| {z,controllergain}=LQRcontrol[system] z controllergain | |
Examples
(1)
Basic Examples
(1)
In[1]:=
system1={{x1,x2,x3},{u1,u2,w1,w2,w3},{y1,y2,z1,z2,z3,z4},{{-1,1,-1,0,0,1,-1,1},{-2,0,1,1,-1,0,0,1},{-3,0,-2,1,1,1,1,0},{1,0,0,0,0,1,0,0},{0,0,1,0,0,0,1,0},{1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0},{0,0,0,1,2,0,0,0},{0,0,0,2,1,0,0,0}},{1,2},{1,2},{1,2},{3,4,5},{1,2},{3,4,5,6}};systemcheck[system1]
Out[1]=
True
In[2]:=
stablizabilityQ[system1〚4〛〚1;;3,1;;3〛,system1〚4〛〚1;;3,4;;5〛]
Out[2]=
True
In[3]:=
{z,controllergain}=
[system1]
 | LQRcontrol |
Out[3]=
{{{1.80331,0.426048,-0.802849},{0.426048,0.650282,-0.169196},{-0.802849,-0.169196,0.536521}},{{-0.336843,-0.631483,0.109582},{0.515253,0.669082,-0.228809}}}
In[4]:=
HurwitzMatrixQ[system1〚4〛〚1;;3,1;;3〛+system1〚4〛〚1;;3,4;;5〛.controllergain]
Out[4]=
True
In[5]:=
Eigenvalues[system1〚4〛〚1;;3,1;;3〛+system1〚4〛〚1;;3,4;;5〛.controllergain]
Out[5]=
{-3.36285+0.,-0.528469+1.52399,-0.528469-1.52399}
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""