Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearQuadraticControl`
LEQGcontrol  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
system1={{x1,x2,x3},{u1,u2,w1,w2,w3},{y1,y2,z1,z2,z3,z4},{{-1,1,-1,0,0,0,0,1},{-2,0,1,1,-1,0,0,1},{-3,0,-2,1,1,0,0,0},{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]:=
controllabilityQandindices[system1〚4〛〚1;;3,1;;3〛,system1〚4〛〚1;;3,4;;5〛]
Out[2]=
True,3,{1,2},-,,,-,0,0,,-,
1
4
1
2
1
2
1
2
1
2
1
2
1
2
In[3]:=
observabilityQandindices[system1〚4〛〚1;;3,1;;3〛,system1〚4〛〚4;;5,1;;3〛]
Out[3]=
{True,3,{2,1},{{1,0,0},{0,1,1},{0,0,1}}}
In[4]:=
{z,controller}=
[system1,0]
 | LEQGcontrol |
Out[4]=
{6.406562650212176852693130824758494506816265367440,{{x1chk,x2chk,x3chk},{y1,y2},{u1,u2},{{-1.90819167916059281109933445350118386671920358397072,1,-0.34552921880401586879097918753611785859877584177928,0.90819167916059281109933445350118386671920358397072,-0.65447078119598413120902081246388214140122415822072},{-3.2323888378384636102044331754746386637140601647651,-1.3005647042230326010568942753084034586021476616347,0.9164965115571667342683466733080936373605221805206,0.38029296273251812308602227485485141153154709560691,0.42189498223415229586333324400585258290788695899479},{-2.1671184179867060438735490654903611544971247665888,0.0375990548657021144590755463682162466964899043906,-2.8575644436507337971607205013681037682775928171466,-0.65447078119598413120902081246388214140122415822072,0.73833757665789318791989271479601460475924707483688},{-0.3368425371443178311004903892870152740404309969839,-0.63148282467866524329890936447009360595282887862205,0.10958231339923921044542606537092852837503169860287,0,0},{0.5152533379616276560179205113327719781420820721743,0.66908187954436735775798491083830985264931878301265,-0.22880918039207981968625385194301769189337744091254,0,0}},{1,2},{1,2},{1,2},{},{1,2},{}}}
In[5]:=
 | LEQGcontrol |
No stabilizing solution found!
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Out[5]=
5625
32768
In[6]:=
N[%]
Out[6]=
0.171661
In[7]:=
N[56/320]
Out[7]=
0.175
In[8]:=
| LEQGcontrol |
Out[8]=
{148.6990648430959728296862173388855720524053781448,{{x1chk,x2chk,x3chk},{y1,y2},{u1,u2},{{-1.8364655948786760695384533303302508111936385116425,1,-0.38339713250516241215057284611030447218871366870278,1.0037587138544112834461439963963009734323662139709,-0.73992344099380510541931258466763463337354359755666},{-46.89979878437097718561484891637117718005564148990,-23.86453800469116595028865725028465024668999006676,20.95707425153055256987860456429478581129569423832,0.41175954543176238460585951767598649541431841628991,0.49714278927127100104190283129635323207644984325829},{2.32578987715940126899843459438079302687155804575,2.26348443436184574860150262115278668570660027123,-4.91315974959190329076307232133130304530466551936,-0.73992344099380510541931258466763463337354359755666,0.84653077555462020811137353636187849161096942756356},{-19.92373941008997242531381260557504546740838554761,-10.80052678516466010084357731456593178049169489777,9.081821236313445976704964608006004601198605722318,0,0},{24.63292641975453610646282004606614296646865726205,13.06401121952650584944507993571871846619829516899,-11.28953867294316576070855898236907557016079671871,0,0}},{1,2},{1,2},{1,2},{},{1,2},{}}}
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""