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ZigangPan`NonlinearCholeskyFactorization`
approximateHJIequation |
| Va=approximateHJIequation[f,s,q,xc,m] ∂ xc ∂ xc ∂ xc Va m | |
Examples
(1)
Basic Examples
(1)
In[1]:=
xc={x1,x2};
In[2]:=
$Assumptions=((x1|x2)∈Reals)
Out[2]=
(x1|x2)∈
In[3]:=
fe[x1_,x2_]:={x2+x1^2,0}
In[4]:=
ge[x1_,x2_]:={{0},{1}}
In[5]:=
he[x1_,x2_]:={{1},{0}}
In[6]:=
qe[x1_,x2_]:=x1^2+x2^2
In[7]:=
γ=4;
In[8]:=
f=Apply[fe,xc];
In[9]:=
g=Apply[ge,xc];
In[10]:=
h=Apply[he,xc];
In[11]:=
r={{1}};
In[12]:=
q=Apply[qe,xc];
In[13]:=
s=(g.Inverse[r].Transpose[g]-h.Transpose[h]/γ^2)/4;
In[14]:=
Va2=
[f,s,q,xc,2]
 | approximateHJIequation |
Out[14]=
1.8717007154895465283161760209428058465234317466386+2.2081249720274031853679747747788583689816484446750x1x2+1.8122664250438800684138278298792941843986802781164
2
x1
2
x2
In[15]:=
Va3=
[f,s,q,xc,3]
| approximateHJIequation |
Out[15]=
1.8717007154895465283161760209428058465234317466386+2.9823690239504571962366257455014334394864580442933+2.2081249720274031853679747747788583689816484446750x1x2+4.338563859297960000755192639715877875550556325191x2+1.8122664250438800684138278298792941843986802781164+2.2304196799928599937349927998131939360983499770050x1+0.4385534995646503487291876620616039596984551071135
2
x1
3
x1
2
x1
2
x2
2
x2
3
x2
In[16]:=
Va4=
[f,s,q,xc,4]
| approximateHJIequation |
Out[16]=
1.8717007154895465283161760209428058465234317466386+2.9823690239504571962366257455014334394864580442933+4.08982743286153112780779453412529514286240722893+2.2081249720274031853679747747788583689816484446750x1x2+4.338563859297960000755192639715877875550556325191x2+6.70781670953482859920650861369622686381082249586x2+1.8122664250438800684138278298792941843986802781164+2.2304196799928599937349927998131939360983499770050x1+4.12671002113425095994678930713021194621344329080+0.4385534995646503487291876620616039596984551071135+1.12367449788032018651636673106187966005697916364x1+0.116732643398511024381327866423151127928885468947
2
x1
3
x1
4
x1
2
x1
3
x1
2
x2
2
x2
2
x1
2
x2
3
x2
3
x2
4
x2
""