%?Example?6.2:?Constrained?Receding?Horizon?Control
%?Demonstration?of?Receding?Horizon?Control?（RHC）?using?LMI

%?###################################################################
%?Edited?by?Giovani?Tonel?（?giotonel@enq.ufrgs.br?）?March?28th?2007
%?###################################################################
%
%?Retired?from?the?book:?
%?Receding?Horizon?Control?-?Model?Predictive?Control?for?State?Models
%?Authors:?W.H.?Kwon?and?S.?Han
%?


clear?all
close?all
clc
disp（‘?‘）;
disp（‘=================================================================================‘）;
disp（‘?	?????????????????Constrained?Receding?Horizon?Control	?‘）;
disp（‘=================================================================================‘）;
disp（‘?‘）;



%%?System?State?Equation
A	=?	[1?0.2212;?0?0.7788];
B?	=?	[0.0288;?0.2212];?
G?	=	[1?0;?0?1;?1.5?1];

%%?Initial?State
x0?		=?	[1;0.3];
[nn]	=	size（A）;?
[nm]	=	size（B）;

%?Let‘s?get?predictor
N?		=?input（‘?Horizon?Length?N:‘?）;?
tsim?=?input（‘Total?simulation?time:‘）;

%?Input?Constraint
u_lim		=	0.5;?
ubar_lim?	=	[];?

for?i=1:N
???ubar_lim=[ubar_lim;?u_lim];
end

%?State?Constraint
x_lim?		=?	[1.5;?0.3];?
G?				=	[1?0;?0?1];
g_lim?		=?	[1.5;?0.3];?
gbar_lim?	=?	[];?

for?i=1:N
???gbar_lim	=	[gbar_lim;?g_lim];
end

[ng_r?ng_c]?=?size（G）;

%?Weighting?Matrix
Q?			=?	1*eye（size（A））;?
R?			=?	1;
A_hat	=	[];?
B_hat	=	[];?

for?i=1:N-1
???A_hat?=?daug（A_hat?A）;
???B_hat?=?daug（B_hat?B）;
end?

A_hat?	=?	[zeros（nn*N）;?A_hat?zeros（n*（N-1）n）];
B_hat?	=?	[zeros（nm*N）;?B_hat?zeros（n*（N-1）m）];
W_hat?	=?	inv（eye（n*N）-A_hat）*B_hat;?
V0_hat?=	inv（eye（n*N）-A_hat）*[x0;zeros（n*（N-1）1）];
B_bar=[];?

for?i=1:N
???B_bar?=?[B_bar?A^（N-i）*B];
end

%?Let‘s?get?stacked?weighting?matrix
[mn]	=	size（Q）;?
[pq]?	=?size（R）;?
Q_hat?	=?[];?
R_hat?	=?[];?


for?i=1:N
???Q_hat?=?daug（Q_hat?Q）;
???R_hat?=?daug（R_hat?R）;
end

%?Let‘s?get?constraint?matrix
G_bar?=?[];?

for?i=1:N
???G_bar?=?daug（G_bar?G）;
end

W		=	W_hat‘*Q_hat*W_hat?+?R_hat;?
W		=	（W+W‘）/2;

%?Simulation?starts?!
t			=?[];?
State?	=?[];?
U?			=?[];?
summed_cost	=	0;?
Summed_cost	=	[];
Cost_at_k		=	[];?
x?=?x0;

R1=[];?
R2=[];?

for?i=0:（tsim-1）
???V0_hat	=?	inv（eye（n*N）-A_hat）*[x;zeros（n*（N-1）1）];
???V?		=?	2*W_hat‘*Q_hat*V0_hat;
???V0?		=?	V0_hat‘*Q_hat*V0_hat;
???
???%%?Solve?LMI
???[XYr1r2opt_u]?=?rhc_lmi（xNABQRW_hatV0_hatQ_hatB_bar...
??????WVV0GG_barubar_limgbar_limu_limg_lim）;
???
???P?=?r2*inv（X）;
???
???if?（i==0）
??????boundary0=[];
??????for?th=0:0.01:2*pi
?????????z?				=?	sqrt（r2）*inv（P^0.5）*[cos（th）;sin（th）];
?????????boundary0	=	[boundary0?z];
??????end
???elseif（i==1）
??????boundary1=[];
??????for?th=0:0.01:2*pi
?????????z?=?sqrt（r2）*inv（P^0.5）*[cos（th）;sin（th）];
?????????boundary1=[boundary1?z];
??????end
???elseif（i==2）
??????boundary2=[];
??????for?th=0:0.01:2*pi
???????

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----
?????文件????????3913??2007-03-28?18:06??rhc_lmi.m
?????文件????????4914??2007-03-28?18:52??RHC.m
?????文件???????63497??2007-03-29?10:46??example6.2.JPG