www.gusucode.com > nncontrol 工具箱 matlab 源码程序 > nncontrol/csrchgol.m
function [up_delta,J,dJdu_old,dJdu,retcode,delta,tol] = csrchgol(up,u_vec,ref,Ai,Nu,N1,N2,d,Ni,Nj,dX, ...
dJdu,J,dperf,delta,rho,dUtilde_dU,alpha,tol,Ts,min_i,max_i,Normalize,minp,maxp)
%CSRCHGOL One-dimensional minimization using golden section search.
%
% Syntax
%
% [up_delta,J,dJdu_old,dJdu,retcode,delta,tol] = csrchgol(up,u_vec,ref,Ai,Nu,N1,N2,d,Ni,Nj,dX, ...
% dJdu,J,dperf,delta,rho,dUtilde_dU,alpha,tol,Ts,min_i,max_i,Normalize)
%
% Description
%
% CSRCHGOL is a linear search routine. It searches in a given direction
% to locate the minimum of the performance function in that direction.
% It uses a technique called the golden section search.
%
% CSRCHGOL(...) takes these inputs,
% up - Plant Inputs during the Control Horizon (Nu).
% u - Plant Inputs during the Cost Horizon (N2).
% ref - Reference input.
% Ai - Initial input delay conditions.
% Nu - Control Horizon.
% N1 - Beginning of the Control and Cost Horizons (Usually 1).
% N2 - Cost Horizon.
% d - Counter that defined initial time (Usually 1).
% Ni - Number of delayed plant inputs.
% Nj - Number of delayed plant outputs.
% dX - Search direction vector for U.
% dJdu - Derivate of the cost function respect U.
% J - Cost function value.
% dperfa - Slope of performance value at current U in direction of dX.
% delta - Initial step size.
% rho - Control weighting factor.
% dUtlde_dU - Derivate of the difference of U(t)-U(t-1) respect U.
% alpha - Search parameter.
% tol - Tolerance on search.
% Ts - Time steps.
% min_i - Minimum Input to the Plant.
% max_i - Maximum Input to the Plant.
% Normalize - Indicate if the NN has input-output normalized.
% and returns,
% up_delta - New Plant Inputs for the Control Horizon (Nu).
% J - New Cost function value.
% dJdu_old - Previous Derivate of the cost function respect U.
% dJdu - New Derivate of the cost function respect U.
% RETCODE - Return code which has three elements. The first two elements correspond to
% the number of function evaluations in the two stages of the search
% The third element is a return code. These will have different meanings
% for different search algorithms. Some may not be used in this function.
% 0 - normal; 1 - minimum step taken; 2 - maximum step taken;
% 3 - beta condition not met.
% DELTA - New initial step size. Based on the current step size.
% TOL - New tolerance on search.
%
% Parameters used for the golden section algorithm are:
% alpha - Scale factor which determines sufficient reduction in perf.
% bmax - Largest step size.
% scale_tol - Parameter which relates the tolerance tol to the initial step
% size delta. Usually set to 20.
% The defaults for these parameters are set in the training function which
% calls it. See TRAINCGF, TRAINCGB, TRAINCGP, TRAINBFG, TRAINOSS
%
% Algorithm
%
% CSRCHGOL locates the minimum of the performance function in
% the search direction dX, using the
% golden section search. It is based on the algorithm as
% described on page 33 of Scales (Introduction to Non-Linear Estimation 1985).
%
% See also CSRCHBAC, CSRCHBRE, CSRCHCHA, CSRCHHYB
%
% References
%
% Scales, Introduction to Non-Linear Estimation, 1985.
% Orlando De Jesus, Martin Hagan, 1-30-00
% Copyright 1992-2002 The MathWorks, Inc.
tiu = d-N1+Ni;
upi = [1:Nu-1 Nu(ones(1,N2-d-Nu+2))];
uvi = [tiu:N2-N1+Ni];
% ALGORITHM PARAMETERS
delta_orig=delta;
scale_tol = 20;
bmax = 26;
norm_dX=norm(dX);
% INTERVAL FOR GOLDEN SECTION SEARCH
tau = 0.618;
tau1 = 1 - tau;
% STEP SIZE INCREASE FACTOR FOR INTERVAL LOCATION (NORMALLY 2)
scale = 2;
% INITIALIZE A AND B
a = 0;
a_old = 0;
b = delta;
perfa = J;
perfa_old = perfa;
dJdua=dJdu;
dJdua_old=dJdua;
cnt1 = 0;
cnt2 = 0;
up_delta = max(min(up + b*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR B
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfb = JJ;
dJdub = dJJ;
cnt1 = cnt1 + 1;
% INTERVAL LOCATION
% FIND INITIAL INTERVAL WHERE MINIMUM PERF OCCURS
while (perfa>perfb)&(b<bmax)
a_old=a;
perfa_old=perfa;
perfa=perfb;
dJdua_old=dJdua;
dJdua=dJdub;
a=b;
b=scale*b;
%============== COMPUTE PREDICTIONS FROM TIME t+N1 TO t+N2 ===============
up_delta = max(min(up + b*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR B
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfb = JJ;
dJdub = dJJ;
cnt1 = cnt1 + 1;
end
% INITIALIZE C AND D (INTERIOR POINTS FOR LINEAR MINIMIZATION)
if (a == a_old)
% COMPUTE C POINT IF NO MIDPOINT EXISTS
c = a + tau1*(b - a);
%============== COMPUTE PREDICTIONS FROM TIME t+N1 TO t+N2 ===============
up_delta = max(min(up + c*dX,max_i),min_i); %up + c*dX; % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR C
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfc = JJ;
dJduc = dJJ;
cnt1 = cnt1 + 1;
else
% USE ALREADY COMPUTED VALUE AS INITIAL C POINT
c = a;
perfc = perfa;
dJduc = dJdua;
a=a_old;
perfa=perfa_old;
dJdua=dJdua_old;
end
% INITIALIZE D POINT
d=b-tau1*(b-a);
%============== COMPUTE PREDICTIONS FROM TIME t+N1 TO t+N2 ===============
up_delta = max(min(up + d*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR D
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfd = JJ;
dJdud = dJJ;
cnt1 = cnt1 + 1;
minperf = min([perfa perfb perfc perfd]);
if perfb <= minperf
a_min = b;
dJdu_min=dJdub;
elseif perfc <= minperf
a_min = c;
dJdu_min=dJduc;
elseif perfd <= minperf
a_min = d;
dJdu_min=dJdud;
else
a_min = a;
dJdu_min=dJdua;
end
% MINIMIZE ALONG A LINE (GOLDEN SECTION SEARCH)
while ((b-a)>tol) & (minperf >= J + alpha*a_min*dperf)
if ( (perfc<perfd)&(perfb>=min([perfa perfc perfd])) ) | perfa<min([perfb perfc perfd])
b=d; d=c; perfb=perfd; dJdub=dJdud;
c=a+tau1*(b-a);
perfd=perfc; dJdud=dJduc;
%============== COMPUTE PREDICTIONS FROM TIME t+N1 TO t+N2 ===============
up_delta = max(min(up + c*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR C
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfc = JJ;
dJduc = dJJ;
cnt2 = cnt2 + 1;
if (perfc < minperf)
minperf = perfc;
a_min = c;
dJdu_min=dJduc;
end
else
a=c; c=d; perfa=perfc; dJdua=dJduc;
d=b-tau1*(b-a);
perfc=perfd; dJduc=dJdud;
%============== COMPUTE PREDICTIONS FROM TIME t+N1 TO t+N2 ===============
up_delta = max(min(up + d*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
% CALCULATE PERFORMANCE FOR D
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfd = JJ;
dJdud = dJJ;
cnt2 = cnt2 + 1;
if (perfd < minperf)
minperf = perfd;
a_min = d;
dJdu_min=dJdud;
end
end
end
a=a_min;
J_delta = minperf;
dJdu_delta = dJdu_min;
%============== COMPUTE PREDICTIONS FROM TIME t+N1 TO t+N2 ===============
up_delta = max(min(up + a*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
J = J_delta;
dJdu_old = dJdu;
dJdu = dJdu_delta;
% CHANGE INITIAL STEP SIZE TO PREVIOUS STEP
delta=a;
if delta < delta_orig
delta = delta_orig;
end
if tol>delta/scale_tol
tol=delta/scale_tol;
end
retcode = [cnt1 cnt2 0];