www.gusucode.com > nncontrol 工具箱 matlab 源码程序 > nncontrol/csrchcha.m
function [up_delta,J,dJdu_old,dJdu,retcode,delta,tol] = csrchcha(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,ch_perf)
%CSRCHCHA One-dimensional minimization using the method of Charalambous.
%
% Syntax
%
% [up_delta,J,dJdu_old,dJdu,retcode,delta,tol] = csrchcha(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,ch_perf)
%
% Description
%
% CSRCHCHA 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 based on the method of Charalambous.
%
% CSRCHCHA(...) 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.
% CH_PERF - Change in performance on previous step.
% 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 Charalombous algorithm are:
% alpha - Scale factor which determines sufficient reduction in perf.
% beta - Scale factor which determines sufficiently large step size.
% gama - Parameter to avoid small reductions in performance. Usually set
% to 0.1.
% 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
%
% CSRCHCHA locates the minimum of the performance function in
% the search direction dX, using an algorithm based on
% the method described in Charalambous (IEE Proc. vol. 139, no. 3, June 1992).
%
% See also CSRCHBAC, CSRCHBRE, CSRCHGOL, CSRCHHYB
%
% References
%
% Charalambous, IEE Proceedings, vol. 139, no. 3, June 1992.
% 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))]; % [1 2 ... Nu Nu ... Nu]
uvi = [tiu:N2-N1+Ni];
% ALGORITHM PARAMETERS
scale_tol = 20;
beta = 0.9;
gama = 0.1;
gama1 = 1 - gama;
delta_orig=delta;
% STEP SIZE INCREASE FACTOR FOR INTERVAL LOCATION
scale = 3;
% INITIALIZE
a = 0;
a_old = 0;
perfa = J;
perfa_old = perfa;
dperfa = dperf;
if dperfa>=0
dperfa=dperfa;
end
dJdua=dJdu;
cnt1 = 0;
cnt2 = 0;
% FIND FIRST STEP SIZE
delta_star = -2*ch_perf/dperf;
delta = max([delta delta_star]);
b = delta;
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, GRADIENT AND SLOPE AT POINT B
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfb = JJ;
dJdub = dJJ;
dperfb = dJdub'*dX;
cnt1 = cnt1 + 1;
if (perfa < perfb)
amin = a; minperf = perfa; dperfmin = dperfa; gX_1 = dJdu;
else
amin = b; minperf = perfb; dperfmin = dperfb; gX_1 = dJdub;
end
bma = b - a;
% LOCATE THE MINIMUM POINT BY THE CHARALAMBOUS METHOD
while ((bma)>tol) & ((minperf > J + alpha*amin*dperf) | abs(dperfmin)>abs(beta*dperf) )
% IF THE SLOPE AT B IS NEGATIVE INCREASE OR DECREASE THE STEP SIZE BY SCALE
if (dperfb < 0)
% IF FUNCTION IS HIGHER, DECREASE STEP SIZE BY SCALE
if (perfb >= perfa) % ODJ 1/28/00 Greater or equal
delta = delta/scale;
% IF FUNCTION IS LOWER, CHANGE THE A POINT AND INCREASE THE STEP SIZE BY SCALE
else
delta = scale*delta;
end
% IF THE SLOPE AT B IS POSITIVE DO A CUBIC INTERPOLATION FOR THE MINIMUM
else
ww = 3*(perfa - perfb)/(b-a) + dperfa + dperfb;
w_gagb = ww^2 - dperfa*dperfb;
if w_gagb<=0
w_gagb=w_gagb;
end
v = sqrt(w_gagb);
delta_star = (b-a)*(1 - (dperfb + v - ww)/(dperfb - dperfa +2*v));
delta = max( [gama*bma min( [delta_star gama1*bma] )] );
end
% CALCULATE PERFORMANCE AND SLOPE AT TEST POINT
b_test = a + delta;
up_delta = max(min(up + b*dX,max_i),min_i); % A priori iteration
u_vec(uvi) = up_delta(upi); % Insert updated controls
%----- Determine prediction yhat(t+k,up_delta) -----
[JJ,dJJ]=calcjjdjj(u_vec,Ni,Nu,Nj,N2,Ai,Ts,ref,tiu,rho,dUtilde_dU,Normalize,minp,maxp);
perfbt = JJ;
dJdubt = dJJ;
dperfbt = dJdubt'*dX;
cnt2 = cnt2 + 1;
% USE TEST POINT TO UPDATE ENDPOINTS
if (b_test > b)
a = b; perfa = perfb; dperfa = dperfb; dJdua = dJdub;
b = b_test; perfb = perfbt; dperfb = dperfbt; dJdub = dJdubt;
else
if (dperfbt > 0) | (perfbt >= perfa) % ODJ 1/28/00 Greater or equal
b = b_test; perfb = perfbt; dperfb = dperfbt; dJdub = dJdubt;
else
a = b_test; perfa = perfbt; dperfa = dperfbt; dJdua = dJdubt;
end
end
bma = b - a;
% FIND THE MINIMUM POINT
if (perfa < perfb)
amin = a; minperf = perfa; dperfmin = dperfa; gX_1 = dJdua;
else
amin = b; minperf = perfb; dperfmin = dperfb; gX_1 = dJdub;
end
end
a = amin;
J = minperf;
dJdu_old=dJdu;
dJdu = gX_1;
% CHANGE INITIAL STEP SIZE TO PREVIOUS STEP
delta=amin;
if delta < delta_orig
delta = delta_orig;
end
if tol>delta/scale_tol
tol=delta/scale_tol;
end
retcode = [cnt1 cnt2 0];