riccati_reduced_cost_functional.m

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function [Jred, lrQ] = riccati_reduced_cost_functional(model, reduced_data, varargin)
%[Jred, lrQ] = riccati_reduced_cost_functional(model, reduced_data,
%varargin)
%
% Calculate the cost functional by solving the corresponding reduced
% Lyapunov equation
% This function returns
%   Jred ..................... the value of the reduced cost functional
%   lrQ ...................... the low rank factor of the solution to the
%                              corresponding Lyapunov equation
%
% Andreas Schmidt, 2015
%
if nargin == 2
    rsim = rb_simulation(model, reduced_data);
else
    rsim = varargin{1};
end

% Assemble the matrices:
[E,A,B,C,x0] = riccati_assemble_system_matrices(model, reduced_data);

P = rsim.PN;
Y = A - B*B'*P*E;

lG = [C; B'*P*E];
lQ = lyap_sgn_fac(Y, lG, E);

Jred = x0'*(E'*lQ')*lQ*(E*x0);
lrQ = lQ;

end