"Inputs must be floats, namely single or double" when running ode45 for LQ tracker

Using matlab 2017b on windows 10 64-bit I am trying to run ode45 to solve the matrix ricatti equation for a discrete time LQ tracker with fixed final time T. When I run the ode45 I get the error "Inputs must be floats, namely single or double.". Any support on getting a result from ode45 would be incredible.

clc
clear 
close all

A=[0 1 0 0;0 -1 -3.22 0.5;0 0 0 1;0 0 17.71 -2.75]; %state matrix
B=[0 0;1 -0.5;0 0;-0.5 2.75]; %input matrix
C=[1 0 0 0;0 0 1 0;0 0 1 0;0 0 0 1]; %output matrix

[An,Am]=size(A);
[Bn,Bm]=size(B);
[Cn,Cm]=size(C);

t0=0;
T=20; %final time (sec)
tspan=[-T,t0]; %for reverse integration of S_dot 

%weighing of cost function
W=[1 0 0 0;0 1 0 0;0 0 1 0; 0 0 0 1]; 
Q=[1 0 0 0;0 1 0 0;0 0 1 0; 0 0 0 1]; 
R=[1 0; 0 1];

%generate symmetric symbolic matrix S(t)
S_t=sym('S_t',[An,Am]);
S_t=tril(S_t,0)+tril(S_t,-1).';

S_dot=-(S_t*A+A'*S_t-S_t*B*(inv(R))*B'*S_t+C'*Q*C); %differential matrix ricatti equation

S_dot = S_dot(:); %Convert from "n"-by-"n" to "n^2"-by-1 (matrix turned into transpose vector for ode45)

S_T=C'*W*C; %boundary condition @ final time T
S_T=S_T(:); %boundary condition as transpose vector 

[time, state]=ode45(@(t,S_t) S_dot,tspan,S_T)

[madhan ravi]

Upload S_dot function

[Chris]

It's stated in the code itself. What are you looking for?

Answer 1

[Walter Roberson]

Replace

[time, state]=ode45(@(t,S_t) S_dot,tspan,S_T)

with

syms t;
F = matlabFunction(S_dot, 'vars', {S_t(:)});
[time, state]  =ode45(F, tspan, S_T)