Yop is a MATLAB Toolbox for numerical optimal control. It utilizes CasADi to interface to integrators and nonlinear optimization solvers, and thereof its name, Yop - Yet Another Optimal Control Problem Parser.
Why yop?
Yop is made to simplify the step from mathematical formulation to code, giving the user time to focus on the optimal control problem.
Take the classical Bryson-Denham optimal control problem with the following formulation:
\[\min_{a(t)} \frac{1}{2} \int_0^1 a(t)^2 dt\] \[\dot{v}(t) = a(t) = u(t)\] \[\dot{x}(t) = v(t)\] \[v(0)=-v(1)=1\] \[x(0)=x(1)=0\] \[x(t) \leq l = \frac{1}{9}\]In yop it is as simple as initializing the variables, formulating the ocp, calculating the solution and plotting the results.
## Solution of the Bryson-Denham problem with yop.
# Initialize the variables
yopvar t0 tf t x1 x2 u
# Formulating the OCP
ocp = yop.ocp('Bryson-Denham Problem');
ocp.min( 1/2 * int(u^2) );
ocp.st( ...
t0==0, tf==1, ...
der(x1) == x2, ...
der(x2) == u, ...
x1(t0) == 0, ...
x1(tf) == 0, ...
x2(t0) == 1, ...
x2(tf) == -1, ...
x1 <= 1/9 ...
);
# Calculate the solution
sol = ocp.solve('intervals', 15, 'degree', 2);
# Plot the results
figure(1);
subplot(311); hold on
sol.plot(t, x1, 'mag', 5);
subplot(312); hold on
sol.plot(t, x2);
subplot(313); hold on
sol.stairs(t, u);
Comparing yop to CasADi and PROPT
To see how yop compares to some of its competition, check the following page. Comparinson between yop and casadi
Getting started
Download yop and then get started by reading our documentation or jumping directly into examples.