I am solving an optimal control problem of the form $$ \min_u \qquad\int_0^T \langle u(t), u(t) \rangle \, \mathrm{d}t \\ s.t. \quad \dot{x} = \tilde{f}(x) + u, \quad x(0)=x_0 \\ \qquad \tilde{\Phi}(x(T)) = 0\} $$ reformulated as $$ \min_{\xi(T)} \qquad \xi(T) \\ s.t. \quad \dot{z} = f(z,u), \quad z(0) = z_0 \\ \qquad \Phi(z(T)) = 0 $$ where the dual variable on the dynamics is denoted by $\lambda$ and the dual variable on the terminal constraint is denoted by $\mu$. Also, we define $z := (x^{\top}, \xi)^{\top}$, $f(z,u) := (f(x,u)^{\top}, \langle u, u \rangle)^{\top}$, and $\Phi(z(T)) := \tilde{\Phi}(x(T))$.

I would like to use a BVP-DAE solver to solve directly the optimality conditions $$ \dot{\lambda} = -\frac{df}{dz}, \quad \lambda(T) = \frac{d\xi(T)}{dz} + \mu \frac{d\Phi(z(T))}{dz} \\ \dot{z} = f(z,p), \quad z(0) = z_0 \\ \Phi(z(T)) = 0 $$ and was wondering what numerical software I could use. Ideally it would be a collocation-based DAE solver. I've looked into Sundials a bit, but was wondering what I should use. I've looked at a few previous questions but am looking for existing software. Thanks!



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.