Isaac Klickstein

Isaac Klickstein

Engineering PhD applying numerical methods to solve controls and optimization problems

Optimal Control Problem: Herding Double Integrators

less than 1 minute read

Published:

Herding Double Integrators

\[\begin{aligned} \min && &J = \frac{1}{2} \int_0^{t_f} \left( u_x^2(t) + u_y^2(t) \right) dt\\ \text{s.t.} && &\dot{x}_i(t) = v_i(t), \quad x_i(0) = x_{i,0}, \quad x_i(t_f) \geq x_f\\ && &\dot{v}_i(t) = u_x(t), \quad v_i(0) = v_{i,0}\\ && &\dot{y}_i(t) = w_i(t), \quad y_i(0) = y_{i,0}, \quad y_i(t_f) \geq y_f\\ && &\dot{w}_i(t) = u_y(t), \quad w_i(0) = w_{i,0}\\ && &i = 0,1,\ldots, M-1 \end{aligned}\]

You May Also Enjoy