Question

Consider the system $\dot{x}_1=\dot{x}_2+u_1 and \dot{x}_2=u_2$ Find the optimal control u for $J=\frac{1}{2}\int\limits^4_0 ({u_1^2+u_2^2}) \, dt$ given that $x_1(0)=x_2(0)=1, x_1(4)=0$

Answer 1

The aim of this article is control of a set of 3-wheel robots with non-holonomic dynamics for hunting and covering around moving target. Robots have mass and inertia, and the wheel mass have been considered in the dynamic model of robots. The output of the controller is wheel’s torque and steering torque of the front wheel.