Non-convex states constrained system control algorithm via geometric techniques

The algorithm of constrained system control via geometric techniques does well in dealing with the control problem of the systems with convex constraints on states and control inputs. In some control applications, the states constraints may be non-convex. It is hard to find a suitable solution for such a system according to the traditional methods. The algorithm of constrained control is on the base of geometric and set theory, so it has the advantage for dealing with such control problems. A new algorithm for controlling the system with non-convex states constraints is proposed on the basis of the algorithm of constrained system control via geometric techniques. The new algorithm ensures that the system states are suitable to the constraints by choosing suitable final set, level sets and control inputs according to the time-optimal function.