Gobal optimization of linear hybrid systems with varying transition times

Open loop optimal control problems with linear hybrid (discrete/continuous) systems embedded are often approximated as dynamic optimization problems. These problems are inherently nonconvex. A deterministic global optimization algorithm for linear hybrid systems with varying transition times is developed. First, the control parametrization enhancing transform is used to transform the problem from a linear hybrid system with scaled discontinuities and varying transition times into a nonlinear one with stationary discontinuities and fixed transition times. Next, a convexity theory is applied to construct a convex relaxation of the original nonconvex problem. This allows the problem to be solved in a branch-and-bound framework that can guarantee the solution to ¿ global optimality within a finite number of iterations.