Optimal Control of Switched Homogeneous Systems

In this paper, we present a method for designing discrete-time state-feedback controllers for a class of continuous-time switched homogeneous systems which includes switched linear systems as a special case. A discrete-time approximate value iteration over a quantization of the unit sphere is used to compute an approximation of the continuous-time value function over the entire unbounded state space. Properties of the value function and its approximations are elicited and used to provide conditions under which state- feedback controllers with provable guarantees in stability and performance can be constructed. To illustrate the results, the methodology is applied to an example switched system possessing two unstable modes, one of which is nonlinear.