ABSTRACT
People, engineers, and scientists encounter a variety of switched systems everyday. Gear selection in automatic transmissions [1], control of robots subject to constraints [2], power management in hybrid electric vehicles [3], load balancing in a computer cluster [4], coordination of flexible AC transmission systems (FACTS) devices [5], and output voltage regulation in DC/DC converters [6-10] are but a few examples. Minimizing energy/power usage and/or tracking errors are typical objectives in these control systems. These objectives are achieved by formulating an appropriate cost function to be optimized over some switching functions in combination with the usual continuous control input. Switched systems
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are a subclass of hybrid systems in which both discrete (switching) and the continuous control inputs are present. Additionally, there may be internal or uncontrolled switches that result when the system trajectory and/or continuous inputs enter certain regions of the state and input spaces, respectively. These switches are called autonomous.
