An optimal on-off controller with switching costs using non-linear binary programming

Autonomous systems based on MEMS devices may often be provided with very limited computational and power capacity, if control circuitry and power sources are to be miniaturized along with the electromechanical components. On-Off control can serve as an efficient methods of regulating motion of MEMS structures when power is extremely limited by allowing control to be performed using simple driving circuits and few transitions between dasiaonpsila- and dasiaoffpsila-states. In particular, this is highly desirable for micro-robotics applications based on piezoelectric actuation. In this paper a binary programming method is used to optimize a cost function that consists of the number of switching transitions and on-time for a linear-discrete system, as the system is steered to a desired final state. This can be used to minimize power consumption in piezoelectric actuators as they move a micro-robotic leg joint to a desired position. A set of test cases is examined to explore behavior of the optimization procedure.