Optimal sampled data control of PWM systems using piecewise affine approximations

Abstract

The paper considers optimal control of a class of pulse-width modulated systems based on sampled data modeling and piecewise affine approximations. The problem of minimizing an integral cost over a finite horizon is stated in discrete time by lifting the system dynamics. By approximating the lifted dynamics with a piecewise affine system the control problem simplifies to a mixed integer quadratic problem. The optimization problem is solved off-line and the solution is represented in a look-up table which can be implemented in a receding horizon control approach. The contribution of the paper is to introduce a sampled data model which allows to better represent the true control objective. This removes the need to filter out the ripple from the measured state and thus has potential for improved performance.

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