Optimal sampled-data control of piecewise affine systems with parameter uncertainty

In this paper, sampled-data control of piecewise affine (PWA) systems with parameter uncertainty is addressed based on the interval method. First, the optimal sampled-data control problem of PWA systems with parameter uncertainty is rewritten as an optimal control problem of discrete-time PWA systems with parameter uncertainty. Then weighting matrices in the obtained cost function are also uncertain. Furthermore, using an over-approximation via interval arithmetic, this problem is reduced to a mixed integer quadratic programming problem, not a min-max optimization problem.