Article ID Journal Published Year Pages File Type
756186 Systems & Control Letters 2015 7 Pages PDF
Abstract

We consider the switched-affine optimal control problem, i.e., the problem of selecting a sequence of affine dynamics from a finite set in order to minimize a sum of convex functions of the system state. We develop a new reduction of this problem to a mixed-integer convex program (MICP), based on perspective functions. Relaxing the integer constraints of this MICP results in a convex optimization problem, whose optimal value is a lower bound on the original problem value. We show that this bound is at least as tight as similar bounds obtained from two other well-known MICP reductions (via conversion to a mixed logical dynamical system, and by generalized disjunctive programming), and our numerical study indicates it is often substantially tighter. Using simple integer-rounding techniques, we can also use our formulation to obtain an upper bound (and corresponding sequence of control inputs). In our numerical study, this bound was typically within a few percent of the optimal value, making it attractive as a stand-alone heuristic, or as a subroutine in a global algorithm such as branch and bound. We conclude with some extensions of our formulation to problems with switching costs and piecewise affine dynamics.

Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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