Antagonistic control

In antagonistic control we find an input sequence that maximizes (or at least makes large) an objective that is minimized in typical control. Applications include designing inputs to attack a control system, worst-case analysis of a control system, and security assessment of a control system. The antagonistic control problem is not convex, and so cannot be efficiently solved. We present here a powerful convex-optimization-based heuristic for antagonistic control, based on the convex-concave procedure, which can be used to find bad, if not the global worst-case, inputs. We also give an S-procedure-based upper bound for antagonistic control, applicable in cases when the objective and constraints can be described by quadratic inequalities, and use this to verify on examples that our method yields inputs very close to the (global) worst-case.