No abstract

In this paper we investigate the problem of optimising the speed of a vehicle over a fixed path for minimum time traversal. We utilise a change of variables that has been known since the 1980s, although the resulting convexity of the problem was not noted until recently. The contributions of this paper are three fold. First, we extend the convexification of the problem to a more general framework. Second, we identify a wide range of vehicle models and constraints which can be included in this expanded framework. Third, we develop and implement an algorithm that allows these problems to be solved in real time, on embedded systems, with a high degree of accuracy.

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.