  Among the intelligent safety technologies for road vehicles, active
suspensions controlled by embedded computing elements for preventing rollover
have received a lot of attention. The existing models for synthesizing and
allocating forces in such suspensions are conservatively based on the
constraint that no wheels lift off the ground. However, in practice,
smart/active suspensions are more necessary in the situation where the wheels
have just lifted off the ground. The difficulty in computing control in the
last situation is that the problem requires satisfying disjunctive constraints
on the dynamics. To the authors',knowledge, no efficient solution method is
available for the simulation of dynamics with disjunctive constraints and thus
hardware realizable and accurate force allocation in an active suspension tends
to be a difficulty. In this work we give an algorithm for and simulate
numerical solutions of the force allocation problem as an optimal control
problem constrained by dynamics with disjunctive constraints. In particular we
study the allocation and synthesis of time-dependent active suspension forces
in terms of sensor output data in order to stabilize the roll motion of the
road vehicle. An equivalent constraint in the form of a convex combination
(hull) is proposed to satisfy the disjunctive constraints. The validated
numerical simulations show that it is possible to allocate and synthesize
control forces at the active suspensions from sensor output data such that the
forces stabilize the roll moment of the vehicle with its wheels just lifted off
the ground during arbitrary fish-hook maneuvers.
