Optimal control of hybrid automata: an application to the design of a semiactive suspension

The optimal control of switched linear autonomous systems with quadratic performance index over infinite time horizon is considered. The decision variables are the switching times and the mode sequence, under the following constraints: the mode sequence has finite length; an automaton restricts the possible switches within adjacent locations, with a cost associated to each switch; the time interval between two consecutive switches is greater than a fixed quantity. A state-feedback solution is computed off-line through a numerical procedure. The method is extended to the case of infinite number of switches