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Summary: 2 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 49, NO. 1, JANUARY 2004
Optimal Control of Switched Systems Based on
Parameterization of the Switching Instants
Xuping Xu, Member, IEEE, and Panos J. Antsaklis, Fellow, IEEE
Abstract--This paper presents a new approach for solving
optimal control problems for switched systems. We focus on
problems in which a prespecified sequence of active subsystems
is given. For such problems, we need to seek both the optimal
switching instants and the optimal continuous inputs. In order
to search for the optimal switching instants, the derivatives of
the optimal cost with respect to the switching instants need to
be known. The most important contribution of the paper is a
method which first transcribes an optimal control problem into an
equivalent problem parameterized by the switching instants and
then obtains the values of the derivatives based on the solution
of a two point boundary value differential algebraic equation
formed by the state, costate, stationarity equations, the boundary
and continuity conditions, along with their differentiations. This
method is applied to general switched linear quadratic problems
and an efficient method based on the solution of an initial value
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