TY - GEN

T1 - Discretized switching time optimization problems

AU - Flasskamp, Kathrin

AU - Murphey, Todd David

AU - Ober-Blobaum, Sina

PY - 2013/12/1

Y1 - 2013/12/1

N2 - A switched system is defined by a family of vector fields together with a switching law which chooses the active vector field at any time. Thus, the switching law encoding the switching times and the sequence of modes may serve as a design parameter. Switching time optimization (STO) focuses on the optimization of the switching times in order to govern the system evolution to a desired behavior described by some cost function. However, it is rare that a STO problem can be solved analytically leading to the use of numerical approximation methods. In this contribution, we directly start with applying integration schemes to approximate the system's state and adjoint trajectories and study the effect of this discretization. It turns out that in contrast to the continuous time problem, the discretized problem loses differentiability with respect to the optimization variables. The isolated nondifferentiable points can be precisely identified though. Nevertheless, to solve the STO problem, nonsmooth optimization techniques have to be applied which we illustrate using a hybrid double pendulum.

AB - A switched system is defined by a family of vector fields together with a switching law which chooses the active vector field at any time. Thus, the switching law encoding the switching times and the sequence of modes may serve as a design parameter. Switching time optimization (STO) focuses on the optimization of the switching times in order to govern the system evolution to a desired behavior described by some cost function. However, it is rare that a STO problem can be solved analytically leading to the use of numerical approximation methods. In this contribution, we directly start with applying integration schemes to approximate the system's state and adjoint trajectories and study the effect of this discretization. It turns out that in contrast to the continuous time problem, the discretized problem loses differentiability with respect to the optimization variables. The isolated nondifferentiable points can be precisely identified though. Nevertheless, to solve the STO problem, nonsmooth optimization techniques have to be applied which we illustrate using a hybrid double pendulum.

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M3 - Conference contribution

AN - SCOPUS:84893296747

SN - 9783033039629

T3 - 2013 European Control Conference, ECC 2013

SP - 3179

EP - 3184

BT - 2013 European Control Conference, ECC 2013

T2 - 2013 12th European Control Conference, ECC 2013

Y2 - 17 July 2013 through 19 July 2013

ER -