TY - JOUR

T1 - The optimal control approach to dynamical inverse problems

AU - Steiner, Wolfgang

AU - Reichl, Stefan

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - This paper considers solution strategies for dynamical inverse problems, where the main goal is to determine the excitation of a dynamical system, such that some output variables, which are derived from the system's state variables, coincide with desired time functions. The paper demonstrates how such problems can be restated as optimal control problems and presents a numerical solution approach based on the method of steepest descent. First, a performance measure is introduced, which characterizes the deviation of the output variables from the desired values, and which is minimized by the solution of the inverse problem. Second, we show, how the gradient of this error functional can be computed efficiently by applying the theory of optimal control, in particular by following an idea of Kelley and Bryson. As the major contribution of this paper we present a modification of this method which allows the application to the case where the state equations are given by a set of differential algebraic equations. This situation has great practical importance since multibody systems are mostly described in this way. For comparison, we also discuss an approach which bases an a direct transcription of the optimal control problem. Moreover, other methods to solve dynamical inverse problems are summarized.

AB - This paper considers solution strategies for dynamical inverse problems, where the main goal is to determine the excitation of a dynamical system, such that some output variables, which are derived from the system's state variables, coincide with desired time functions. The paper demonstrates how such problems can be restated as optimal control problems and presents a numerical solution approach based on the method of steepest descent. First, a performance measure is introduced, which characterizes the deviation of the output variables from the desired values, and which is minimized by the solution of the inverse problem. Second, we show, how the gradient of this error functional can be computed efficiently by applying the theory of optimal control, in particular by following an idea of Kelley and Bryson. As the major contribution of this paper we present a modification of this method which allows the application to the case where the state equations are given by a set of differential algebraic equations. This situation has great practical importance since multibody systems are mostly described in this way. For comparison, we also discuss an approach which bases an a direct transcription of the optimal control problem. Moreover, other methods to solve dynamical inverse problems are summarized.

UR - http://www.scopus.com/inward/record.url?scp=84855935341&partnerID=8YFLogxK

U2 - 10.1115/1.4005365

DO - 10.1115/1.4005365

M3 - Article

VL - 134

JO - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

JF - Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

SN - 0022-0434

IS - 2

M1 - 021010

ER -