Computational Optimal Control pp 177-191 | Cite as

# Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations

## Abstract

An algorithm is described for computing time-varying controls and time-invariant parameters to optimize the performance of a dynamic system whose behaviour is described by differential-algebraic equations (DAEs) of arbitrary index.

The problem formulation deals with a multistage system, in which each stage has its own describing equations. It also accommodates end-point, interior point, and path constraints which can be equalities or inequalities.

The algorithm uses a parameterization of the controls in terms of a given set of basis functions. Path constraints are dealt with via integral constraints. The problem is thus converted into a nonlinear programming problem, for which the objective and constraint functions are evaluated by integration of the system equation of the sensitivity equations.

The special problems arising when the DAE system has index greater than one are explicitly dealth with, using automatic differentiation to generate the necessary additional equations, thus reducing the system index. A constraint stabilization technique for the resulting low index system is proposed.

## Keywords

Optimal Control Problem Gaussian Elimination Multistage System Sensitivity Equation Automatic Differentiation## Preview

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