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.KeywordsOptimal Control ProblemGaussian EliminationMultistage SystemSensitivity EquationAutomatic DifferentiationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.