OPTIMAL CONTROL COMPUTATION FOR DIFFERENTIAL-ALGEBRAIC PROCESS SYSTEMS WITH GENERAL CONSTRAINTS

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Abstract
This paper is concerned with the combined problem of optimal parameter selection and control for differential-algebraic system (DASs) involving various constraints. The control parameterization technique of using piecewise constant functions is used to approximate the original problem into a sequence of finite-dimensional parameter selection problems. Based on characterizing the Hamiltonian function and adjoint system associated with a DAS and transforming different types of constraints into a cononical function which has the same form as the cost functional, a unified gradient computation algorithm for the controls and parameters is derived. This algorithm makes the resulting approximate problems be effectively solved by gradient-based optimization methods. As a specific example, the singular control problem of finding the optimal feeding policy for a fed-batch fermentation process governed by the product and substrate inhibited specific growth and product formation kinetics is solved. The computed results show that such a singular control problem can also be effectively solved by the proposed optimization scheme.