3-D filter SQP method for optimal control of the multistage differential-algebraic systems with inconsistent initial values

In the article a 3-dimensional filter method for solving optimal control problems of differential-algebraic equations (DAEs) was presented. Direct multiple shooting method, which is appropriate for the control problems of the multistage DAE systems, leads to the large-scale nonlinear programming problems. In the proposed approach the extended Fletcher´s filter with three inputs was used. The filter method promotes global convergence without the need to use a penalty function. The first input of the filter denotes the value of the cost function. The second and third inputs come from two types of equality constraints - consistent initial conditions of the DAE system and continuity constraints on the state trajectories. The new algorithm was tested on the optimal control problem of a fed-batch fermentor for penicillin production. The numerical simulations were executed in MATLAB environment using Wroclaw Center for Networking and Supercomputing.