Pawel Drag

The matrix-based description approach for the multistage differential-algebraic processes

In the article a new insight into an optimal control problem of the multistage processes has been given. The multistage descriptor processes with differential-algebraic constraints are under considerations. The new representation of the descriptor model has been presented. Moreover, the new structures to represent the differential state variables, algebraic state variables, control function, as well the global parameters have been introduced. The generalized description enables the unified representation of a broad group of the multistage processes with differential-algebraic relations and indicates on the physical interpretation of the process variables.

Simulated annealing with constraints aggregation for control of the multistage processes

In the article the control and optimization of multistage technological processes were discussed. In the presented research, it was assumed, that in the complex technological processes, the multistage differential-algebraic constraints with unknown consistent initial conditions were considered. To rewrite the infinite-dimensional optimal control problem into the finite-dimensional optimization task, the direct shooting method was applied. Simulated annealing algorithm was proposed as the method for solving nonlinear optimization problem with constraints. Stretching function was used to allow us to locate the globally optimal solution. The complex process constraints were treated using constraints aggregation methods. The presented methodology was tested with optimal control problem of the two-reactors system. The numerical simulations were executed in MATLAB environment using Wroclaw Center for Networking and Supercomputing.

Inexact Newton matrix-free methods for solving complex biotechnological systems

In the article a new approach for solving complex and highly nonlinear differential-algebraic equations (DAEs) was presented. An important kind of applications of DAE systems is modeling of biotechnological processes, which can have a very different course. An efficient solving of equations describing biotechnological industrial inlets results in better optimization of the processes and has a positive impact on the environment. Some of the mentioned processes were characterized by a highly nonlinear dynamics. To obtain the trajectories of the state numerically, the backward differentiation formula was used in the presented method. As a result, a large-scale system of nonlinear algebraic equations was obtained. To solve a such system, the inexact Newton matrix-free approach was proposed. The new algorithm was tested on a mathematical model of a fed-batch fermentor for penicillin production. The numerical simulations were executed in MATLAB using Wroclaw Center for Networking and Supercomputing.

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 Fletchers 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.