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In the article a new approach for aircraft landing with the presence of the windshear phenomena was presented. The differential-algebraic model with variability constraints was under considerations. To transform the optimal control problem into a nonlinear optimization task, a modified direct shooting method was used. Then, to solve the obtained large-scale nonlinear optimization problem, a barrier...
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...
In the article the methods of solution quality evaluation in context of optimal control were presented and discussed. The quality of the solution plays a key role in control of nonlinear processes with descriptor constraints. The multiple shooting method enables us to transform the optimal control problem into a nonlinear optimization task. Therefore, the well adjusted quality evaluation function...
This paper deals with optimal periodic control problems for distributed-parameter systems with many kinds of controls (lumped and distributed). Descent optimization methods reduced to the control space are proposed. The formulas of partial gradients with respect to lumped and distributed controls are derived and their applicability to technological and biological problems is pointed-out.
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 classical inexact Newton method was presented as a tool for solving nonlinear differential algebraic equations (DAEs) in a fully implicit form F(y, y, t) = 0. This is especially in chemical engineering where describing the DAE system in a different form can be difficult or even impossible to realize. The appropriate rewriting of the DAEs using the backward Euler method makes it possible to present...
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...
In the article a new approach for optimal control of the multistage differential-algebraic systems was presented. A merit function based on Fletcher's augmented Lagrangian was used. The necessary optimality conditions for the optimal control of multistage index-1 DAE systems were stated and locally optimal solution was obtained using the inexact Newton method. The only constraints for decision variables...
In the article a new approach for control of a pressure-constrained batch reactor and a new multi-step optimization algorithm were presented. The considered batch reactor was described by both differential and algebraic equations. State constraints incorporate always difficulties into a mathematical model of the reactor, so a new algorithm based on a multiple shooting SQP-line search method was proposed...
The inexact Newton method is commonly known from its ability to solve large-scale systems of nonlinear equations. In the paper the classical inexact Newton method is presented as a tool for solving differential-algebraic equations (dae) in fully-implicit form F(ẏ, y, t) = 0. The appropriate statement of dae using the backward Euler method makes the possiblity to see the differential-algebraic system...
In the paper two approaches of parallelization for solving optimal control problems of ODE and index-1 DAE systems were presented and discussed. DAE Optimization Problem can be treated by Direct Nonlinear Programming Approach in two manners, known as Sequential Approach and Simultaneous Approach. Simultaneous Approach seems to be more reliable, because provides initial states in periods and discretized...
Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is...
Optimal control problem for state-constrained differential-algebraic (DAE) systems is considered. Such problems can be attacked by the multiple shooting approach well suited to unstable and ill-conditioned dynamic systems. According to this approach the control interval is partitioned into shorter intervals allowing the parallelization of computations with the reliable using of DAE solvers. A new...
Optimal control problem for parabolic differential-algebraic equations (PDAE) systems with spatially sensitive state-constraints and technological constraints is considered. Multipoint shooting approach is proposed to attack such problems. It is well suited to deal with unstable and ill-conditioned PDAE systems. This approach consists in the partitioning of the time-space domain into shorter layers,...
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