scholarly journals Optimal control of a chemical reactor

1997 ◽  
Vol 39 (1) ◽  
pp. 61-76
Author(s):  
K. H. Wong ◽  
N. Lock
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Differential Equations ◽  
Quadratic Programming ◽  
Original Problem ◽  
Chemical Reactor ◽  
Galerkin Scheme ◽  
Actual Output ◽  
Quadratic Programming Problems ◽  
Linearly Constrained

AbstractA chemical reactor problem is considered governed by partial differential equations. We wish to control the input temperature and the input oxygen concentration so that the actual output temperature can be as close to the desired output temperature as possible. By linearizing the differential equations around a nominal equation and then applying a finite-element Galerkin Scheme to the resulting system, the original problem can be converted into a sequence of linearly-constrained quadratic programming problems.

Linear Quadratic Optimal Control Via Fourier-Based State Parameterization

1991 ◽  
Vol 113 (2) ◽  
pp. 206-215 ◽  
Author(s):  
V. Yen ◽  
M. Nagurka
Keyword(s):  
Optimal Control ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Quadratic Programming Problem ◽  
Necessary Condition ◽  
Mathematical Programming Problem ◽  
Linear Quadratic ◽  
Linear Algebraic Equations ◽  
Linearly Constrained ◽  
Lq Problem

A method for determining the optimal control of unconstrained and linearly constrained linear dynamic systems with quadratic performance indices is presented. The method is based on a modified Fourier series approximation of each state variable that converts the linear quadratic (LQ) problem into a mathematical programming problem. In particular, it is shown that an unconstrained LQ problem can be cast as an unconstrained quadratic programming problem where the necessary condition of optimality is derived as a system of linear algebraic equations. Furthermore, it is shown that a linearly constrained LQ problem can be converted into a general quadratic programming problem. Simulation studies for constrained LQ systems, including a bang-bang control problem, demonstrate that the approach is accurate. The results also indicate that in solving high order unconstrained LQ problems the approach is computationally more efficient and robust than standard methods.

Implementation of an Algorithm for the Direct Solution of Optimal Control Problems

2011 ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Optimal Control ◽  
Nonlinear Programming ◽  
Differential Equations ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Optimal Control Problems ◽  
The State ◽  
Control Problems ◽  
Direct Solution ◽  
Sqp Method

This paper presents the implementation of a numerical algorithm for the direct solution of optimal control and parameter identification problems. The problems may include differential equations that define the state, inequality constraints, and equality constraints at the initial and final times. The numerical method is based on transforming the infinite dimensional optimal control problem into a finite dimensional nonlinear programming problem. The transformation technique involves dividing the time interval of interest into a mesh that need not be uniform. In each subinterval of the mesh the control input is approximated using a piecewise polynomial. In particular, the control can be approximated using: (i) piecewise constant, (ii) piecewise linear, or (iii) piecewise cubic polynomials. The explicit Runge-Kutta method is used to obtain an approximate solution of the differential equations that define the state. With the approach used here the states do not appear in the nonlinear programming (NLP) problem. As a result the NLP problem is very compact relative to other numerical methods used to solve nonlinear optimal control problems. The NLP problem is solved using a sequential quadratic programming (SQP) technique. The SQP method is based on minimizing the L1 exact penalty function. Each major step of the SQP method solves a strictly convex quadratic programming problem. The paper also describes a simplified interface to the computer programs that implement the method. An example is presented to demonstrate the algorithm.

scholarly journals Strength optimization of structural elements by means of optimal control

2019 ◽  
Vol 262 ◽  
pp. 10006
Author(s):  
Dorota Jasinska ◽  
Leszek Mikulski
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Differential Equations ◽  
Control Theory ◽  
Boundary Value Problem ◽  
Structural Elements ◽  
Finite Element Software ◽  
Portal Frame ◽  
Multipoint Boundary Value Problem ◽  
The Web

This paper investigates the optimal shaping of the web height of an I-section steel portal frame. The problem is formulated as a control theory task. From a mathematical perspective, the task involves solving the multipoint boundary value problem for the system of forty-three differential equations. The solution is compared to results obtained from the finite element software Abaqus.

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