Stable Decomposition for Dynamic Optimization

Abstract

Abstract, Dynamic optimisation problems axe usually solved by transforming them to nonlinear programming (NLP) problems with either sequential or simultaneous approaches. However, both approaches can still be inefficient to tackle complex problems. In addition, many problems in chemical engineering have unstable components which lead to unstable intermediate profiles during the solution procedure. If the numerical algorithm chosen utilises an initial value formulation, the error from decomposition or integration can accumulate and the Newton iteration* then faiL On the other hand, by njiiigsmUhkŜ hooting or collocation, our algorithm has favorable numerical characteristics for both stable and unstable problems; by exploiting the structure of the resulting system, a stable and efficient decomposition algorithm results.'Here solution of this NLP formulation is considered through a reduced Hessian Successive Quadratk Programming (SQP) approach. The routine chosen for the decomposition of the system equations is CX)LDAE, in which the stable multipk shooting scheme is implemented. To address the mesh selection, we will introduce a new bilevd framework that wiD decouple the element placement from the optimal control procedure. We will also provide a proof for the connection of our algorithm and the calculus of variations.

Stochastic optimization for optimal and model-predictive control

“…represented by polynomials in time with unknown coefficients) and the differential-algebraic equations (DAEs) are integrated using the coefficients adjusted in each iteration of an optimization algorithm (Vassiliadis, 1993). In the simultaneous strategy (Biegler, 1984;Logsdon and Biegler, 1989;Tanartkit and Biegler, 1995;Tieu et al, 1995), both the unknowns of the DAEs (state and other variables) and the coefficients of the polynomials for the manipulated variables are adjusted simultaneously to satisfy the stationarity conditions. Luus (1990Luus ( , 1992Luus ( , 1994Luus ( , 1995 computed improved performance indices, compared with those obtained with these strategies, through the use of penalty functions and his iterative dynamic programming (IDP) method.…”

Global and Dynamic Optimization using the Artificial Chemical Process Paradigm and Fast Monte Carlo Methods for the Solution of Population Balance Models

“…Figure 8 shows the solution of four optimization problems used by several authors as benchmark problems. The Van der Pol oscillator problem has been studied by Vassiliadis (1993), Tanartkit and Biegler (1995), Banga, Irizarry-Rivera and Seider (1998), and Vassiliadis et al (1999). This problem was solved using the generalized control function, where each element can be represented by either linear or quadratic Lagrange polynomials.…”

A Multiplier-Free, Reduced Hessian Method for Process Optimization

“…This was demonstrated for flowsheet optimization through the use of block tridiagonal distillation models. Recent studies [24], [25] also describe the integration of the multiplier free approach to the optimization of systems described by boundary value problems (BVPs). In this case, the BVP solver COLDAE [l] was combined with the multiplier free method to solve problems in parameter estimation, optimal control and reactor design.…”