D. Sourlas

A GLOBAL OPTIMIZATION APPROACH TO RATIONALLY CONSTRAINED RATIONAL PROGRAMMING

Abstract The rationally constrained rational programming (RCR) problem is shown, for the first time, to be equivalent to the quadratically constrained quadratic programming problem with convex objective function and constraints that are all convex except for one that is concave and separable. This equivalence is then used in developing a novel implementation of the Generalized Benders Decomposition (GBDA) which, unlike all earlier implementations, is guaranteed to identify the global optimum of the RCRP problem. It is also shown, that the critical step in the proposed GBDA implementation is the solution of the master problem which is a quadratically constrained, separable, reverse convex programming problem that must be solved globally. Algorithmic approaches to the solution of such problems are discussed and illustrative examples are presented.

Best achievable control system performance: the saturation paradox

This paper proposes a methodology for the quantification of the best achievable closed loop control system performance for a linear process in the presence of input saturation constraints. Closed loop stability is guaranteed through the use of a parametrization of all nonlinear stabilizing controllers in terms of a finite gain stable parameter Q. Closed loop performance is quantified with respect to a finite number of disturbances. The best achievable performance is quantified over a class of nonlinear stabilizing controllers parametrized in terms of absolutely summable second order Volterra operators. The proposed computational procedure involves the solution of a sequence of mixed integer linear programs. Through the example it is shown that, in certain cases, there may exist a value of the saturation bound for which the best achievable control system performance is significantly better than the corresponding best achievable linear performance.<<ETX>>

Optimization-based decoupling controller design for discrete systems

Decoupling has been studied as a means of improving control loop behavior in the presence of strong interactions, particularly in high-purity distillation. The design of optimal multivariable decoupling controllers is the main topic of this work. The stabilizing and decoupling controllers are described through the Youla parametrization and linear equalities. Then, for given time-domain performance envelopes, a numerical optimization method based on exact penalty functions and linear programming is presented that identifies the multivariable controller that decouples the closed loop and optimizes its performance. It is also shown that this approach can be extended to encompass traditional decoupling techniques based on (possibly low order) decouplers. Finally, the problem of decoupling is discussed in relation to simultaneous and decentralized multivariable control where it is demonstrated that approximate decoupling may be a necessary compromise when there are not enough degrees of freedom.

On simultaneously optimal decentralized performance

This work focuses on the simultaneously optimal decentralized performance problem. Specifically, a method that quantifies the best (in an l/sup 1/-l/sup /spl infin// sense) dynamic performance achievable by one decentralized dynamic feedback compensator, for a finite family of process models, is presented. To achieve this goal, necessary and sufficient conditions for decentralized simultaneous stabilization are introduced. These conditions are realized through a set of quadratic equality constraints. Consequently, the decentralized simultaneous performance problem is formulated as a quadratically constrained minimax problem that is nondifferentiable and infinite dimensional. This problem is solved through iterative solution of appropriately constructed finite dimensional nonlinear programming problems. For small horizons, /spl epsi/-globally optimal solutions of these NLPs can be achieved. These concepts are employed in the solution of an illustrative example.<<ETX>>

Resin transfer molding: nonlinear model development from a control perspective

Resin transfer molding (RTM) is employed in the manufacture of complex 3D polymer composite parts. Resin curing is one of two critical steps in RTM where the injected resin polymerizes and cross-links. Because of the exothermic nature of these reactions, the temperature evolution of the system is distributed in time and space. The development of computationally tractable process models for the curing process is essential for the development of model-based process control algorithms that minimize the spatial gradients during the curing process. A reduced-order model that consist of a finite number of nonlinear ordinary differential equations (ODEs) is obtained from detailed continuum cure models using proper orthogonal decomposition (POD) and Galerkin projection. The accuracy and predictive capabilities of such models are assessed.

On l/sup 1/ and H/sup infinity /-optimal decentralized performance

The Manousiouthakis parametrization of all decentralizing stabilizing controllers is employed in mathematically formulating the optimal decentralized controller synthesis problem. The performance problem is formulated in the l/sup 1/ and H/sup infinity / frameworks. In both cases, the resulting optimization problems are infinite dimensional and therefore not directly amenable to computations. It is shown that finite dimensional optimization problems that have value arbitrarily close to the infinite dimensional ones can be constructed. Based on this result algorithms that solve the l/sup 1/ and the H/sup infinity / decentralized performance problems are presented.<<ETX>>