A stable elemental decomposition for dynamic process optimization

AbstractIn Cervantes and Biegler (A.I.Ch.E.J. 44 (1998) 1038), we presented a simultaneous nonlinear programming problem (NLP) formulation for the solution of DAE optimization problems. Here, by applying collocation on finite elements, the DAE system is transformed into a nonlinear system. The resulting optimization problem, in which the element placement is fixed, is solved using a reduced space successive quadratic programming (rSQP) algorithm. The space is partitioned into range and null spaces. This partitioning is performed by choosing a pivot sequence for an LU factorization with partial pivoting which allows us to detect unstable modes in the DAE system. The system is stabilized without imposing new boundary conditions. The decomposition of the range space can be performed in a single step by exploiting the overall sparsity of the collocation matrix but not its almost block diagonal structure. In order to solve larger problems a new decomposition approach and a new method for constructing the quadratic programming (QP) subproblem are presented in this work. The decomposition of the collocation matrix is now performed element by element, thus reducing the storage requirements and the computational effort. Under this scheme, the unstable modes are considered in each element and a range-space move is constructed sequentially based on decomposition in each element. This new decomposition improves the efficiency of our previous approach and at the same time preserves its stability. The performance of the algorithm is tested on several examples. Finally, some future directions for research are discussed

Efficient Nonlinear Optimization with Rigorous Models for Large Scale Industrial Chemical Processes

Large scale nonlinear programming (NLP) has proven to be an effective framework for obtaining profit gains through optimal process design and operations in chemical engineering. While the classical SQP and Interior Point methods have been successfully applied to solve many optimization problems, the focus of both academia and industry on larger and more complicated problems requires further development of numerical algorithms which can provide improved computational efficiency. The primary purpose of this dissertation is to develop effective problem formulations and an advanced numerical algorithms for efficient solution of these challenging problems. As problem sizes increase, there is a need for tailored algorithms that can exploit problem specific structure. Furthermore, computer chip manufacturers are no longer focusing on increased clock-speeds, but rather on hyperthreading and multi-core architectures. Therefore, to see continued performance improvement, we must focus on algorithms that can exploit emerging parallel computing architectures. In this dissertation, we develop an advanced parallel solution strategy for nonlinear programming problems with block-angular structure. The effectiveness of this and modern off-the-shelf tools are demonstrated on a wide range of problem classes. Here, we treat optimal design, optimal operation, dynamic optimization, and parameter estimation. Two case studies (air separation units and heat-integrated columns) are investigated to deal with design under uncertainty with rigorous models. For optimal operation, this dissertation takes cryogenic air separation units as a primary case study and focuses on formulations for handling uncertain product demands, contractual constraints on customer satisfaction levels, and variable power pricing. Multiperiod formulations provide operating plans that consider inventory to meet customer demands and improve profits. In the area of dynamic optimization, optimal reference trajectories are determined for load changes in an air separation process. A multiscenario programming formulation is again used, this time with large-scale discretized dynamic models. Finally, to emphasize a different decomposition approach, we address a problem with significant spatial complexity. Unknown water demands within a large scale city-wide distribution network are estimated. This problem provides a different decomposition mechanism than the multiscenario or multiperiod problems; nevertheless, our parallel approach provides effective speedup

Approximate Dynamic Programming with Feasibility Guarantees

Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In applications, these schemes, however, often require solving large-scale optimization problems. Iterative techniques from distributed optimization are frequently proposed for complexity reduction. Yet, they achieve feasibility only asymptotically, which induces a substantial computational burden. This work presents an approximate dynamic programming scheme, which is guaranteed to deliver a feasible solution in "one shot", i.e., in one backward-forward iteration over all subproblems provided they are coupled by a tree structure. Our proposed scheme generalizes methods from seemingly disconnected domains such as power systems and optimal control. We demonstrate its efficacy for problems with nonconvex constraints via numerical examples from both domains

Stable Adaptive Control Using New Critic Designs

Classical adaptive control proves total-system stability for control of linear plants, but only for plants meeting very restrictive assumptions. Approximate Dynamic Programming (ADP) has the potential, in principle, to ensure stability without such tight restrictions. It also offers nonlinear and neural extensions for optimal control, with empirically supported links to what is seen in the brain. However, the relevant ADP methods in use today -- TD, HDP, DHP, GDHP -- and the Galerkin-based versions of these all have serious limitations when used here as parallel distributed real-time learning systems; either they do not possess quadratic unconditional stability (to be defined) or they lead to incorrect results in the stochastic case. (ADAC or Q-learning designs do not help.) After explaining these conclusions, this paper describes new ADP designs which overcome these limitations. It also addresses the Generalized Moving Target problem, a common family of static optimization problems, and describes a way to stabilize large-scale economic equilibrium models, such as the old long-term energy model of DOE.Comment: Includes general reviews of alternative control technologies and reinforcement learning. 4 figs, >70p., >200 eqs. Implementation details, stability analysis. Included in 9/24/98 patent disclosure. pdf version uploaded 2012, based on direct conversion of the original word/html file, because of issues of format compatabilit

A model-based methodology for managing technological risk

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Energy management in communication networks: a journey through modelling and optimization glasses

The widespread proliferation of Internet and wireless applications has produced a significant increase of ICT energy footprint. As a response, in the last five years, significant efforts have been undertaken to include energy-awareness into network management. Several green networking frameworks have been proposed by carefully managing the network routing and the power state of network devices. Even though approaches proposed differ based on network technologies and sleep modes of nodes and interfaces, they all aim at tailoring the active network resources to the varying traffic needs in order to minimize energy consumption. From a modeling point of view, this has several commonalities with classical network design and routing problems, even if with different objectives and in a dynamic context. With most researchers focused on addressing the complex and crucial technological aspects of green networking schemes, there has been so far little attention on understanding the modeling similarities and differences of proposed solutions. This paper fills the gap surveying the literature with optimization modeling glasses, following a tutorial approach that guides through the different components of the models with a unified symbolism. A detailed classification of the previous work based on the modeling issues included is also proposed