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dynamic optimization of constrained semi-batch processes using Pontryagin's minimum principle An effective quasi-Newton approach

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COMPUTERS & CHEMICAL ENGINEERING 2017年 99卷 135-144页

作者： Aydin, Erdal Bonvin, Dominique Sundmacher, Kai Max Planck Inst Dynam Complex Tech Syst Sandtorstr 1 D-39106 Magdeburg Germany Ecole Polytech Fed Lausanne Lab Automat CH-1015 Lausanne Switzerland Otto von Guericke Univ Univ Pl 2 D-39106 Magdeburg Germany

This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise between feasibility and computational burden. Indirect methods, such as Pontryagin's Minimum Principle (PMP), reformulate the optimization problem. The main solution technique is the shooting method, which however often leads to convergence problems and instabilities caused by the integration of the co-state equations forward in time. This study presents an alternative indirect solution technique. Instead of integrating the states and co-states simultaneously forward in time, the proposed algorithm parameterizes the inputs, and integrates the state equations forward in time and the co-state equations backward in time, thereby leading to a gradient-based optimization approach. Constraints are handled by indirect adjoining to the Hamiltonian function, which allows meeting the active constraints explicitly at every iteration step. The performance of the solution strategy is compared to direct methods through three different case studies. The results show that the proposed PMP-based quasi-Newton strategy is effective in dealing with complicated constraints and is quite competitive computationally. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： constrained dynamic optimization Pontryagin's minimum principle Indirect optimization methods Quasi-Newton algorithm Semi-batch processes

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An effective simultaneous approach with variable time nodes for dynamic optimization problems

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ENGINEERING optimization 2017年第10期49卷 1761-1776页

作者： Xiao, Long Ying, Jiong Liu, Xinggao Ma, Liang Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou Zhejiang Peoples R China

An effective simultaneous approach with variable time nodes is proposed to solve the dynamic optimization problems with multiple control components, where the variable time nodes for each control component are considered as parameters directly and the interval between the neighbouring variable nodes is further refined uniformly to ensure accuracy. Consequently, the method does not treat all the nodes as parameters to ensure efficiency. The gradient formulae and the sensitivities of the states with respect to the controls and the variable time nodes are further derived to solve the nonlinear programming problem transformed from the original dynamic optimization problem. The complete framework and detailed steps of the proposed method are also given. Two classic constrained dynamic optimization problems have been tested as an illustration, and detailed comparisons of the reported literature methods are carried out. The research results show the characteristics and the effectiveness of the proposed approach.

关键词： constrained dynamic optimization control and state parameterization nonlinear programming problem simultaneous approach

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Online and hard constrained adaptive dynamic programming algorithm for energy storage control in smart buildings

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OPTIMAL CONTROL APPLICATIONS & METHODS 2023年第3期44卷 1074-1091页

作者： Chen, Zitao Chen, Si-zhe Zhang, Yun Deng, Quanbin Zeng, Xianxian Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China

The high computational complexity caused by static optimization is the key factor to hinder the development of energy management systems. Adaptive dynamic programming (ADP) is an effective dynamic optimization method to break through the bottleneck. However, the hard constraints of energy system have not been fully considered due to the non-convexity and nonlinearity of the value function, which makes the theoretical analysis complicated and brings safe security problems in battery systems. In this article, a systematic online ADP control framework is proposed for smart buildings control to ensure hard constraints to be satisfied. The second-order local expansion at the current state is used to replace the nonlinear value function to simplify the theoretical analysis with the error of the reminder term. Based on the local property of value function, a method for the determination of adaptive parameters is first designed. It is proven that the solution of adaptive parameters not only prevents over-charged and over-discharged of the battery but also limits the charging and discharging power of the battery to be less than the rated power. In addition, long-short term memory (LSTM) neural networks, a type dynamic network with memory characteristics, are used for the implementation of the present algorithm instead of the static networks to help realize the algorithm online. Due to the hidden state of LSTM, the performance of the online algorithm is improved after running the energy system. Numerical results verify the effectiveness of the proposed online control algorithm.

关键词： adaptive dynamic programming constrained dynamic optimization energy storage control online algorithm smart buildings

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Control vector parameterization approach in optimization of alternating aerobic-anoxic systems

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OPTIMAL CONTROL APPLICATIONS & METHODS 2009年第6期30卷 573-584页

作者： Balku, Saziye Yuceer, Mehmet Berber, Ridvan Inonu Univ Dept Chem Engn TR-44280 Malatya Turkey Atilim Univ Ind Liaison Off TR-06836 Ankara Turkey Ankara Univ Fac Engn Dept Chem Engn TR-06100 Ankara Turkey

Determination of the optimal aeration profile for an activated sludge system in which nitrification and denitrification take place sequentially in a single reactor (alternating aerobic-anoxic) is an attractive optimization problem because of complexities involved in, and high computational times required for solution. The rigorous dynamic modeling and start-up simulation of such a system, together with aeration profile optimization by an evolutionary algorithm (EA), were tackled in a previous study. In this paper an easy-to-implement dynamic optimization technique based on sequential quadratic programming method and control vector parameterization approach is provided. In comparison with EA, the proposed algorithm gives better results in shorter computation times. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： wastewater treatment constrained dynamic optimization SQP alternating aerobic-anoxic systems ASM3

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A predicted optimal performance of the Yurchenko layout vault in women's artistic gymnastics

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JOURNAL OF APPLIED BIOMECHANICS 2003年第3期19卷 187-204页

作者： Koh, M Jennings, L Elliott, B Lloyd, D Univ Western Australia Dept Human Movement & Exercise Sci Nedlands WA 6009 Australia Univ Western Australia Ctr Appl Dyanm & Optismisat Dept Math & Stat Nedlands WA 6009 Australia Nanyang Technol Univ Natl Inst Educ Phys Educ & Sports Sci Acad Grp Singapore Singapore

The Yurchenko layout vault is the base vault from which more advanced forms of the Yurchenko family of vaults have evolved. The purpose of the study was to predict an individual's optimal Yurchenko layout vault by modifying selected critical mechanical variables. The gymnast's current performance characteristics were determined using the Peak-Motus video analysis system. Body segment parameters were determined using the elliptical zone mathematical modeling technique of Jensen (1978). A 5-segment computer simulation model was personalized for the gymnast comprising the hands, upper limbs, upper trunk, lower trunk, and lower limbs. Symmetry was assumed, as the motion was planar in nature. An objective function was identified which translated the subjective points-evaluation scheme of the Federation of International Gymnastics (FIG) Code of Points to an analytic expression that was mathematically tractable. The objective function was composed of performance variables that, if maximized, would result in minimal points being deducted and bonus points being allocated. A combined optimal control and optimal parameter selection approach was applied to the model to determine an optimum technique. The predicted optimal vault displayed greater postflight amplitude and angular momentum when compared with the gymnast's best trial performance. Increased angular velocity, and consequently greater angular momentum at impact and greater shoulder flexion angle at impact with the horse, were related with this optimum technique. The impact phase therefore serves to increase the angular momentum during horse contact. Since the optimized parameters at impact with the horse were within the accepted physical capacity limits observed for the individual, the predicted vault is viable.

关键词： constrained dynamic optimization biomechanics optimal control

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Decentralized dynamic optimization for Power Network Voltage Control

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2017年第3期3卷 568-579页

作者： Liu, Hao Jan Shi, Wei Zhu, Hao Univ Illinois Dept Elect & Comp Engn 1406 W Green St Urbana IL 61801 USA Boston Univ Dept Elect & Comp Engn Boston MA 02215 USA

Voltage control in power distribution networks has been greatly challenged by the increasing penetration of volatile and intermittent devices. These devices can also provide limited reactive power resources that can be used to regulate the network-wide voltage. A decentralized voltage control strategy can be designed by minimizing a quadratic voltage mismatch error objective using gradient-projection (GP) updates. Coupled with the power network flow, the local voltage can provide the instantaneous gradient information. This paper aims to analyze the performance of this decentralized GP-based voltage control design under two dynamic scenarios: First, the nodes perform the decentralized update in an asynchronous fashion. Second, the network operating condition is time varying. For the asynchronous voltage control, we improve the existing convergence condition by recognizing that the voltage-based gradient is always up-to-date. By modeling the network dynamics using an autoregressive process and considering time-varying resource constraints, we provide an error bound in tracking the instantaneous optimal solution to the quadratic error objective. This result can be extended to more general constrained dynamic optimization problems with smooth strongly convex objective functions under stochastic processes that have bounded iterative changes. Extensive numerical tests have been performed to demonstrate and validate our analytical results for realistic power networks.

关键词： constrained dynamic optimization decentralized control droop control reactive power support voltage regulation

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Alternative sustainability criteria, externalities, and welfare in a simple agroecosystem model: A numerical analysis

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ENVIRONMENTAL & RESOURCE ECONOMICS 2008年第3期40卷 383-399页

作者： Bond, Craig A. Farzin, Y. Hossein Colorado State Univ Dept Agr & Resource Econ Ft Collins CO 80523 USA Univ Calif Davis Dept Agr & Resource Econ Davis CA 95616 USA

Using the numerical technique of value iteration, this paper imposes several sustainability constraints on a simple multi-sector agroecosystem model, and provides analysis of the costs tradeoffs of the product and externality is insufficient for intergenerationally equitable welfare paths, while sustaining a physical resource over time in the interests of equitability can result in a less equitable distribution of welfare across generations. Furthermore, a value sustainability constraint imposed on the social welfare maximization problem acts as a welfare transfer mechanism from the productive sector to the sector affected by the externality, but implies growth in profits for the productive sector and declining utility for the non-productive sector.

关键词： Chebychev polynomial constrained dynamic optimization intergenerational equity social welfare stock externality sustainability criteria

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Nonlinear model predictive control of a pusher-type slab reheating furnace based on a continuous-time state-space model.

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ELEKTROTECHNIK UND INFORMATIONSTECHNIK 2012年第1期129卷 3-10页

作者： Steinboeck, A. Kugi, A. TU Wien Inst Automatisierungs & Regelungstech Vienna Austria TU Wien Komplexe Dynam Syst Vienna Austria

A nonlinear model predictive controller is developed as part of a cascade temperature control system for a continuous furnace that reheats steel slabs. Using a continuous-time state-space model based on first principles, a constrained dynamic optimization problem is formulated. It is converted into an unconstrained optimization problem by means of an input transformation and additional penalty terms in the cost functional. With the help of the quasi-Newton method, the optimization problem is recurrently solved for finite time horizons. The measured furnace temperatures as well as the slab temperatures, which are estimated by an extended Kalman filter, are used as feedback. Results from the application of the control system in a slab furnace of a rolling mill demonstrate the high accuracy of the slab reheating process and significant energy savings.

关键词： nonlinear model predictive control switched nonlinear system constrained dynamic optimization slab reheating furnace

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