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AN SQP TRUST REGION METHOD FOR SOLVING THE DISCRETE-TIME LINEAR quadratic CONTROL PROBLEM

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE 2012年第2期22卷 353-363页

作者： Mostafa, El-Sayed M. E. Alexandria Univ Moharam Bey Fac Sci Dept Math Alexandria 21511 Egypt

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution to initiate the proposed SQP trust region method. To demonstrate the effectiveness of the method, some numerical results are presented in detail.

关键词： output feedback control design sequential quadratic programming trust region method

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A NEIGHBORING EXTREMAL SOLUTION FOR OPTIMAL SWITCHED IMPULSIVE CONTROL PROBLEMS WITH LARGE PERTURBATIONS

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2012年第9期8卷 6235-6257页

作者： Jiang, Canghua Teo, Kok Lay Loxton, Ryan Duan, Guang-Ren Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia

This paper presents an approach to compute the neighboring extremal solution for an optimal switched impulsive control problem with a pre-specified sequence of modes and a large perturbation in the initial state. The decision variables - the subsystem switching times and the control parameters - are subject to inequality constraints. Since the active status of these inequality constraints may change under the large perturbation, we add fractions of the initial perturbation separately such that the active status of the inequality constraints is invariant during each step, and compute the neighboring extremal solution iteratively by solving a sequence of quadratic programming problems. First, we compute a correction direction for the control in the perturbed system through an extended backward sweep technique. Then, we compute the maximal step size in this direction and derive the solution iteratively by using a revised active set strategy. An example problem involving a shrimp harvesting operation demonstrates that our solution approach is faster than the sequential quadratic programming approach.

关键词： Optimal control Neighboring extremal Impulsive control Switched system sequential quadratic programming Active set strategy

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Nonlinear Model Predictive Control of a Distillation Column Using Wavenet Based Hammerstein Model

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ENGINEERING LETTERS 2012年第4期20卷 330-335页

作者： Ramesh, K. Hisyam, A. Aziz, N. Shukor, S. R. Abd Univ Malaysia Pahang Fac Chem & Nat Resources Engn Proc Syst Engn Grp Kuantan 26300 Pahang Malaysia Univ Sains Malaysia Seri Ampangan Sch Chem Engn Engn Campus Nibong Tebal 14300 Pulau Pinang Malaysia

Distillation columns are fairly complex multivariable systems and needs to be controlled close to optimum operating conditions because of economic incentives. Nonlinear Model Predictive Control (NMPC) scheme is one of the best options to be explored for proper control of distillation columns. In the present work, a new wavenet based Hammerstein model NMPC has been developed to control distillation column. An experimentally validated equilibrium model was used as plant model in nonlinear system identification and in NMPC. Two multiple-input-single-output (MISO) wavenet based Hammerstein models are developed to model the dynamics of the distillation column. The nonlinear model parameters were estimated using iterative predictionerror minimization method. The Unscented Kalman Filter (UKF) was used to estimate the state variables in NMPC and the NLP problem was solved using sequential quadratic programming (SQP) method. The closed loop control studies have indicated that the performance of developed NMPC scheme was good in controlling the distillation column.

关键词： Distillation column Nonlinear model predictive control sequential quadratic programming Wavenet based Hammerstein model

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Optimization of Impulsive Trajectories from Circular Orbit to an Excess Velocity Vector

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第1期35卷 234-244页

作者： Jones, D. R. Ocampo, C. Univ Texas Austin Dept Aerosp Engn & Engn Mech WR Woolrich Labs Austin TX 78712 USA

Feasible transfer trajectories are constructed to serve as initial guesses for determining constrained optimal impulsive escape trajectories, from a circular orbit to a target hyperbolic excess velocity vector. The proximity of these feasible solutions to their corresponding optima are quantified. The objective of this work is to improve the feasible solutions, thereby enabling general anytime escape trajectories to be targeted that result in substantially reduced fuel expenditure. The procedure is currently restricted to one- and three-impulse escape trajectories from a circular parking orbit. Two separate three-impulse methods are presented, each specific to whether the time of flight is free or fixed. Numerical results, obtained using nonlinear programming algorithms, are presented to validate the robustness of the method. Analysis and results are nondimensional, and therefore are applicable to departures from a circular orbit about any celestial body.

关键词： Trans Earth Injection Parking Orbit Nonlinear programming Periapsis sequential quadratic programming Kepler's Equation Earth Trajectory Optimization Numerical Integration Space Exploration

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A hybrid FCASO-SQP method for solving the economic dispatch problems with valve-point effects

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ENERGY 2012年第1期38卷 346-353页

作者： Cai, Jiejin Li, Qiong Li, Lixiang Peng, Haipeng Yang, Yixian Sun Yat Sen Univ Sch Phys & Engn Guangzhou 510275 Guangdong Peoples R China Sun Yat Sen Univ Sino French Inst Nucl Engn & Technol Guangzhou 510275 Guangdong Peoples R China S China Univ Technol State Key Lab Subtrop Bldg Sci Guangzhou 510640 Guangdong Peoples R China Beijing Univ Posts & Telecommun Informat Secur Ctr Beijing 100876 Peoples R China

In this paper, a hybrid method integrating the fuzzy adaptive chaotic ant swarm optimization (FCASO) algorithm and the sequential quadratic programming (SQP) techniques, named FCASO-SQP method, is presented for solving the economic dispatch (ED) problems in power systems. The FCASO algorithm is the main optimizer in the hybrid method and the SQP technique is used to fine tune its results to improve the solution. The FCASO algorithm introduces a fuzzy system to dynamically tune the characteristic parameters psi(d) and r(i) of chaotic ant swarm optimization (CASO). The proposed method was applied to three different cases of power systems with three units, thirteen units and forty units, and the simulation results demonstrate its applicability and effectiveness to solve the ED problems with valve-point effect. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Economic dispatch Fuzzy adaptive chaotic ant swarm optimization sequential quadratic programming Evolutionary algorithm Power system

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Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2012年第1期51卷 77-123页

作者： Kulkarni, Ankur A. Shanbhag, Uday V. Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA

In this paper, we study recourse-based stochastic nonlinear programs and make two sets of contributions. The first set assumes general probability spaces and provides a deeper understanding of feasibility and recourse in stochastic nonlinear programs. A sufficient condition, for equality between the sets of feasible first-stage decisions arising from two different interpretations of almost sure feasibility, is provided. This condition is an extension to nonlinear settings of the "W-condition," first suggested by Walkup and Wets (SIAM J. Appl. Math. 15:1299-1314, 1967). Notions of complete and relatively-complete recourse for nonlinear stochastic programs are defined and simple sufficient conditions for these to hold are given. Implications of these results on the L-shaped method are discussed. Our second set of contributions lies in the construction of a scalable, superlinearly convergent method for solving this class of problems, under the setting of a finite sample-space. We present a novel hybrid algorithm that combines sequential quadratic programming (SQP) and Benders decomposition. In this framework, the resulting quadratic programming approximations while arbitrarily large, are observed to be two-period stochastic quadratic programs (QPs) and are solved through two variants of Benders decomposition. The first is based on an inexact-cut L-shaped method for stochastic quadratic programming while the second is a quadratic extension to a trust-region method suggested by Linderoth and Wright (Comput. Optim. Appl. 24:207-250, 2003). Obtaining Lagrange multiplier estimates in this framework poses a unique challenge and are shown to be cheaply obtainable through the solution of a single low-dimensional QP. Globalization of the method is achieved through a parallelizable linesearch procedure. Finally, the efficiency and scalability of the algorithm are demonstrated on a set of stochastic nonlinear programming test problems.

关键词： Stochastic programming Nonlinear programming Almost-sure feasibility Recourse W-condition sequential quadratic programming Benders' decomposition

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Placement and operation strategy of FACTS devices using optimal continuous power flow

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SCIENTIA IRANICA 2012年第6期19卷 1683-1690页

作者： Aghaei, J. Gitizadeh, M. Kaji, M. Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

In this paper, an effective method is presented to determine the security margin against voltage collapse, and improve it by means of FACTS devices in the optimal continuous power flow framework. The primary methods for determining the system's critical states of voltage collapse points are based on the convergence of the Newton-Raphson method in various iterations. Unlike these methods, in this investigation, a method based on sequential quadratic programming is proposed to overcome the divergence of the problem near the critical states, and also to incorporate operation and control constraints through optimal continuous power flow. Furthermore, two FACTS devices, the Thyristor-Controlled Series Capacitor (TCSC) and the Static VAR Compensator (SVC), are mathematically represented and employed in the optimization process to improve the security margin. The proposed method is implemented on a practical power network to investigate the efficacy of the method. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.

关键词： Voltage collapse sequential quadratic programming FACTS devices Voltage security margin Optimal continuous power flow

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Microgrid management with a quick response optimization algorithm for active power dispatch

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2012年第1期43卷 465-473页

作者： Alvarez, Eduardo Campos, Antonio M. Arboleya, Pablo Gutierrez, Antonio J. Fdn CTIC Gijon 33203 Asturias Spain Univ Oviedo Dept Elect Gijon 33203 Asturias Spain Univ Oviedo Dept Energy Oviedo 33004 Asturias Spain

A fast response algorithm has been developed for active-power dispatch to microsources in a distributed generation microgrid. It is capable of adjusting microgrid generation to demand on-line in grid-connected-mode. The algorithm performs an optimization of fuel consumption and emissions costs functions, of microsources using a heuristic approach. It and has been tested to solve different power dispatch cost optimization problems. The tests realized show a maximum execution time of about 1 ms, which is several orders of magnitude faster than the results obtained with other state-of-the-art optimization methods currently employed in these applications. It has also shown better performance in terms of global cost and microsources stability. The fast response implies a substantial reduction of the computational resources needed, allowing the use of a low-cost programmable logic controller or microcontroller for microsources active power dispatching. Thus, the infrastructure requirements and new investments are reduced and the penetration of microgrids based on renewable energies is improved. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Microgrids Microsource Distributed generation Power dispatch Cost function sequential quadratic programming

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Trajectory Design Combining Invariant Manifolds with Discrete Mechanics and Optimal Control

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第5期35卷 1507-1525页

作者： Moore, Ashley Ober-Bloebaum, Sina Marsden, Jerrold E. CALTECH Pasadena CA 91125 USA Univ Paderborn D-33098 Paderborn Germany

A mission design technique that combines invariant manifold techniques, discrete mechanics, and optimal control produces locally optimal low-energy trajectories. Previously, invariant manifolds of the planar circular restricted three-body problem have been used to design trajectories with relatively small midcourse change in velocity Delta V . A different method of using invariant manifolds is explored to design trajectories directly in the four-body problem. Then, using the local optimal control method DMOC (Discrete Mechanics and Optimal Control), it is possible to reduce the midcourse Delta V to zero. The influence of different boundary conditions on the optimal trajectory is also demonstrated. These methods are tested on a trajectory that begins in Earth orbit and ends in ballistic capture at the moon. Impulsive DMOC trajectories require up to 19% less Delta V than trajectories using a Hohmann transfer. When applied to low-thrust trajectories, DMOC produces an improvement of up to 59% in the mass fraction and 22% in travel time when compared with results from shooting methods.

关键词： Bang Bang Control Earth Moon Elliptical Orbit Low Energy Trajectory Earth Centered Inertial Lagrange Points Periapsis sequential quadratic programming Lagrange D'Alembert Principle

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Automated Mission Planning via Evolutionary Algorithms

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第6期35卷 1878-1887页

作者： Englander, Jacob A. Conway, Bruce A. Williams, Trevor Univ Illinois Dept Aerosp Engn Urbana IL 61801 USA NASA Goddard Space Flight Ctr Nav & Mission Design Branch Greenbelt MD 20770 USA

Many space mission planning problems may be formulated as hybrid optimal control problems, that is, problems that include both real-valued variables and categorical variables. In orbital mechanics problems, the categorical variables will typically specify the sequence of events that qualitatively describe the trajectory or mission, and the real-valued variables will represent the launch date, flight times between planets, magnitudes and directions of rocket burns, flyby altitudes, etc. A current practice is to preprune the categorical state space to limit the number of possible missions to a number whose cost may reasonably be evaluated. Of course, this risks pruning away the optimal solution. The method to be developed here avoids the need for prepruning by incorporating a new solution approach. The new approach uses nested loops: an outer-loop problem solver that handles the finite dynamics and finds a solution sequence in terms of the categorical variables, and an inner-loop problem solver that finds the optimal trajectory for a given sequence A binary genetic algorithm is used to solve the outer-loop problem, and a cooperative algorithm based on particle swarm optimization and differential evolution is used to solve the inner-loop problem. The hybrid optimal control solver is successfully demonstrated here by reproducing the Galileo and Cassini missions.

关键词： Particle Swarm Optimization Gas Giant Interplanetary Mission Genetic Algorithm Gravity Assist Maneuver Rockets Trajectory Optimization Deep Space Maneuver Interplanetary Trajectories sequential quadratic programming

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