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Backstepping Control Design with Actuator Torque Bound for Spacecraft Attitude Maneuver

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第1期33卷 254-259页

作者： Ali, Imran Radice, Gianmarco Kim, Jongrae Univ Glasgow Dept Aerosp Engn Glasgow G12 8QQ Lanark Scotland

A nonlinear backstepping attitude controller using the inverse tangent-based tracking function and a family of augmented Lyapunov functions is proposed. The bound is effectively used to tune the control parameters so that, for the given settling time specification, the upper bound of the control input is minimized. The spacecraft is assumed to be a rigid body and three mutually perpendicular axes fixed in the spacecraft define a body frame B with origin at the center of mass of the spacecraft. The spacecraft is assumed to be equipped with the actuators that can provide torques about the axes of the body frame B. The bounds for the control torque components are derived analytically as a function of the initial tracking error and the gains involved in the control design procedure. The proposed controller has been shown to perform adequately in the numerical simulations.

关键词： Proportional Integral Derivative Control Spacecraft Attitude Actuator Torque Quaternions Numerical Simulation sequential quadratic programming Attitude Stabilization Attitude Tracking Variable Structure Control Euler Angles

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The elucidation of metabolic pathways and their improvements using stable optimization of large-scale kinetic models of cellular systems

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METABOLIC ENGINEERING 2010年第1期12卷 26-38页

作者： Nikolaev, Evgeni V. Thomas Jefferson Univ Daniel Baugh Inst Funct Genom & Computat Biol Dept Pathol Anat & Cell Biol Philadelphia PA 19107 USA

Metabolic engineering of cellular systems to maximize reaction fluxes or metabolite concentrations still presents a significant challenge by encountering unpredictable instabilities that can be caused by simultaneous or consecutive enhancements of many reaction steps. It can therefore be important to select carefully small subsets of key enzymes for their subsequent stable modi. cation compatible with cell physiology. To address this important problem, we introduce a general mixed integer non-linear problem (MINLP) formulation to compute automatically which enzyme levels should be modulated and which enzyme regulatory structures should be altered to achieve the given optimization goal using non-linear kinetic models of relevant cellular systems. The developed MINLP formulation directly employs a stability analysis constraint and also includes non-linear biophysical constraints to describe homeostasis conditions for metabolite concentrations and protein machinery without any preliminary model simplification (e.g. linlog kinetics approximation). The framework is demonstrated on a well-established large-scale kinetic model of the Escherichia coli central metabolism used fort he optimization of the glucose uptake through the phosphotransferase transport system (PTS) and serine biosynthesis. Computational results show that substantial stable improvements can be predicted by manipulating only small subsets of enzyme levels and regulatory structures. This means that while more efforts can be required to elucidate larger stable optimal enzyme level/regulation choices, no further significant increase in the optimized fluxes can be obtained and, therefore, such choices may not be worth the effort due to the potential loss of stability properties. The source for instability through saddle-node and Hopf bifurcations is identified, and all results are contrasted with predictions from metabolic control analysis. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Mixed integer non-linear problem (MINLP) Simulated annealing sequential quadratic programming Biochemical engineering of cellular systems Kinetic models

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Reliability-Based Design Optimization of Nonlinear Aeroelasticity Problems

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JOURNAL OF AIRCRAFT 2010年第3期47卷 992-998页

作者： Missoum, Samy Dribusch, Christoph Beran, Philip Univ Arizona Tucson AZ 85721 USA USAF Res Lab Design & Anal Methods Branch Wright Patterson AFB OH 45433 USA

This paper introduces a methodology for the reliability-based design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently evaluate probabilities of failure and solve the reliability-based design optimization problem. Another major advantage of the approach is that it efficiently manages the discontinuities that might appear during subcritical limit cycle oscillations. The proposed approach is applied to the construction of flutter and subcritical limit cycle oscillation boundaries for a two-degree-of-freedom airfoil with nonlinear stiffnesses. The solution of a reliability-based design optimization problem with a constraint on the probability of subcritical limit cycle oscillation is also provided.

关键词： Nonlinear Aeroelasticity Airfoil Support Vector Machine Angle of Attack sequential quadratic programming Finite Element Modeling Structural Nonlinearities Cumulative Distribution Function Radius of Gyration High Aspect Ratio

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Optimized Switching Scheme of a Cascade Multi-level Inverter

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2010年第4期38卷 445-464页

作者： Kumar, Jagdish Das, Biswarup Agarwal, Pramod Indian Inst Technol Dept Elect Engn Roorkee 247667 Uttar Pradesh India

In this article, an optimization procedure for calculating the switching angles of a cascade multi-level inverter is presented. Specifically, the objective is to calculate the switching angles for a fundamental frequency switching scheme such that the individual harmonic components, as well as the total harmonic distortion in the inverter output voltage, satisfy the limit set by various standards. The feasibility of the proposed methodology has been validated through computational, simulation, and experimental studies on an 11-level cascade multi-level inverter, where close agreement among the results obtained by these three studies (computational, simulation, and experimental) have been observed.

关键词： cascade multi-level inverter total harmonic distortion sequential quadratic programming

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A novel PID controller tuning method based on optimization technique

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Journal of Central South University 2010年第5期17卷 1036-1042页

作者：梁昔明李山春 HASSAN A B School of Information Science and Engineering Central South University

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was ***/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM *** task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control *** assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) *** results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

关键词： PID controller optimization infeasible interior point method sequential quadratic programming simulation

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An adjoint-based SQP algorithm with quasi-Newton Jacobian updates for inequality constrained optimization

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OPTIMIZATION METHODS & SOFTWARE 2010年第4期25卷 531-552页

作者： Diehl, Moritz Walther, Andrea Bock, Hans Georg Kostina, Ekaterina Univ Paderborn Inst Math Paderborn Germany Katholieke Univ Leuven OPTEC&ESAT SCD Leuven Belgium Heidelberg Univ Interdisciplinary Ctr Sci Comp Heidelberg Germany Univ Marburg Dept Math & Comp Sci Marburg Germany

We present a sequential quadratic programming (SQP) type algorithm, based on quasi-Newton approximations of Hessian and Jacobian matrices, which is suitable for the solution of general nonlinear programming problems involving equality and inequality constraints. In contrast to most existing SQP methods, no evaluation of the exact constraint Jacobian matrix needs to be performed. Instead, in each SQP iteration only one evaluation of the constraint residuals and two evaluations of the gradient of the Lagrangian function are necessary, the latter of which can efficiently be performed by the reverse mode of automatic differentiation. Factorizations of the Hessian and of the constraint Jacobian are approximated by the recently proposed STR1 update procedure. Inequality constraints are treated by solving within each SQP iteration a quadratic program (QP), the dimension of which equals the number of degrees of freedom. A recently proposed gradient modification in these QPs takes account of Jacobian inexactness in the active set determination. Superlinear convergence of the procedure is shown under mild conditions. The convergence behaviour of the algorithm is analysed using several problems from the Hock-Schittkowski test library. Furthermore, we present numerical results for an optimization problem based on a small periodic adsorption process, where the Jacobian of the equality constraints is dense.

关键词： automatic differentiation inequality constraints sequential quadratic programming inexact newton methods nonlinear optimization quasi-newton updates

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A SECOND DERIVATIVE SQP METHOD: LOCAL CONVERGENCE AND PRACTICAL ISSUES

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SIAM JOURNAL ON OPTIMIZATION 2010年第4期20卷 2049-2079页

作者： Gould, Nicholas I. M. Robinson, Daniel P. Rutherford Appleton Lab Numer Anal Grp Didcot OX11 0QX Oxon England Univ Oxford Inst Math Oxford OX1 3LB England

Gould and Robinson [SIAM J. Optim., 20 (2010), pp. 2023-2048] proved global convergence of a second derivative SQP method for minimizing the exact l(1)-merit function for a fixed value of the penalty parameter. This result required the properties of a so-called Cauchy step, which was itself computed from a so-called predictor step. In addition, they allowed for the additional computation of a variety of (optional) accelerator steps that were intended to improve the efficiency of the algorithm. The main purpose of this paper is to prove that a nonmonotone variant of the algorithm is quadratically convergent for two specific realizations of the accelerator step;this is verified with preliminary numerical results on the Hock and Schittkowski test set. Once fast local convergence is established, we consider two specific aspects of the algorithm that are important for an efficient implementation. First, we discuss a strategy for defining the positive-definite matrix B(k) used in computing the predictor step that is based on a limited-memory BFGS update. Second, we provide a simple strategy for updating the penalty parameter based on approximately minimizing the l(1)-penalty function over a sequence of increasing values of the penalty parameter.

关键词： nonlinear programming nonlinear inequality constraints sequential quadratic programming l(1)-penalty function nonsmooth optimization

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Covariance matrix adapted evolution strategy-based decentralised congestion management for multilateral transactions

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IET GENERATION TRANSMISSION & DISTRIBUTION 2010年第3期4卷 400-417页

作者： Visalakshi, S. Baskar, S. St Josephs Coll Engn Dept EEE Madras 600119 Tamil Nadu India Thiagarajar Coll Engn CAREC Madurai 625015 Tamil Nadu India

This study proposes AC load flow-based decentralised model for congestion management in the forward markets using resource allocation technique. In this model, each transaction maximises its profit under the limits of transmission line capacities allocated by independent system operator. The voltage and reactive power impact of the system are also incorporated in the model. A covariance matrix adapted evolution strategy (CMAES) algorithm is used to solve decentralised congestion management problem for multilateral transactions. The proposed approach is tested on IEEE 30 bus, IEEE 118 bus and practical Indian utility 62 bus systems for three, six and two multilateral transactions, respectively, with smooth and non-smooth cost functions. The results obtained for decentralised model using CMAES algorithm is compared with particle swarm optimisation (PSO) algorithm and sequential quadratic programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare for 20 independent trials are given. To prove the validity of the proposed improved decentralised model, the results obtained are also compared with centralised model. Simulation results clearly demonstrate the better performance of CMAES algorithm over PSO and SQP.

关键词： particle swarm optimisation statistical analysis Power transmission, distribution and supply covariance matrix transmission line capacities Power system management, operation and economics SQP Optimisation techniques multilateral transactions power markets sequential quadratic programming resource allocation technique voltage-reactive power covariance matrices AC load flow-based decentralised model IEEE 30 bus Algebra quadratic programming evolution strategy-based decentralised congestion management reactive power evolutionary computation covariance matrix adapted evolution strategy load flow PSO power transmission lines IEEE 118 bus Other topics in statistics

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SHARP PRIMAL SUPERLINEAR CONVERGENCE RESULTS FOR SOME NEWTONIAN METHODS FOR CONSTRAINED OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2010年第6期20卷 3312-3334页

作者： Fernandez, D. Izmailov, A. F. Solodov, M. V. Univ Nacl Cordoba FAMAF RA-5000 Cordoba Argentina Moscow MV Lomonosov State Univ VMK Fac OR Dept Moscow 119991 Russia Inst Matematica Pura & Aplicada BR-22460320 Rio De Janeiro Brazil

As is well known, Q-superlinear or Q-quadratic convergence of the primal-dual sequence generated by an optimization algorithm does not, in general, imply Q-superlinear convergence of the primal part. Primal convergence, however, is often of particular interest. For the sequential quadratic programming (SQP) algorithm, local primal-dual quadratic convergence can be established under the assumptions of uniqueness of the Lagrange multiplier associated to the solution and the second-order sufficient condition. At the same time, previous primal Q-superlinear convergence results for SQP required strengthening of the first assumption to the linear independence constraint qualification. In this paper, we show that this strengthening of assumptions is actually not necessary. Specifically, we show that once primal-dual convergence is assumed or already established, for primal superlinear rate one needs only a certain error bound estimate. This error bound holds, for example, under the second-order sufficient condition, which is needed for primal-dual local analysis in any case. Moreover, in some situations even second-order sufficiency can be relaxed to the weaker assumption that the multiplier in question is noncritical. Our study is performed for a rather general perturbed SQP framework which covers, in addition to SQP and quasi-Newton SQP, some other algorithms as well. For example, as a byproduct, we obtain primal Q-superlinear convergence results for the linearly constrained (augmented) Lagrangian methods for which no primal Q-superlinear rate of convergence results were previously available. Another application of the general framework is sequential quadratically constrained quadratic programming methods. Finally, we discuss some difficulties with proving primal superlinear convergence for the stabilized version of SQP.

关键词： Newton methods sequential quadratic programming linearly constrained Lagrangian methods superlinear convergence critical multipliers

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An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

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EVOLUTIONARY COMPUTATION 2010年第3期18卷 403-449页

作者： Deb, Kalyanmoy Sinha, Ankur Indian Inst Technol Kanpur Dept Mech Engn Kanpur 208016 Uttar Pradesh India Aalto Univ Sch Econ Dept Business Technol Helsinki 00076 Finland

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

关键词： Bilevel optimization evolutionary multi-objective optimization NSGA-II test problem development problem difficulties hybrid evolutionary algorithms self-adaptive algorithm sequential quadratic programming

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