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A CONSTRAINED MIN MAX ALGORITHM FOR RIVAL MODELS OF THE SAME ECONOMIC-SYSTEM

MATHEMATICAL programming 1992年第3期53卷 279-295页

作者： RUSTEM, B IMPERIAL COLL SCI TECHNOL & MED DEPT COMPLONDON SW7 2BZENGLAND

There are well established rival theories about the economy. These have, in turn, led to the development of rival models purporting to represent the economic system. The models are large systems of discrete-time nonlinear dynamic equations. Observed data of the real system does not, in general, provide sufficient information for statistical methods to invalidate all but one of the rival models. In such a circumstance, there is uncertainty about which model to use in the formulation of policy. Prudent policy design would suggest that a model-based policy should take into account all the rival models. This is achieved as a pooling of the models. The pooling that yields the policy which is robust to model choice is formulated as a constrained min-max problem. The minimization is over the decision variables and the maximization is over the rival models. Only equality constraints are considered. A successive quadratic programming algorithm is discussed for the solution of the min-max problem. The algorithm uses a stepsize strategy based on a differentiable penalty function for the constraints. Two alternative quadratic subproblems can be used. One is a quadratic min-max and the other a quadratic programming problem. The objective function of either subproblem includes a linear term which is dependent on the penalty function. The penalty parameter is determined at every iteration, using a strategy that ensures a descent property as well as the boundedness of the penalty term. The boundedness follows since the strategy is always satisfied for finite values of the parameter which needs to be increased a finite number of times. The global and local convergence of the algorithm is established. The conditions, involving projected Hessian approximations, are discussed under which the algorithm achieves unit stepsizes and subsequently Q-superlinear convergence.

关键词： CONSTRAINED MIN MAX sequential quadratic programming PENALTY FUNCTION STEPSIZE STRATEGY RIVAL MODELS ECONOMIC SYSTEMS

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Nonlinear Optimal Control Analysis Using State-Dependent Matrix Exponential and Its Integrals

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第1期32卷 309-313页

作者： Kim, Chang-Joo Park, Soo Hyung Sung, Sang Kyung Jung, Sung-Nam Konkuk Univ Seoul 14370 South Korea

THERE exist various strategies [1,2] for reaching numerical 1 solutions to the nonlinear optimal control problem. The directmultiple-shooting (DMS) method is usually preferred for analyzing general nonlinear optimal control problems due to its convenience in handling system constraints and a large convergence radius compared with other methods. However, these advantages can be decreased in case the estimation of the related Karush-Kuhn-Tucker (KKT) system is not accurate enough to guarantee robust analyses. The related estimation errors are originated from time integration and finite difference approximation in the standard DMS method. The present work intends to propose a new method of accurately estimating the KKT system. For this purpose, the state-dependent coefficient (SDC) factorization method, which has been successfully implemented in the state-dependent Riccati equation (SDRE) technique [3-5], is used to derive a linear system structure from the nonlinear motion equation. Applying the linear system theory to the resultant SDC form of equations, the KKT system can be built without resorting to any time integration and finite difference formula to calculate of gradients and Hessian matrices, as opposed to the standard DMS method. The present paper proves that the convergence and the accuracy of the DMS method can be greatly enhanced through the applications of the new method to the rotorcraft trajectory tracking problem.

关键词： Optimal Control Nonlinear Systems State Dependent Riccati Equation Nonlinear programming sequential quadratic programming Runge Kutta Methods Rotorcrafts Finite Difference Approximation Collective Pitch Control Linear System Theory

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VARIATIONAL-PRINCIPLES FOR ASCENT SHAPES OF LARGE SCIENTIFIC BALLOONS

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AIAA JOURNAL 1995年第4期33卷 764-768页

作者： BAGINSKI, F RAMAMURTI, S George Washington University Washington D.C 20052

Current mathematical models of large scientific balloons assume an axisymmetric ascent shape, sharply contrasting what is observed in real balloons. We propose an approach to computing nonaxisymmetric shapes of balloons which is based on the inextensibility of certain balloon fibers and a set of rules that model how excess material must fold away. The energy of a balloon configuration is modeled as the sum of the gravitational potentials of the lifting gas and balloon fabric. We evolve an initial guess to a shape that minimizes this energy while satisfying certain material constraints. We refer to a shape determined in this fashion as an energy-minimizing (EM) shape. Using our approach to compute axisymmetric EM shapes, we find our results agree with those obtained by solving the standard Sigma-shape model. For nonaxisymmetric shapes, we are able to compute shapes that possess features observed in actual balloons, including internally folded material, nat wing sections, and periodic lobe-like structures surrounding the gas bubble.

关键词： Computing Mathematical Models Gas Balloon sequential quadratic programming MATLAB Wallops Flight Facility

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Heliocentric solar sail orbit transfers with locally optimal control laws

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JOURNAL OF SPACECRAFT AND ROCKETS 2007年第1期44卷 273-276页

作者： Macdonald, Malcolm McInnes, Colin R. Dachwald, Bernd Univ Glasgow Glasgow G12 8QQ Lanark Scotland Univ Strathclyde Glasgow G1 1XJ Lanark Scotland German Aerosp Ctr DLR D-51170 Cologne Germany

A previous (planetocentric) method of assessing the relative importance oforbit elements during solar sail transfers called accessibility and deficit, A~nD, blending has beenevolved, allowing rapid generation of heliocentric trajectories by blending locally optimal controllaws. An Earth-Mercury trajectory was presented to demonstrate the capability of A~nD blending whenattempting to find planet-to-planet transfer trajectories. It was found that the A~nD generatedtrajectory duration was within 1% of the sequential quadratic programming, SQP, generatedtrajectory. Thus, A~nD blending can provide a very good rapid assessment of such a mission scenario,or provide an excellent initial guess for further optimization as part of a detailed missionanalysis. The A~nD blending method has also been demonstrated for generation of sail trajectories to200 AU, where it was repeatedly shown that A~nD generated trajectories were very similar induration to the transfer time found using an evolutionary neurocontroller, which is expected to benear global optimal. Furthermore, the A~nD generated trajectories were consistently more efficientthan SQP generated trajectories. A~nD blending has been shown to be able to optimize a solar sailtrajectory using a nonideal sail force model. The A~nD blending results clearly demonstrate that anonideal sail will require a characteristic acceleration of approximately 1.5 mm · s~(-1) to reach200 AU in 25 years, assuming no optical surface degradation.

关键词： Solar Electric Propulsion Trajectory Optimization sequential quadratic programming Earth Perihelion Solar System Propulsion System Sample Return Missions Space Environment Osculating Orbit

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USE OF APPROXIMATE GRADIENTS IN TRAJECTORY OPTIMIZATION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1992年第5期15卷 1299-1301页

作者： LU, P Iowa State University Ames Iowa 50011

Approximate gradient update formulas have been derived to enhance the efficiency of the nonlinear programming approach when used to solve the optimal control problem. They are shown to be more accurate than the well known Broyden rank one update. The application in trajectory optimization for advanced launch system shows that the number of trajectory integrations is reduced by more than 40% with a slight increase in the performance index.

关键词： Trajectory Optimization Nonlinear programming Advanced Launch System Liquid Rocket Booster Lift Coefficient Aerodynamic Force Earth sequential quadratic programming Augmented Lagrangian Method Flight Path Angle

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Comet rendezvous mission design using solar electric propulsion spacecraft

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JOURNAL OF SPACECRAFT AND ROCKETS 2000年第5期37卷 698-700页

作者： Kluever, CA Univ Missouri Dept Mech & Aerosp Engn Columbia MO 65211 USA

Several maximum-payload rendezvous trajectories to the short-period comet Wilson-Harringon (WH) using solar electric propulsion (SEP) are obtained. The mission design incorporates a detailed accounting of the spacecraft system mass as well as current-term electric propulsion technology. Constraints on the ion thruster lifetime and comet rendezvous date help assess design tradeoffs between payload mass, mission complexity, and scientific return. It is shown that an SEP spacecraft with two ion thrusters can deliver a scientific payload mass of 203 kg 30 days before the comet's perihelion pass. It is suggested that a comet rendezvous mission utilizing SEP and a small launch vehicle is feasible and therefore may be a potential candidate for a Discover-class mission. (CSA)

关键词： Spacecrafts Solar Electric Propulsion Aerodynamic Characteristics Ion Engines Propellant Perihelion Turbulent Boundary Layer sequential quadratic programming Spacecraft System Earth

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Optimal earth-capture trajectories using electric propulsion

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第3期25卷 604-606页

作者： Kluever, CA Univ Missouri Dept Mech & Aerosp Engn Columbia MO 65211 USA

A new approach for computing minimum-propellant, Earthcapture electric propulsion (EP) trajectories is presented. The initial phase of the trajectory (from hyperbolic approach to capture) is numerically computed using the combined gravity fields of the Earth, sun, and moon. The solution method eliminates the computational burden of simulating the hundreds of near-circular revolutions of the inward spiral transfer to LEO by utilizing curve fits of universal low-thrust solutions. This strategy requires few optimization variables and readily yields a minimum-propellant solution. A full numerical simulation of the inward spiral transfer (with Earth-shadow effects and J2) exhibits a very good match with the curve-fit results in terms of propellant load. Furthermore, the resulting optimal thrust steering program for the capture phase exhibits a smooth profile with linear segments, which may simplify implementing an onboard guidance strategy. (CSA)

关键词： Earth Electric Propulsion Propellant Yaw Thrust to Weight Ratio Orbital Inclination sequential quadratic programming Trajectory Optimization Earth Centered Inertial Sample Return Missions

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Inverse dynamics of aircraft via reduced-order shooting methods

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第6期25卷 1158-1162页

作者： Bernelli-Zazzera, F Cappello, G Mantegazza, P Politecn Milan Dept Aerosp Engn I-20158 Milan Italy

The inverse simulation of a military trainer aircraft is treated. The inverse simulation problem requires the determination of control inputs that will make a set of specified states follow a prescribed trajectory. The method proposed here allows an arbitrary combination of very general path and dynamics constraints, and, at the same time, it optimizes a defined performance index. The method departs from the classical approach for trajectory optimization based on direct transcription. It arises from the concept of combining collocation and direct transcription and has the advantage of minimizing the number of variables and constraints involved in the numerical optimization with special regard to the equality constraints deriving from the direct transcription. This minimization of constraints and variables allowed the study of the inverse problem of the aircraft, including the dynamics of the actuators, on a personal computer, in a reasonable time, and without the need of using any specialized sparse optimization tool. It has been shown that the use of direct methods avoids both the explicit specification of, and the analytical conditions for, the Lagrange multipliers and the analytical differentiation of constraints on the path and on the state, thus making it simpler to use tabulated aeromechanics databases. (Author)

关键词： Trainer Aircraft Numerical Optimization Trajectory Optimization Mathematical Models Ailerons Numerical Integration Inverse Problems sequential quadratic programming Angle of Attack Integration Algorithm

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Autonomous Trajectory Planning with Event-Trigger Constraints Using Nonsingular Convex Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第12期47卷 2649-2660页

作者： Zhao, Zichen Shang, Haibin Liu, Jizhong Zhang, Guoxu Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Beijing Inst Technol Inst Deep Space Explorat Technol Beijing 100081 Peoples R China China Natl Space Adm Lunar Explorat & Space Program Ctr Beijing 100190 Peoples R China Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China

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THE LAGRANGE-NEWTON METHOD FOR INFINITE-DIMENSIONAL OPTIMIZATION PROBLEMS

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 1990年第3-4期11卷 201-224页

作者： ALT, W UNIV BAYREUTH INST MATHW-8580 BAYREUTHGERMANY

This paper investigates local convergence properties of the Lagrange-Newton method for optimization problems in reflexive Banach spaces. Sufficient conditions for quadratic convergence of optimal solutions and Lagrang... 详细信息

关键词： AMS subject classification. 49D05 AMS subject classification. 49D15 AMS subject classification. 65K05 Lagrange-Newton method sequential quadratic programming infinite-dimensional optimization

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