A dynamic programming method is presented for solving constrained, discrete-time, optimal control problems. The method is based on an efficient algorithm for solving the subproblems of sequential quadratic programming...
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A dynamic programming method is presented for solving constrained, discrete-time, optimal control problems. The method is based on an efficient algorithm for solving the subproblems of sequential quadratic programming. By using an interior-point method to accommodate inequality constraints, a modification of an existing algorithm for equality constrained problems can be used iteratively to solve the subproblems. Two test problems and two application problems are presented. The application examples include a rest-to-rest maneuver of a flexible structure and a constrained brachistochrone problem.
A procedure for calculating the analytical derivatives required to optimize long duration constant specific impulse finite burns and multiple gravity assist trajectories is presented. The analytical derivatives are ca...
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A procedure for calculating the analytical derivatives required to optimize long duration constant specific impulse finite burns and multiple gravity assist trajectories is presented. The analytical derivatives are calculated using the state transition matrix associated with the complete set of the Euler-Lagrange equations of the optimal control problem on each trajectory segment. Another transition matrix maps perturbations across any discontinuities in the state due to a zero sphere of influence patched conic flyby or discontinuities in the equations of motion that occur when the engine turns on or off. As applications, the method is used to find optimal Earth to Saturn trajectories. The state transition matrix derivatives are shown to find optimal trajectories from sets of initial conditions where finite difference derivatives fail to converge..
PurposeThis paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non...
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PurposeThis paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon. Design/methodology/approachA general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models. FindingsResults show that both approaches are relevant for solving the energy management problem of the building MG. Originality/valueIntroduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. Linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.
In this paper, an efficient procedure based on the neural networks methodology is presented for the solution of the fuel ignition model in one dimension. The neural networks were optimised with the particle swarm opti...
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In this paper, an efficient procedure based on the neural networks methodology is presented for the solution of the fuel ignition model in one dimension. The neural networks were optimised with the particle swarm optimisation algorithm hybridised with sequential quadratic programming. The accuracy and convergence of the scheme are analysed by Monte Carlo simulations and their statistical analyses for three test cases of the problem represented by Bratu-type equations. It was found that the hybrid approach converges in all cases, and can solve the problem with higher accuracy and reliability than most of the methodologies used so far to solve this problem.
作者：
Celi, RUniv Maryland
Alfred Gessow Rotorcraft Ctr Dept Aerosp Engn College Pk MD 20742 USA
An inverse simulation methodology based on numerical optimization is presented. The methodology is applied to a simplified version of the slalom maneuver in the ADS-33D helicopter handling qualities specification. The...
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An inverse simulation methodology based on numerical optimization is presented. The methodology is applied to a simplified version of the slalom maneuver in the ADS-33D helicopter handling qualities specification. The inverse simulation is formulated as an optimization problem with trajectory. and dynamic constraints, pilot inputs as design variables, and an objective function that depends on the specific problem being solved. A maximum speed solution is described. The results show that numerical optimization is a reliable and flexible tool for inverse simulation, both when the required trajectory is prescribed explicitly and when it is defined indirectly through geometric and dynamic constraints. When the trajectory is defined indirectly, there is not a single acceptable trajectory but rather an entire family with noticeable differences in the helicopter dynamics and in the required pilot inputs. Even when the trajectory is prescribed explicitly, multiple solutions exist. For handling qualities studies, the multiple solutions may provide an indication of tbe amount of scatter in pilot ratings to be expected for a given aircraft and a given maneuver. However, if the inverse simulation is used for simulation validation, then additional constraints may have to be placed on the solution to make it unique.
The application of dynamical systems techniques to trajectory design has demonstrated that employing invariant manifolds and resonant flybys expands the trajectory options and potentially reduces the Delta V requireme...
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The application of dynamical systems techniques to trajectory design has demonstrated that employing invariant manifolds and resonant flybys expands the trajectory options and potentially reduces the Delta V requirements. Low-cost transfer trajectories from two- and three-dimensional resonant orbits are explored in the Saturn-Titan system via Poincare mapping techniques and the application of dynamical systems theory. Natural maneuver-free transfers between resonant orbits and libration point orbits are constructed with the aid of a trajectory design tool that blends manifold arcs associated with unstable resonant orbits. Homoclinic-type resonant connections exist in two and three dimensions and are computed employing the transfer design tool. As an application of resonant transitions to preliminary mission design, the accessibility of Hyperion from orbits that are resonant with Titan is examined, and two transfer trajectories to the orbit of Hyperion are constructed by exploiting the invariant manifolds associated with unstable resonant orbits. A local optimization algorithm is employed to further decrease the cost of insertion and to illustrate the relationship between the local minimum and the invariant manifolds.
The objective of this paper is to investigate the efficiency of combinatorial optimization methods and in particular algorithms based on evolution strategies, when incorporated into shape optimization problems. Evolut...
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The objective of this paper is to investigate the efficiency of combinatorial optimization methods and in particular algorithms based on evolution strategies, when incorporated into shape optimization problems. Evolution strategy algorithms are used either on a stand-alone basis, or combined with a conventional mathematical programming technique. The numerical tests presented demonstrate the computational advantages of the proposed approach which become more pronounced in large-scale optimization problems and/or parallel computing environment.
The integrated design of a structure and its control system is treated as a multiobjective optimization problem. Structural mass and a quadratic performance index constitute the vector objective function. The closed-l...
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The integrated design of a structure and its control system is treated as a multiobjective optimization problem. Structural mass and a quadratic performance index constitute the vector objective function. The closed-loop performance index is taken as the time integral of the Hamiltonian. Constraints on natural frequencies, closed-loop damping, and actuator forces are also considered. Derivatives of the objective and constraint functions with respect to structural and control design variables are derived for a finite element beam model of the structure and constant feedback gains determined by independent modal space control. Pareto optimal designs generated for a simple beam demonstrate the benefit of solving the integrated structural and control optimization problem.
This paper presents an algorithm for the numerical solution of constrained parameter optimization problems. The solution strategy is based on a sequential quadratic programming (SQP) technique that uses the L-infinity...
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This paper presents an algorithm for the numerical solution of constrained parameter optimization problems. The solution strategy is based on a sequential quadratic programming (SQP) technique that uses the L-infinity exact penalty function. Unlike similar SQP algorithms the method proposed here solves only strictly convex quadratic programs to obtain the search directions. The global convergence properties of the algorithm are enhanced by the use of a nonmonotone line search and second-order corrections to avoid the Maratos effect. The paper also presents an ANSI C implementation of the algorithm. The effectiveness of the proposed method is demonstrated by solving numerous parameter optimization and optimal control problems that have appeared in the literature. (C) 2007 Elsevier Inc. All rights reserved.
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 freque...
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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.
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