Author: Jarrell R. Elliott
Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 52
Book Description
A Method for Reducing the Sensitivity of Optimal Nonlinear Systems to Parameter Uncertainty
Computational Optimal Control of Nonlinear Systems with Parameter Uncertainty
Author:
Publisher:
ISBN: 9781321540970
Category :
Languages : en
Pages : 140
Book Description
A number of emerging applications in the field of optimal control theory require the computation of an open-loop control for a dynamical system with uncertain parameters. In this dissertation we examine a class of uncertain optimal control problems, in which the goal is to minimize the expectation of a predetermined cost functional subject to such an uncertain system. We provide a computational framework for this class of problems based on a discretization of the parameter space. In this approach, a set of nodes from the parameter space and corresponding weights are selected, and the expectation of the cost functional is approximated by a finite sum. This process results in a sequence of standard optimal control problems which can be solved using existing techniques. However, it is well-known that an inappropriately designed discretization scheme for an optimal control problem may fail to converge to the optimal solution, therefore further analysis must be performed to examine the convergence properties of the scheme. We provide this analysis for a scheme based on quadrature methods for the approximation of the expectation in the cost functional. This analysis demonstrates that an accumulation point of a sequence of optimal solutions to the approximate problem is an optimal solution of the original problem. Furthermore, we examine the convergence of the adjoint states for the approximation based on the quadrature scheme, which leads to a Pontryagin-like necessary condition which must be satisfied by these accumulation points. To address the exponential growth of computational cost with respect to the dimension of the parameters, we introduce a numerical algorithm based on sample average approximations, in which an independently drawn random sample is taken from the parameter space, and the expectation in the objective functional is approximated by the sample mean. Using a generalization of the strong law of large numbers, we analyze the convergence properties of this approximation. In addition, we develop an optimality function for the class of uncertain optimal control problems based on the L2-Frechet derivative of the objective functional, which provides a necessary condition for an optimal solution. By demonstrating that an accumulation point of a sequence of stationary points for the approximate problem is a stationary point of the original problem, we demonstrate the approximation scheme based on sample averages is consistent in the sense of Polak. These numerical algorithms for the uncertain optimal control problem are applied to real-world scenarios from the fields of optimal search theory and ensemble control.
Publisher:
ISBN: 9781321540970
Category :
Languages : en
Pages : 140
Book Description
A number of emerging applications in the field of optimal control theory require the computation of an open-loop control for a dynamical system with uncertain parameters. In this dissertation we examine a class of uncertain optimal control problems, in which the goal is to minimize the expectation of a predetermined cost functional subject to such an uncertain system. We provide a computational framework for this class of problems based on a discretization of the parameter space. In this approach, a set of nodes from the parameter space and corresponding weights are selected, and the expectation of the cost functional is approximated by a finite sum. This process results in a sequence of standard optimal control problems which can be solved using existing techniques. However, it is well-known that an inappropriately designed discretization scheme for an optimal control problem may fail to converge to the optimal solution, therefore further analysis must be performed to examine the convergence properties of the scheme. We provide this analysis for a scheme based on quadrature methods for the approximation of the expectation in the cost functional. This analysis demonstrates that an accumulation point of a sequence of optimal solutions to the approximate problem is an optimal solution of the original problem. Furthermore, we examine the convergence of the adjoint states for the approximation based on the quadrature scheme, which leads to a Pontryagin-like necessary condition which must be satisfied by these accumulation points. To address the exponential growth of computational cost with respect to the dimension of the parameters, we introduce a numerical algorithm based on sample average approximations, in which an independently drawn random sample is taken from the parameter space, and the expectation in the objective functional is approximated by the sample mean. Using a generalization of the strong law of large numbers, we analyze the convergence properties of this approximation. In addition, we develop an optimality function for the class of uncertain optimal control problems based on the L2-Frechet derivative of the objective functional, which provides a necessary condition for an optimal solution. By demonstrating that an accumulation point of a sequence of stationary points for the approximate problem is a stationary point of the original problem, we demonstrate the approximation scheme based on sample averages is consistent in the sense of Polak. These numerical algorithms for the uncertain optimal control problem are applied to real-world scenarios from the fields of optimal search theory and ensemble control.
NASA Technical Note
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 684
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 684
Book Description
Scientific and Technical Aerospace Reports
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1460
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1460
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Monthly Catalog of United States Government Publications, Cumulative Index
Author: United States. Superintendent of Documents
Publisher:
ISBN:
Category : United States
Languages : en
Pages : 1408
Book Description
Publisher:
ISBN:
Category : United States
Languages : en
Pages : 1408
Book Description
NASA Technical Paper
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 50
Book Description
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 50
Book Description
Monthly Catalog of United States Government Publications
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1388
Book Description
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1388
Book Description
Monthly Catalogue, United States Public Documents
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 794
Book Description
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 794
Book Description
NASA Contractor Report
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 352
Book Description
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 352
Book Description
Applied Mechanics Reviews
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 636
Book Description
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 636
Book Description