Multivariate Interpolation in Continuous State Binary Control Stochastic Dynamic Programming with Application to Plant Pathogen Control
Author: Elizabeth Allen Eschenbach
Publisher:
Published: 1991
Total Pages: 250
ISBN-13:
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Author: Elizabeth Allen Eschenbach
Publisher:
Published: 1991
Total Pages: 250
ISBN-13:
DOWNLOAD EBOOKAuthor: Elizabeth Allen Eschenbach
Publisher:
Published: 1994
Total Pages: 148
ISBN-13:
DOWNLOAD EBOOKAuthor: Bertsekas
Publisher: Academic Press
Published: 1976-11-26
Total Pages: 415
ISBN-13: 0080956343
DOWNLOAD EBOOKDynamic Programming and Stochastic Control
Author: Xi-Ren Cao
Publisher: Springer Nature
Published: 2020-05-13
Total Pages: 376
ISBN-13: 3030418464
DOWNLOAD EBOOKThis monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.
Author: W. H. Shafer
Publisher: Springer Science & Business Media
Published: 1993
Total Pages: 368
ISBN-13: 9780306444951
DOWNLOAD EBOOKVolume 36 reports (for thesis year 1991) a total of 11,024 thesis titles from 23 Canadian and 161 US universities. The organization of the volume, as in past years, consists of thesis titles arranged by discipline, and by university within each discipline. The titles are contributed by any and all a
Author: Peter Whittle
Publisher:
Published: 1982
Total Pages: 336
ISBN-13:
DOWNLOAD EBOOKAuthor: Adrian Martell Thompson
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
Published: 2005
Total Pages: 460
ISBN-13: 9780494025994
DOWNLOAD EBOOKThe second algorithm, a policy iteration (PI) variant employing Nystrom's discretization method, allows computation of continuous stochastic ROC policies without quadrature, function approximation, interpolation, or Monte Carlo methods. Lipschitz continuity assumptions allow reformulation of the original problem into an equivalent finite state problem solvable in a Luus-Jaakola global optimization framework. This enables exponential computation reductions relative to standard PI. Simulations, involving stochastic ROC of a nonlinear reactor, exhibited a 99.9% reduction in computation with identical accuracy. Additionally, the average performance of the policy obtained was 58.2% better than the certainty equivalence policy. The first, a Monte Carlo extension of iterative dynamic programming (IDP), reduces discretization requirements by restricting the control policy to the dominant portion of the state space. A proof of strong probabilistic convergence of IDP is derived, and is shown to extend to the new stochastic IDP (SIDP) algorithm. Simulations demonstrate that SIDP can provide significant COD mitigation in DAC applications, relative to the standard SDP approach. Specifically, a 96% computation reduction, 92% storage reduction and less than 2% accuracy loss were simultaneously achieved using SIDP. Optimal control of chemical processes in the presence of stochastic model uncertainty is addressed. Contributions are made in two areas of process control interest: dual adaptive control (DAC) and robust optimal control (ROC). These are synergistic in that DAC involves sequences of stochastic ROC problems. In chemical engineering, these problems typically have continuous state and control spaces, and are subject to a curse of dimensionality (COD) within the stochastic dynamic programming (SDP) framework. The main novelty presented here is the method by which this COD is mitigated. Existing methods to mitigate the COD include state space aggregation, function approximation (FA), or exploitation of problem structure, e.g. system linearity. The first two yield problems of reduced but still large complexity. The third is problem specific and does not generalize well to non-linear, non-convex or non-Gaussian structures. Here, two new algorithms are developed that mitigate the COD without these simplifications, with only minimal restrictions imposed on problem structure.
Author: C. Russ Philbrick
Publisher:
Published: 1996
Total Pages: 381
ISBN-13: 9781423575948
DOWNLOAD EBOOKThis thesis presents new systems analysis methods that are appropriate for complex, nonlinear systems that are driven by uncertain inputs. These methods extend the ability of discrete dynamic programming (DDP) to system models that include six or more state variables and a similar number of stochastic variables. This is accomplished by interpolation and quadrature methods that have high-order accuracy and that provide significant computational savings over traditional DDP interpolation and quadrature methods. These new methods significantly improve our ability to apply DDP to large-scale systems. Using these methods, DDP can solve a variety of systems analysis problems without resorting to the simplifying assumptions required by other stochastic optimization methods. This is demonstrated in the application of DDP to problems with as many as seven state variables. Of particular interest, this thesis applied DDP to the practical problem of conjunctively managing groundwater and surface water. Moreover, the applications also demonstrate that DDP can be a powerfill planning tool, such as when evaluating a range of capacity expansion alternatives.
Author: Jakob Almerud
Publisher:
Published: 2017
Total Pages: 29
ISBN-13:
DOWNLOAD EBOOKWe propose two modifications to the method of endogenous grid points that greatly decreases the computational time for life cycle models with many exogenous state variables. First, we use simulated stochastic grids on the exogenous state variables. Second, when we interpolate to find the continuation value of the model, we split the interpolation step into two: We use nearest-neighbor interpolation over the exogenous state variables, and multilinear interpolation over the endogenous state variables. We evaluate the numerical accuracy and computational efficiency of the algorithm by solving a standard consumption/savings life-cycle model with an arbitrary number of exogenous state variables. The model with eight exogenous state variables is solved in around eight minutes on a standard desktop computer. We then use a more realistic income process estimated by Guvenen et al (2015) to demonstrate the usefulness of the algorithm. We demonstrate that the consumption dynamics differ compared to agents facing a more traditional income process.
Author: Peter Whittle
Publisher:
Published: 1982
Total Pages: 317
ISBN-13:
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