2,078 research outputs found
Control of singularly perturbed hybrid stochastic systems
In this paper, we study a class of optimal stochastic
control problems involving two different time scales. The fast
mode of the system is represented by deterministic state equations
whereas the slow mode of the system corresponds to a jump disturbance
process. Under a fundamental “ergodicity” property for
a class of “infinitesimal control systems” associated with the fast
mode, we show that there exists a limit problem which provides
a good approximation to the optimal control of the perturbed
system. Both the finite- and infinite-discounted horizon cases are
considered. We show how an approximate optimal control law
can be constructed from the solution of the limit control problem.
In the particular case where the infinitesimal control systems
possess the so-called turnpike property, i.e., are characterized by
the existence of global attractors, the limit control problem can be
given an interpretation related to a decomposition approach
A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control
We present a numerical method for finite-horizon stochastic optimal control models. We derive a stochastic minimum principle (SMP) and then develop a numerical method based on the direct solution of the SMP. The method combines Monte Carlo pathwise simulation and non-parametric interpolation methods. We present results from a standard linear quadratic control model, and a realistic case study that captures the stochastic dynamics of intermittent power generation in the context of optimal economic dispatch models.National Science Foundation (U.S.) (Grant 1128147)United States. Dept. of Energy. Office of Science (Biological and Environmental Research Program Grant DE-SC0005171)United States. Dept. of Energy. Office of Science (Biological and Environmental Research Program Grant DE-SC0003906
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Optimisation of systems with storage with application to to time-varying electricity tariffs
Systems with storage allow the production and use of a commodity to be separated in time
to reduce costs or to make better use of available capacity. Hydro-reservoirs play a central
role in many electricity systems. On the demand side there is a much greater variety of
storage plant; buffer storages in manufacturing, ice storage systems and compressed air
systems. Battery storage can also be used in remote area power supply systems (RAPS).
Determining an effective and efficient operating strategy for storages can be difficult. The
literature reveals a wide variety of approaches to the hydro-dispatch problem. More recently
more emphasis has been placed on the operation of distributed demand-side storages, be
they centrally controlled or individually influenced through time-of-use or spot pricing
tariffs.
The difficulty of modelling and optimising the operation of storage systems arises from
the separation over time of production and use of the stored commodity. Determining the
optimal operating strategy is a time-staged problem, presenting practical difficulties with
problem size. The operating strategy also depends on expectations of future plant operation
and external conditions which cannot always be known with certainty.
This thesis presents an exact and efficient solution method for a general class of deterministic,
single storage systems. While many real systems are more complex than this, the
approach developed combines elements of both dynamic programming and general
mathematical programming methodology and so offers good prospects for extension to
more complex multiple storage or stochastic systems.
An important insight used throughout this thesis is that, for a large class of storage problems,
the "production" and "storage" elements of the system can be separated. This leads to the
further insight that the behaviour of a wide variety of production systems can be
encapsulated in a single "production cost function" which describes the way all the system
costs per unit time vary with the rate of flow into (or out of) the store. For the purpose of
this thesis, this function is taken to be piece-wise linear and convex, although such
restrictions can largely be removed if the algorithm is modified.
Once the production element of the system can be described in this standardised way, it
is possible to write both linear programming and dynamic programming representations
of the time-staged optimisation problem to be solved. By analysing the mathematical
properties of this formulation and the conditions for its solution, a simple, exact and highly
efficient solution algorithm is developed. One advantage of the algorithm is that it has a
simple and intuitive graphical representation.
The algorithm combines the best features of the linear and dynamic programming
approaches while eliminating their worst features for the class of problem addressed. As
a dynamic programming approach, the solution is obtained by solving a sequence of small,
single period optimisations, which is much more efficient than solving a time-stage linear
program. As a linear programming approach, the solution is exact and obtained without
discretising the storage variable. The dual properties of the linear programming solution
also provide useful supplementary information such as the shadow value of the storage
contents over time. As a practical matter, commercial codes for the storage algorithm can
be developed by extending existing mathematical programming codes.
Two examples are presented. The first works through a simple model analytically to
illustrate the workings of the algorithm. The second is a larger and more complex model
of a pumped storage hydro-electric system.
While the thesis concentrates on single storage, deterministic systems, possible extensions
to deal with multiple storage and stochastic systems are also reviewed
Facility location, capacity acquisition and technology selection models for manufacturing strategy planning
Ankara : The Institute of Engineering and Science, Bilkent Univ., 1993.Thesis (Ph.D.) -- Bilkent University, 1993.Includes bibliographical references leaves 129-141.The primary aim of this dissertation research is to contribute to the manufacturing strategy planning process. The firm is perceived as a value chain which can be represented by a production-distribution network. Structural decisions regarding the value chain of a firm are the means to implement the firm’s manufacturing strategy. Thus, development of analytical methods to aid the design of production-distribution sytems constitutes the essence of this study. The differentiating features of the manufacturing strategy planning process within the multinational companies are especially taken into account due to the significance of the globalization in product, factor, and capital markets.
A review of the state-of-the-art in production-distribution system design reveals that although the evaluation of strategy alternatives received much attention, the existing analytical methods are lacking the capability to produce manufacturing strategy options. Further, it is shown that the facility location, capacity acquisition, and technology selection decisions have been dealt with separately in the literature. Whereas, the interdependencies among these structural decisions are pronounced within the international context, and hence global manufacturing strategy planning requires their simultaneous optimization. Thus, an analytical method is developed for the integration of the facility location and sizing decisions in producing a single commodity. Then, presence of product-dedicated technology alternatives in acquiring the required production capacity at each facility is incorporated. The analytical method is further extended to the multicommodity problem where product- flexible technology is also available as a technology alternative. Not only the arising models facilitate analysis of the trade-offs associated with the scale and scope economies in capacity/technology acquisition on the basis of alternative facility locations, but they also provide valuable insights regarding the presence of some dominance properties in manufacturing strategy design.Verter, VedatPh.D
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