8 research outputs found
Using a finite horizon numerical optimisation method for a periodic optimal control problem
Computing a numerical solution to a periodic optimal control problem is difficult. A method of approximating a solution to a given (stochastic) optimal control problem using Markov chains was developed in [3]. This paper describes an attempt at applying this method to a periodic optimal control problem introduced in [2].Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains
Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems
We show that necessary and sufficient conditions of optimality in periodic
optimization problems can be stated in terms of a solution of the corresponding
HJB inequality, the latter being equivalent to a max-min type variational
problem considered on the space of continuously differentiable functions. We
approximate the latter with a maximin problem on a finite dimensional subspace
of the space of continuously differentiable functions and show that a solution
of this problem (existing under natural controllability conditions) can be used
for construction of near optimal controls. We illustrate the construction with
a numerical example.Comment: 29 pages, 2 figure
On average control generating families for singularly perturbed optimal control problems with long run average optimality criteria
The paper aims at the development of tools for analysis and construction of
near optimal solutions of singularly perturbed (SP) optimal controls problems
with long run average optimality criteria. The idea that we exploit is to first
asymptotically approximate a given problem of optimal control of the SP system
by a certain averaged optimal control problem, then reformulate this averaged
problem as an infinite-dimensional (ID) linear programming (LP) problem, and
then approximate the latter by semi-infinite LP problems. We show that the
optimal solution of these semi-infinite LP problems and their duals (that can
be found with the help of a modification of an available LP software) allow one
to construct near optimal controls of the SP system. We demonstrate the
construction with a numerical example.Comment: 36 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1309.373
Averaging and linear programming in some singularly perturbed problems of optimal control
The paper aims at the development of an apparatus for analysis and
construction of near optimal solutions of singularly perturbed (SP) optimal
controls problems (that is, problems of optimal control of SP systems)
considered on the infinite time horizon.
We mostly focus on problems with time discounting criteria but a possibility
of the extension of results to periodic optimization problems is discussed as
well. Our consideration is based on earlier results on averaging of SP control
systems and on linear programming formulations of optimal control problems. The
idea that we exploit is to first asymptotically approximate a given problem of
optimal control of the SP system by a certain averaged optimal control problem,
then reformulate this averaged problem as an infinite-dimensional (ID) linear
programming (LP) problem, and then approximate the latter by semi-infinite LP
problems. We show that the optimal solution of these semi-infinite LP problems
and their duals (that can be found with the help of a modification of an
available LP software) allow one to construct near optimal controls of the SP
system. We demonstrate the construction with two numerical examples.Comment: 53 pages, 10 figure
Optimality conditions for nonsmooth optimization problems via generalised derivatives
Aquatic plants are integral components of freshwater ecosystems and provide essential ecosystem services. However, when invasive species establish in new aquatic environments, there are few natural checks and balances to inhibit their growth and spread. Overabundant aquatic vegetation can harm aquatic systems if left unchecked and negatively impact on agricultural productivity, social amenity and biodiversity values. Prevention and early intervention are recognised as the most cost effective means to manage invasive species that pose a biosecurity risk. This thesis contributes to the development of effective management strategies for one of the world’s most invasive aquatic plant species, known as alligator weed (Alternanthera philoxeroides (Mart.) Griseb.). It focusses on developing management strategies in an early stage of invasion, in order to achieve extirpation of this species from catchments and waterways. Developing effective detection and surveillance strategies are required for invasive aquatic plants, as a key impediment to achieving extirpation is the ability to detect infestations, so that control strategies can be enacted. This thesis investigates the effectiveness of aerial surveillance for detection of alligator weed at different spatial scales, using high altitude aerial imagery (orthophotos) and unmanned aerial vehicle (UAV) technology. An examination of the growth rate of alligator weed in Victoria, Australia, over a five year period, demonstrates the effective use of orthophotos to detect and monitor large infestations of aquatic alligator weed. The efficacy of unmanned aerial vehicle technology, including the use of automated algorithms, to detect patches of alligator weed growing in waterways is evaluated against current detection techniques. Effective management of invasive aquatic plants targeted for extirpation requires the coupling of effective detection and control efforts to prevent reproduction. To date, development of control strategies for aquatic alligator weed has been limited to evaluating the efficacy of short-term control at a local scale without regard to the effects of management strategies on dispersal of propagules throughout catchments. This thesis determines that viable alligator weed stem fragments are produced following herbicide application, which comprises extirpation efforts. This thesis has gone further than current practice in that it has evaluated the efficacy of current and novel control techniques, in both laboratory and field trials and has developed methods to manage viable fragment production post-herbicide application, to limit dispersal throughout catchments. In this respect, the application of the herbicides glyphosate, metsulfuron-methyl and imazapyr, and their effectiveness when incorporating surfactant systems and plant growth regulators, have been evaluated in field and laboratory studies to optimise control techniques for aquatic alligator weed. Results have shown that our approaches, when used in an early stage of invasion, are capable of eliminating patches of alligator weed in two to three years. Integral to the research is an experiment to determine the effect of herbicide treatments on the production of alligator weed stem fragments and their subsequent viability. Further investigation to determine the usefulness of commercially available plant growth regulators (PGRs) to reduce the number of viable propagules produced by alligator weed post-herbicide application was found to be ineffective. This thesis also evaluates the impact of herbicides and surfactant systems, on all key alligator weed response metrics in aquatic environments including; above ground biomass, below ground biomass and viable stem fragmentation. No previous studies have looked simultaneously at these three important measures for determining the efficacy of a particular control regime, and we have determined that this is essential for effective management of aquatic alligator weed in an early stage of invasion. The thesis has underscored the notion that development of more effective management strategies, based upon experimental trials, will result in an increased likelihood of eradicating invasive aquatic plants that pose a biosecurity risk, and thus move toward the mitigation of the threat that high-risk species pose to aquatic ecosystems. PLEASE NOTE: Portions of the full text have been removed due to copyright restrictions.Doctor of Philosoph
Data-driven system modeling and optimal control for nonlinear dynamical systems
With the increasing complexity of modern industry processes, robotics, transportation, aerospace,
power grids, an exact model of the physical systems are extremely hard to obtain whereas abundant
of time-series data can be captured from these systems. This makes it a important and
demanding research area to investigate feasibility of using data to learn behaviours of systems and
design controllers where the end goal generally evolves around stabilization. Transfer operators
i.e. Perron-Frobenius and Koopman operators play an undeniable role in advanced research of
nonlinear dynamical system stabilization. These operators have been a alternate direction of how
we generally approach dynamical systems, providing linear representations for even strongly nonlinear
dynamics. There is tremendous benet of acquiring a linear model of a system using these
models but, there remains a challenge of innite dimension for such models. To deal with it, we can
approximate a nite dimensional matrix of these operators e.g. Koopman matrix using Extended
Dynamic Mode Decomposition (EDMD) or Naturally Structured Dynamic Mode Decomposition
(NSDMD). Using duality property of Koopman and P-F operators we can derive formulation for
P-F matrix from Koopman matrix. Once we have a linear approximation of the system, Lyapunov
measure approach can be used along with a linear programming based computational framework for
stability analysis and design of almost everywhere stabilizing controller. In this work, we propose
a complete structure to stabilize a system that does not have an explicit model and only requires
black box input output time-series data. On a separate work, we show a set-oriented approach can
be used to control and stabilize systems with known dynamics model however having stochastic
parameters. Essentially, this work proposes two approaches to stabilize a nonlinear system using
both of known system model with inherent uncertainty and stabilize a black box system entirely
using input-output data