190 research outputs found
Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-III and Holling Type-IV Functional Responses
In recent years, time-optimal control studies on additional food provided
prey-predator systems have gained significant attention from researchers in the
field of mathematical biology. In this study, we initially consider an
additional food provided prey-predator model exhibiting Holling type-III
functional response and the intra-specific competition among predators. We
prove the existence and uniqueness of global positive solutions for the
proposed model. We do the time optimal control studies with respect quality and
quantity of additional food as control variables by transforming the
independent variable in the control system. Making use of the Pontraygin
maximum principle, we characterize the optimal quality of additional food and
optimal quantity of additional food. We show that the findings of these
time-optimal control studies on additional food provided prey-predator systems
involving Holling type III functional response have the potential to be applied
to a variety of problems in pest management. In the later half of this study,
we consider an additional food provided prey-predator model exhibiting Holling
type-IV functional response and study the above aspects for this system
Exponential decay properties of a mathematical model for a certain fluid-structure interaction
In this work, we derive a result of exponential stability for a coupled
system of partial differential equations (PDEs) which governs a certain
fluid-structure interaction. In particular, a three-dimensional Stokes flow
interacts across a boundary interface with a two-dimensional mechanical plate
equation. In the case that the PDE plate component is rotational inertia-free,
one will have that solutions of this fluid-structure PDE system exhibit an
exponential rate of decay. By way of proving this decay, an estimate is
obtained for the resolvent of the associated semigroup generator, an estimate
which is uniform for frequency domain values along the imaginary axis.
Subsequently, we proceed to discuss relevant point control and boundary control
scenarios for this fluid-structure PDE model, with an ultimate view to optimal
control studies on both finite and infinite horizon. (Because of said
exponential stability result, optimal control of the PDE on time interval
becomes a reasonable problem for contemplation.)Comment: 15 pages, 1 figure; submitte
A Study of Qualitative Correlations Between Crucial Bio-markers and the Optimal Drug Regimen of Type-I Lepra Reaction: A Deterministic Approach
Mycobacterium leprae is a bacteria that causes the disease Leprosy (Hansen's
disease), which is a neglected tropical disease. More than 200000 cases are
being reported per year world wide. This disease leads to a chronic stage known
as Lepra reaction that majorly causes nerve damage of peripheral nervous system
leading to loss of organs. The early detection of this Lepra reaction through
the level of bio-markers can prevent this reaction occurring and the further
disabilities. Motivated by this, we frame a mathematical model considering the
pathogenesis of leprosy and the chemical pathways involved in Lepra reactions.
The model incorporates the dynamics of the susceptible schwann cells, infected
schwann cells and the bacterial load and the concentration levels of the bio
markers , , , , and . We
consider a nine compartment optimal control problem considering the drugs used
in Multi Drug Therapy (MDT) as controls. We validate the model using 2D - heat
plots. We study the correlation between the bio-markers levels and drugs in MDT
and propose an optimal drug regimen through these optimal control studies. We
use the Newton's Gradient Method for the optimal control studies
Stochastic Time-Optimal Control Studies for Additional Food provided Prey-Predator Systems involving Holling Type-IV Functional Response
We consider an additional food provided prey-predator model exhibiting
Holling type IV functional response with combined continuous white noise and
discontinuous L\'evy noise. We prove the existence and uniqueness of global
positive solutions for the considered model. By considering the quality and
quantity of additional food as control parameters, we formulate a time-optimal
control problem. We obtain the condition for the existence of an optimal
control. Furthermore, making use of the arrow condition of the sufficient
stochastic maximum principle, we characterize the optimal quality of additional
food and optimal quantity of additional food. Numerical results are given to
illustrate the theoretical findings with applications in biological
conservation and pest management
Stochastic Optimal and Time-Optimal Control Studies for Additional Food provided prey-predator Systems involving Holling Type-III Functional Response
This paper consists of a detailed and novel stochastic optimal control
analysis of a coupled non-linear dynamical system. The state equations are
modeled as additional food provided prey-predator system with Holling Type-III
functional response for predator and intra-specific competition among
predators. We firstly discuss the optimal control problem as a Lagrangian
problem with a linear quadratic control. Secondly we consider an optimal
control problem in the time-optimal control setting. Stochastic maximum
principle is used for establishing the existence of optimal controls for both
these problems. Numerical simulations are performed based on stochastic
forward-backward sweep methods for realizing the theoretical findings. The
results obtained in these optimal control problems are discussed in the context
of biological conservation and pest management
Alternatives for Jet Engine Control
Approaches are developed as alternatives to current design methods which rely heavily on linear quadratic and Riccati equation methods. The main alternatives are discussed in two broad categories, local multivariable frequency domain methods and global nonlinear optimal methods
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