As a rule, harvesting leads to dynamics stabilization. We apply the Pontryagin minimum principle and numerically explore the impact of seasonality, human behaviour and latency rate on the control and spread of the target disease. This optimal pest control problem is modeled by integrodifference equations and we illustrate how to construct the necessary conditions. The book is intended for graduate students and researchers in mathematics, biology, economics, engineering, and other fields. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Georges, Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model,, in Proceeding of the Conference on Decision and Control, 1999. A general convergence theorem for the gradient methodis proved under hypotheses which are given below.
Teo, Optimal discrete-valued control computation,, Journal of Global Optimization, 56 2013 , 503. We make an analysis of variance of the code. The calculation of the gradient of the cost functional allows us to develop gradient-type algorithms. Also an adjoint technique is used to effectively evaluate the gradient. The periodic case, in Advances in Dynamics and Control: Theory, Methods and Applications Editors: S. Krstic, Finite-time multi-agent deployment: A nonlinear pde motion planning approach,, Automatica, 47 2011 , 2534. The formulation described here makes use of exact results derived by means of the path-integral approach of quantum dynamics, so that no approximation is invoked.
Vineyard replacement is a common practice in every wine-growing farm since the grapevine production decays over time and requires a new vine to ensure the business sustainability. We consider two optimal harvesting problems related to age-structured population dynamics with logistic term and time-periodic of period T control and vital rates. We present a general formulation of a stochastic dynamic multiobjective optimization model and we provide different solution concepts based on its transformation into different deterministic equivalent models. The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. An adaptive nonmonotone spectral gradient method for the solution of distributed optimal control problem for the viscous Burgers equation is presented in a black-box framework. Morale Springer, Heidelberg, 2006, 219-228. On the system of partial differential equations arising in mean field type control.
Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 2011 , 291. Our underlying mathematical model extends other results in the literature along different directions. The solutions and the stability of the system are considered. Ye, Leakage Detection and Localization of Long Distance Fluid Pipelines,, Tsinghua University Press, 2010. This chapter is devoted to approximation methods, mainly of gradient type, for optimal control problems governed by ordinary differential equations.
Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. First, we will describe the physical origin of the equations. Some numerical tests are given to illustrate the effectiveness of the results for a particular optimal harvesting problem. This paper is the formal mixture of three different areas of knowledge, two from applied math and engineering, and one from applied medicine and pharmacology. In the case of juvenile harvest, the way of stability loss does not depend on the harvest rate. The gradient and necessary condition for an extremum are derived.
This paper concerns the optimal control and stabilization for some Fisher - like models with control acting in a subdomain ω. In this paper, we investigate a mathematical model for age-structured forest—beetle interactions that includes harvesting of trees. It is my object in this lecture to pay homage to J. Professor Anita is the author of more than 50 scientific papers in refereed international journals, one monograph, and three textbooks. Zhou, Fast leak detection and location of gas pipelines based on an adaptive particle filter,, International Journal of Applied Mathematics and Computer Science, 15. In the second phase a rapidly convergent algorithm determines the exact location.
Numerical tests are used to illustrate the effectiveness of the theoretical results. The Pontryagin maximum principle with delay is used to characterize these optimal controls. Instead of Sobolev type inequalities, only algebraic inequalities are requested. We just want to implement a simple tool that may be used to find reasonable approximations for typical examples. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations that summarize much of the dynamical behavior. Professor Anita is the author of more than 50 scientific papers in refereed international journals, one monograph, and three textbooks. It is thenshown that the usual steepest descent and modified steepestdescent algorithms converge under the some hypotheses.
Formulation of the Problem and Existence. Combining two important and growing areas of applied mathematics-control theory and modeling-this textbook introduces and builds on methods for simulating and tackling problems in a variety of applied sciences. Population size is expressed as total biomass. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. A sufficient condition for the zero-stabilizability eradicability of predators is given in terms of the sign of the principal eigenvalue of an appropriate operator that is not self-adjoint, and a stabilizing feedback control with a very simple structure is indicated. Some partially observed multi-agent linear exponential quadratic stochastic differential games. The technique requires no more than defining a few analogous formulas to the problem mathematical equations using basic spreadsheet operations, and no programming skills are needed.