Dynamics, Control, and Optimization with Applications

The Implicit Function Theorem with Applications in Dynamics and Control

The implicit function theorem is a statement of the existence, continuity, and differentiability of a function or set of functions. The theorem is closely related to the convergence of Newton’s method for nonlinear equations, the existence and uniqueness of solutions to nonlinear differential equations, and the sensitivity of solutions to these nonlinear problems. The implicit function theorem ...

Control of a Chemical Reactor with Chaotic Dynamics

In this paper, control of a non-isothermal continuous stirred tank reactor in which two parallel autocatalytic reactions take place has been addressed. The reactor shows chaotic behavior for a certain set of reactor parameters. In order to control the product concentration, an optimal state feedback controller has been designed. Since concentrations of reactor species are ...

Distribution-dependent robust linear optimization with applications to inventory control

This paper tackles linear programming problems with data uncertainty and applies it to an important inventory control problem. Each element of the constraint matrix is subject to uncertainty and is modeled as a random variable with a bounded support. The classical robust optimization approach to this problem yields a solution with guaranteed feasibility. As this approach tends to be too conserv...

Global Optimization Using Local Information with Applications to Flow Control

Flow control in high speed networks requires distributed routers to make fast decisions based only on local information in allocating bandwidth to connections. While most previous work on this problem focuses on achieving local objective functions, in many cases it may be necessary to achieve global objectives such as maximizing the total ow. This problem illustrates one of the basic aspects of...

Optimal Singular Control With Applications to .Trajectory Optimization