Control and Optimization of Nonlinear Systems in Operator Form
Sajjad Edalatzadeh, TU Chemnitz
Abstract: The state of many physical systems is distributed over space, and thus described by partial differential equations (PDEs). For linear PDEs, it is useful to formulate and study a system in an operator setting. This often makes the results applicable to general classes of linear PDEs. This generalization however is still in early stages for nonlinear PDEs. In this talk, general classes of nonlinear PDEs are introduced with examples. An interesting optimization problem that aims to concurrently find an optimal control and actuator design is discussed for each class. New existence results as well as optimality conditions will be presented. Further analysis is conducted for some nonlinear PDE models including railway track model and micro-beam model. Shape optimization, input-to-state stability and non-collocated observation are among the topics that will be discussed for these models. The talk will conclude with some future research directions.