Convergence analysis of Taylor models and McCormick-Taylor models

From Taylor Series to Taylor Models

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on ...

Rigorous Reachability Analysis and Domain Decomposition of Taylor Models

Taylor approximation of incomplete Radner equilibrium models

In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a coupled set of Riccati equations. Finally, we prove that these exponential-qu...

Reachability Analysis of Non-Linear Hybrid Systems Using Taylor Models

With the ubiquitous use of computers in controlling physical systems, it requires to have a new formalism that could model both continuous flows and discrete jumps. Hybrid systems are introduced to this purpose. A hybrid system, which is modeled by a hybrid automaton in the thesis, is equipped with finitely many discrete modes and continuous real-valued variables. A state of it is then represen...

Formal Global Optimisation with Taylor Models