Browsing by Author "Teatro, Timothy A.V."

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Categories in control systems software: toward a unified theory of programming & control
(2023-12-01) Teatro, Timothy A.V.; Eklund, J. Mikael; Milman, Ruth
Category theory is applied to the design and modeling of control systems application software with emphasis on feedback control. The language of application is iso standard C++17, though the design is abstract and can be gainfully applied in any language expressive enough to embed domain specific languages for event stream processing with sufficient structure. The design is derived in a category, Cpp, of a subset of C++ programs where types are modelled as sets and programs/routines are modelled as functions. This gives a forgetful functor from Cpp to 𝕊𝗲𝘁, the category of sets which, in theory, facilitates broader compatibility with theories of dynamical systems in concrete categories. A library of abstract datatypes (struct templates) and natural transformations (parametrically polymorphic function templates) is developed to demonstrate that (1) Cpp carries a bicartesian closed structure and (2) this structure has representation as standard compliant code. The axioms of this structure are encoded as unit-tests. And from this structure we specialize “machines” in the sense of Goguen (or more generally, Arbib & Manes), which actualise in Cpp as Moore machines. These Moore machines are then used as a basic model for the I/S/O structure of a control program. Categorical Moore machines can be cast in terms of algebra and coalgebra which give natural mechanism to the input-driven evolution of internal state of the control programs, and infinite records of behaviour. The internal language of that model is consonant with sufficiently structured domain specific event-stream processing languages. The core examples and a case study use Rx, but FRP is a stated ideal and avenue for future work for modeling of interconnected and hybrid systems with computer controlled components. The architecture is applied in two examples: (1) a simulated spring-mass- damper system with PID-force control, where comparison is made to analytical results, and (2) NMPC path tracking of a mobile robot with obstacle avoidance through soft constraint.
Dynamical effects in crystalline solid state systems: theory of temperature dependent optical response of bulk gaAs and vibrational modification of C(111) 2 x 1 Surface in Comparison to Experiment
(2009-08-01) Teatro, Timothy A.V.; Chkrebtii, Anatoli
This thesis presents a new theoretical formalism which incorporates dynamical effects in atomistic electronic structure and related calculations. This research, fundamental by nature, brings about a deeper understanding of the dynamical processes in a range of materials. This establishes technologically important correlation with experimentally measured macroscopic properties and materials characterization. This method—the first of its kind—is a natural and long overdue extension of customary adiabatically separated time-independent electronic structure methods. It accounts explicitly for atomic motion due to thermal and zero-point vibration. The approach developed requires no direct treatment of time dependence in the quantum mechanical calculations, making the method widely applicable utilizing currently available electronic structure and ab-initio molecular dynamics software. The formalism is extensively applied and demonstrated for the linear optical response of bulk gallium arsenide and electronic structure of the C(111) 2 x 1 surface. Both cases are complimented by comparison of key observables to experimental data which may be used to judge the quality of the results. The results are found to be in good agreement with experimental data, with most exceptions being readily explainable and well understood.