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End date: 2024 × DDC: 510 × Has files: Yes × Type: Article × Subject: Dynamical systems × WGL Institute: PIK ×

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Now showing 1 - 2 of 2
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    Sequential decision problems, dependent types and generic solutions
    (Braunschweig : Department of Theoretical Computer Science, Technical University of Braunschweig, 2017) Botta, N.; Jansson, P.; Ionescu, C.; Christiansen, D.R.; Brady, E.
    We present a computer-checked generic implementation for solving finite-horizon sequential decision problems. This is a wide class of problems, including inter-temporal optimizations, knapsack, optimal bracketing, scheduling, etc. The implementation can handle time-step dependent control and state spaces, and monadic representations of uncertainty (such as stochastic, non-deterministic, fuzzy, or combinations thereof). This level of genericity is achievable in a programming language with dependent types (we have used both Idris and Agda). Dependent types are also the means that allow us to obtain a formalization and computer-checked proof of the central component of our implementation: Bellman’s principle of optimality and the associated backwards induction algorithm. The formalization clarifies certain aspects of backwards induction and, by making explicit notions such as viability and reachability, can serve as a starting point for a theory of controllability of monadic dynamical systems, commonly encountered in, e.g., climate impact research.
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    A reconfigurable logic cell based on a simple dynamical system
    (New York, NY : Hindawi Publishing Corporation, 2013) Li, L.; Yang, C.; Hui, S.; Yu, W.; Kurths, J.; Peng, H.; Yang, Y.
    This paper introduces a new scheme to achieve a dynamic logic gate which can be adjusted flexibly to obtain different logic functions by adjusting specific parameters of a dynamical system. Based on graphical tools and the threshold mechanism, the distribution of different logic gates is studied, and a transformation method between different logics is given. Analyzing the performance of the dynamical system in the presence of noise, we discover that it is resistant to system noise. Moreover, we find some part of the system can be considered as a leaky integrator which has been already widely applied in engineering. Finally, we provide a proof-of-principle hardware implementation of the proposed scheme to illustrate its effectiveness. With the proposed scheme in hand, it is convenient to build the flexible, robust, and general purpose computing devices such as various network coding routers, communication encoders or decoders, and reconfigurable computer chips.