Optimal control of two coupled spinning particles in the Euler-Lagrange picture
Autor: | Alberto Ibort, R. Salmoni, T. Rodríguez de la Peña, M. Delgado-Téllez |
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Jazyk: | angličtina |
Rok vydání: | 2015 |
Předmět: |
Statistics and Probability
Integrable system Differential equation General Physics and Astronomy Lie group Statistical and Nonlinear Physics 010103 numerical & computational mathematics 02 engineering and technology 021001 nanoscience & nanotechnology Optimal control 01 natural sciences Hamiltonian system Matrix (mathematics) Maximum principle Optimization and Control (math.OC) Modeling and Simulation Ordinary differential equation FOS: Mathematics Applied mathematics 0101 mathematics 0210 nano-technology Mathematics - Optimization and Control Mathematical Physics Mathematics |
Popis: | A family of optimal control problems for a single and two coupled spinning particles in the Euler–Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction procedure to deal with them must be carried out. The reduction of the implicit control equations arising in these problems will be discussed in the slightly more general setting of implicit equations defined by invariant one-forms on Lie groups. As an example the first order differential equations describing the extremal solutions of an optimal control problem for a single spinning particle, obtained by using Pontryagin’s Maximum Principle (PMP), will be found and shown to be completely integrable. Then, again using PMP, solutions for the problem of two coupled spinning particles will be characterized as solutions of a system of coupled non-linear matrix differential equations. The reduction of the implicit system will show that the reduced space for them is the product of the space of states for the independent systems, implying the absence of ‘entanglement’ in this instance. Finally, it will be shown that, in the case of identical systems, the degree three matrix polynomial differential equations determined by the optimal feedback law, constitute a completely integrable Hamiltonian system and some of its solutions are described explicitly. |
Databáze: | OpenAIRE |
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