Sommario
Il problema dell'ottimizzazione dei Funzionali di Lyapunov è posto nei termini specifici del problema particolare. Il processo di ottimizzazione è basato sul “Path Integral Synthesis,” un metodo per la costruzione di Funzionali di Lyapunov elaborato dagli autori. Partendo da una generica forma del gradiente del funzionale definito in termini di un gruppo di parametri, il procedimento di ottimizzazione viene effettuato scegliendo questi parametri in modo da ottimizzare (nei termini specifici del problema) la regione di stabilità nello spazio dei parametri fisici che regolano la stabilità del problema. Applicazioni a problemi pratici descritti da equazioni lineari paraboliche sono svolte per illustrare il procedimento.
Summary
The problem of optimality of Lyapunov Functionals is posed in terms of the requirements of a specific problem. The optimizationprocess is based on a method used to construct Lyapunov Functionals called “Path Integral Synthesis” proposed by the authors. By starting with a gradient of a functional, defined in terms of a set of free parameters, the optimization procedure is performed by choosing those free parameters to optimize (in the term of the requirements of the problem) the resulting stability region in the space of the physical parameters of the problem. Practical applications to linear parabolic problems are performed in order to illustrate such procedure.
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Golia, C., Abel, J.M. Optimization of lyapunov functionals. Meccanica 10, 183–187 (1975). https://doi.org/10.1007/BF02149031
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DOI: https://doi.org/10.1007/BF02149031