Energy control of distributed parameter systems via speed-gradient method: case study of string and sine-Gordon benchmark models |
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| Authors: | Y V Orlov A L Fradkov B Andrievsky |
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| Affiliation: | 1. Department of Electronics and Telecommunications, Mexican Scientific Research and Advanced Studies Center of Ensenada, Ensenada, Mexico;2. ITMO University, Saint Petersburg, Russia;3. ITMO University, Saint Petersburg, Russia;4. Saint Petersburg State University, Saint Petersburg, Russia;5. Institute for Problems of Mechanical Engineering of RAS, Saint Petersburg, Russia |
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| Abstract: | Energy control problems are analysed for infinite dimensional systems. Benchmark linear wave equation and nonlinear sine-Gordon equation are chosen for exposition. The relatively simple case of distributed yet uniform over the space control is considered. The speed-gradient method for energy control of Hamiltonian systems proposed by A. Fradkov in 1996, has already successfully been applied to numerous nonlinear and adaptive control problems is presently developed and justified for the above partial differential equations (PDEs). An infinite dimensional version of the Krasovskii–LaSalle principle is validated for the resulting closed-loop systems. By applying this principle, the closed-loop trajectories are shown to either approach the desired energy level set or converge to a system equilibrium. The numerical study of the underlying closed-loop systems reveals reasonably fast transient processes and the feasibility of a desired energy level if initialised with a lower energy level. |
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| Keywords: | Sine-Gordon equation energy control speed-gradient |
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