2000 character limit reached
Energy Optimal Control of a Harmonic Oscillator with a State Inequality Constraint (2309.16834v1)
Published 28 Sep 2023 in eess.SY and cs.SY
Abstract: In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical solution with both small and large terminal time is found for a special case when the undriven oscillator system is initially at rest. For other initial states of the Harmonic oscillator, the optimal solution is found to have three modes: wait-move, move-wait, and move-wait-move given a longer terminal time.
- A. Ovseevich, “Complexity of the minimum-time damping of a physical pendulum,” SIAM Journal on Control and Optimization, vol. 52, no. 1, pp. 82–96, 2014. [Online]. Available: https://doi.org/10.1137/13091107X
- A. Galyaev, “Problem of optimal oscillator control for nulling its energy under bounded control action,” Automation and Remote Control - AUTOMAT REMOTE CONTR-ENGL TR, vol. 70, pp. 366–374, 03 2009.
- B. Andresen, K. H. Hoffmann, J. Nulton, A. Tsirlin, and P. Salamon, “Optimal control of the parametric oscillator,” European Journal of Physics, vol. 32, no. 3, p. 827, apr 2011. [Online]. Available: https://dx.doi.org/10.1088/0143-0807/32/3/018
- A. Rao, “A survey of numerical methods for optimal control,” Advances in the Astronautical Sciences, vol. 135, 01 2010.
- M. P. Kelly, “Transcription methods for trajectory optimization: a beginners tutorial,” 2017.
- R. F. Hartl, S. P. Sethi, and R. G. Vickson, “A survey of the maximum principles for optimal control problems with state constraints,” SIAM Review, vol. 37, no. 2, pp. 181–218, 1995. [Online]. Available: https://doi.org/10.1137/1037043
- Y. Nie, O. Faqir, and E. C. Kerrigan, “Iclocs2: Try this optimal control problem solver before you try the rest,” in 2018 UKACC 12th International Conference on Control (CONTROL), 2018, pp. 336–336.
- M. Zhou, E. I. Verriest, Y. Guan, and C. Abdallah, “Jump law of co-state in optimal control for state-dependent switched systems and applications,” in 2023 American Control Conference (ACC), 2023, pp. 3566–3571.