A data-driven indirect method for nonlinear optimal control
- 107 Downloads
Nonlinear optimal control problems are challenging to solve due to the prevalence of local minima that prevent convergence and/or optimality. This paper describes nearest-neighbors optimal control (NNOC), a data-driven framework for nonlinear optimal control using indirect methods. It determines initial guesses for new problems with the help of precomputed solutions to similar problems, retrieved using k-nearest neighbors. A sensitivity analysis technique is introduced to linearly approximate the variation of solutions between new and precomputed problems based on their variation of parameters. Experiments show that NNOC can obtain the global optimal solution orders of magnitude faster than standard random restart methods, and sensitivity analysis can further reduce the solving time almost by half. Examples are shown on optimal control problems in vehicle control and agile satellite reorientation demonstrating that global optima can be determined with more than 99% reliability within time at the order of 10–100 milliseconds.
Keywordsdata-driven approach indirect method optimal control sensitivity analysis
This work was partially supported by NSF (Grant No. IIS-1816540).
- Bryson Jr, A. E., Ho Y. C. Applied Optimal Control: Optimization, Estimation and Control. CRC Press, 1975.Google Scholar
- Tang, G., Sun, W. D., Hauser, K. Learning trajectories for real-time optimal control of quadrotors. In: Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2018, 3620–3625.Google Scholar
- Tang, G., Hauser, K. Discontinuity-sensitive optimal control learning by mixture of experts. arXiv preprint arXiv:1803.02493, 2018.Google Scholar
- Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E. N. The explicit solution of model predictive control via multiparametric quadratic programming. In: Proceedings of 2000 American Control Conference, 2000, 872–876.Google Scholar
- Furfaro, R., Bloise, I., Orlandelli, M., Di Lizia, P., Topputo, F., Linares, R. Deep learning for autonomous lunar landing. In: Proceedings of 2018 AAS/AIAA Astrodynamics Specialist Conference, 2018, 1–22.Google Scholar
- Ampatzis, C., Izzo, D. Machine learning techniques for approximation of objective functions in trajectory optimisation. In: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) 2009, Workshop on Artificial Intelligence in Space, 2009, 1–6.Google Scholar
- Mereta, A., Izzo, D., Wittig, A. Machine learning of optimal low-thrust transfers between near-earth objects. In: Proceedings of the 12th International Conference on Hybrid Artificial Intelligence Systems, 2017, 543–553.Google Scholar
- Izzo, D., Sprague, C., Tailor, D. Machine learning and evolutionary techniques in interplanetary trajectory design. arXiv preprint arXiv:1802.00180, 2018.Google Scholar
- Tang, G., Hauser, K. A data-driven indirect method for nonlinear optimal control. In: Proceedings of 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2017, 4854–4861.Google Scholar
- Moré, J. J., Garbow, B. S., Hillstrom, K. E. User guide for MINPACK-1. Argonne National Laboratory Report ANL-80-74, Argonne National Laboratory, 1980.Google Scholar
- Ritz, R., Hehn, M., Lupashin, S., D’Andrea, R. Quadrocopter performance benchmarking using optimal control. In: Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011, 5179–5186.Google Scholar