A Switching Time Optimization Strategy for Optimal Control Problems

doi:10.1007/s40305-023-00499-9

Abstract

Abstract: The time-scaling transformation is a widely used approach within the computational framework of control parameterization for optimizing the switching times of control variables. However, the conventional time-scaling transformation has the limitation that the switching times and the number of switches for each control component must be the same. In this paper, we present a novel technique to solve constrained optimal control problems that allows for adaptively optimizing the switching times for each control component. Numerical results demonstrate that this proposed method provides better flexibility in control strategy and yields improved performance.

Key words: Optimal control, Control parameterization, Time-scaling transformation, Sequential adaptive switching time optimization technique, Co-state method

CLC Number:

Yin Chen, Chang-Jun Yu, Xi Zhu. A Switching Time Optimization Strategy for Optimal Control Problems[J]. Journal of the Operations Research Society of China, 2025, 13(2): 393-414.

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References

[1] Misra, A.K., Tripathi, A.: An optimal control model for cloud seeding in a deterministic and stochastic environment. Optim. Control Appl. Methods 41, 2166-2189 (2020)
[2] Nabi, S., Grover, P., Caulfield, C.P.: Nonlinear optimal control strategies for buoyancy-driven flows in the built environment. Comput. Fluids 194, 104313 (2019)
[3] Jensen, J.H.M., Mller, F.S., Srensen, J.J., Sherson, J.F.: Achieving fast high-fidelity optimal control of many-body quantum dynamics. Phys. Rev. A 104, 052210 (2021)
[4] Zhang, H.W., Kuang, Z.Y., Puri, S., Miller, O.D.: Conservation-law-based global bounds to quantum optimal control. Phys. Rev. Lett. 127, 110506 (2021)
[5] Hu, B., Tamba, T.A.: Optimal codesign of industrial networked control systems with state-dependent correlated fading channels. Int. J. Robust Nonlinear Control 29, 4472-4493 (2019)
[6] Li, L.L., Ding, S.X., Zhang, Y., Yang, Y.: Optimal fault detection design via iterative estimation methods for industrial control systems. J. Frankl. Inst. 353, 359-377 (2016)
[7] Blanchard, E.A., Loxton, R., Rehbock, V.: A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations. Appl. Math. Comput. 219, 8738-8746 (2013)
[8] Caillau, J.B., Cerf, M., Sassi, A., Trélat, E., Zidani, H.: Solving chance constrained optimal control problems in aerospace via kernel density estimation. Optim. Control Appl. Methods 39, 1833-1858 (2018)
[9] Trélat, E.: Optimal control and applications to aerospace: Some results and challenges. J. Optim. Theory Appl. 154, 713-758 (2012)
[10] Lin, Q., Loxton, R., Teo, K.L.: The control parameterization method for nonlinear optimal control: a survey. J. Ind. Manag. Optim. 10, 275-309 (2014)
[11] Lee, H.W.J., Teo, K.L., Rehbock, V., Jennings, L.S.: Control parametrization enhancing technique for time optimal control problems. Dyn. Syst. Appl. 6, 243-261 (1997)
[12] Lee, H.W.J., Teo, K.L., Cai, X.Q.: An optimal control approach to nonlinear mixed integer programming problems. Comput. Math. Appl. 36, 87-105 (1998)
[13] Lin, Q., Loxton, R., Teo, K.L., Wu, Y.H.: A new computational method for optimizing nonlinear impulsive systems. Dyn. Contin. Discrete Impuls. Syst.-Ser. B: Appl. Algorithms 1, 59-76 (2011)
[14] Siburian, A., Rehbock, V.: Numerical procedure for solving a class of singular optimal control problems. Optim. Methods Softw. 19, 413-426 (2004)
[15] Guo, X., Ren, H.: A switching control strategy based on switching system model of three-phase vsr under unbalanced grid conditions. IEEE Trans. Ind. Electron. 68, 5799-5809 (2021)
[16] Jin, J.F., Ramirez, J.P., Wee, S.G., Lee, D.H., Kim, Y.G., Gans, N.: A switched-system approach to formation control and heading consensus for multi-robot systems. Intel. Serv. Robot. 11, 207-224 (2018)
[17] Zhu, X., Yu, C.J., Teo, K.L.: A new switching time optimization technique for multi-switching systems. J. Ind. Manag. Optim. 19, 2838-2854 (2023)
[18] Zhu, X., Yu, C.J., Teo, K.L.: Sequential adaptive switching time optimization technique for optimal control problems. Automatica 146, 110565 (2022)
[19] Kaya, C.Y., Noakes, J.L.: Computational method for time-optimal switching control. J. Optim. Theory Appl. 117, 69-92 (2003)
[20] Loxton, R., Teo, K.L., Rehbock, V.: Optimal control problems with multiple characteristic time points in the objective and constraints. Automatica 44, 2923-2929 (2008)
[21] Goh, C.J., Teo, K.L.: Control parametrization: a unified approach to optimal control problems with general constraints. Automatica 24, 3-18 (1988)
[22] Teo, K.L.: A unified computational approach to optimal control problems, pp. 2763-2774. De Gruyter (1996)
[23] Teo, K.L., Li, B., Yu, C.J., Rehbock, V.: Applied and Computational Optimal Control: A Control Parametrization Approach. Springer, Cham (2021)
[24] Ahmed, N.U.: Elements of Finite Dimensional Systems and Control Theory. Wiley, New York (1988)
[25] Ahmed, N.U.: Dynamic Systems and Control with Applications. World Scientific, Singapore (2006)
[26] Loxton, R., Lin, Q., Teo, K.L.: Switching time optimization for nonlinear switched systems: direct optimization and the time-scaling transformation. Pac. J. Optim. 10, 537-560 (2014)
[27] Ma, C.F.: Optimization Method and its Matlab Program Design. Science Press, Beijing (2010)
[28] Yang, F., Teo, K.L., Loxton, R., Rehbock, V., Li, B., Yu, C.J., Jennings, L.: Visual miser: An efficient user-friendly visual program for solving optimal control problems. J. Ind. Manag. Optim. 12, 781-810 (2016)
[29] Banihashemi, N., Kaya, C.Y.: Inexact restoration for Euler discretization of box-constrained optimal control problems. J. Optim. Theory Appl. 156, 726-760 (2013)
[30] Liu, L.X., Hong, M.Q., Gu, X.T., Ding, M., Guo, Y.: Fixed-time anti-saturation compensators based impedance control with finite-time convergence for a free-flying flexible-joint space robot. Nonlinear Dyn. 109, 1671-1691 (2022)
[31] Li, M.W., Peng, H.J.: Solutions of nonlinear constrained optimal control problems using quasilinearization and variational pseudospectral methods. ISA Trans. 62, 177-192 (2016)