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The Exact Solution of Min-Time Optimal Control Problem in Constrained LTI Systems: A State Transition Matrix Approach | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 3، دوره 51، شماره 2، اسفند 2019، صفحه 103-110 اصل مقاله (1.7 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2019.14999.5119 | ||
| نویسنده | ||
| Valiollah Ghaffari* | ||
| Electrical Engineering Department, Persian Gulf University | ||
| چکیده | ||
| In this paper, the min-time optimal control problem is mainly investigated in the linear time invariant (LTI) continuous-time control system with a constrained input. A high order dynamical LTI system is firstly considered for this purpose. Then the Pontryagin principle and some necessary optimality conditions have been simultaneously used to solve the optimal control problem. These optimality conditions would usually lead to some complicated equations while some integral terms may be presented. Then a systematic procedure based on state transition matrix will be addressed to overcome and simplify the mentioned complexities. Therefore the state transition matrix would be used to determine the exact solution of the min-time control problem in a typical LTI system. The mintime problem would be converted to some algebraic nonlinear equations by using of the state transition matrix. These algebraic equations are depended on some definite parameters. Hence the required design parameters as well as switching times and the possible minimum time would be analytically determined in the minimum-time optimal control problem. Thus the min-time control signal would be explicitly determined by computing of the switching times and also some other constants. The proposed control scheme is applied in some typical dynamical examples to show the effectiveness of the suggested control method | ||
| کلیدواژه‌ها | ||
| Constrained LTI system؛ optimal control؛ min-time problem؛ state transition matrix | ||
| مراجع | ||
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[1] F.L. Lewis, D. Vrabie, V.L. Syrmos, Optimal control, John Wiley & Sons, 2012.
[2] A.E. Bryson, Applied optimal control: optimization, estimation and control, CRC Press, 1975.
[3] D.E. Kirk, Optimal control theory: an introduction, Courier Corporation, 2012.
[4] S. Yu, N. Li, P. Wei, Z. Xi, Time-optimal control for hybrid systems based on the nitrogen-vacancy center, Control Theory and Technology, 15(3) (2017) 219-225.
[5] X. Liu, P. Lu, Solving nonconvex optimal control problems by convex optimization, Journal of Guidance, Control, and Dynamics, 37(3) (2014) 750-765 .
[6] R. Kosut, Suboptimal control of linear time-invariant systems subject to control structure constraints, IEEE Transactions on Automatic Control, 15(5) (1970) 557-563.
[7] W.L. Garrard, Suboptimal feedback control for nonlinear systems, Automatica, 8(2) (1972) 219-221.
[8] T. Abualrub, I. Sadek, F. El Nachar, Wavelet based approximations in the optimal control of parabolic problems, Journal of Control Theory and Applications, 11(1) (2013) 103-107.
[9] M.R. Jardin, A.E. Bryson Jr, Methods for computing minimum-time paths in strong winds, Journal of Guidance, Control and Dynamics, 35(1) (2012) 165-171.
[10]N. Kim, S. Cha, H. Peng, Optimal control of hybrid electric vehicles based on Pontryagin’s minimum principle, IEEE Transactions on Control Systems Technology, 19(5) (2011) 1279-1287.
[11]G. Boone, Minimum-time control of the acrobot, in: IEEE International Conference Proceedings on Robotics and Automation, IEEE, 1997, pp. 3281-3287.
[12]Y. Chen, A.A. Desrochers, Minimum-time control laws for robotic manipulators, International Journal of Control, 57(1) (1993) 1-27.
[13]K. Shin, N. McKay, Minimum-time control of robotic manipulators with geometric path constraints, IEEE Transactions on Automatic Control, 30(6) (1985) 531-541.
[14]X. Sun, S. Kuang, Y. Liu, J. Zhou, S. Cong, Feedback stabilization of N-dimensional stochastic quantum systems based on bang-bang control, Control Theory and Technology, 15(3) (2017) 206-218.
[15] S. Gutman, On optimal guidance for homing missiles, Journal of Guidance, Control, and Dynamics, 2(4) (1979) 296-300
[16]C.-H. Lee, M.-J. Tahk, J.-I. Lee, Generalized formulation of weighted optimal guidance laws with impact angle constraint, IEEE Transactions on Aerospace and Electronic Systems, 49(2) (2013) 1317-1322.
[17] S. Bichiou, M.K. Bouafoura, N. benhadj Braiek, Minimum time control synthesis for high order LTI systems, in: International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), IEEE, 2014, pp. 1-6.
[18]R.E. Kopp, Pontryagin maximum principle, Mathematics in Science and Engineering, 5 (1962) 255-279. [19]G. Strang, Differential equations and linear algebra, Wellesley-Cambridge Press, 2014. | ||
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