Abstract
Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV problems without delay and advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original OTC problem. The obtained OTC law consists of analytic state feedback terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. By using a finite term of the adjoint vector sequence, a suboptimal tracking control law is revealed. Numerical examples show the effectiveness of the algorithm.
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References
Liu T, Zhang W, Gu D. Analytical design of two-degree-of-freedom control scheme for open-loop unstable processes with time delay. Journal of Process Control, 2005, 15(5): 559–572
Gallina P, Trevisani A. Delayed reference control of a two-mass elastic system. Journal of Vibration and Control, 2004, 10(1): 135–159
Carevic D. Tracking target in cluttered environment using multilateral time-delay measurements. Journal of the Acoustical Society of America, 2004, 115(3): 1198–1206
Liu T, He X, Gu D Y, et al. Analytical decoupling control design for dynamic plants with time delay and double integrators. IEE Proceedings: Control Theory and Applications, 2004, 151(6): 745–753
Cai G P, Huang J Z, Yang S X. An optimal control method for linear systems with time delay. Computers and Structures, 2003, 81(15): 1539–1546
Tang G-Y, Zhao Y-D, Chen X-L. Suboptimal control for time-delay linear systems under sinusoidal disturbances. Control and Decision (in Chinese), 2004, 19(5): 529–533
Tang G-Y. Suboptimal control for nonlinear systems: A successive approximation approach. Systems and Control Letters, 2005, 54(5): 429–434
Huang C M, Tsai J S, Provence R S, et al. The observer-based linear quadratic sub-optimal digital tracker for analog systems with input and state delays. Optimal Control Applications and Methods, 2003, 24(4): 197–236
Chou J H, Hsieh C H, Sun J H. On-line optimal tracking control of continuous-time systems. Mechatronics, 2004, 14(5): 587–597
Lancaster P, Lerer L, Tismenetsky M. Factored forms for solutions of AX−XB=C and X−AXB=C in companion matrices. Linear Algebra and Its Applications, 1984, 62: 19–49
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Tang, G., Li, C. & Zhao, Y. Approximate design of optimal tracking controller for time-delay systems. CHINESE SCI BULL 51, 2158–2163 (2006). https://doi.org/10.1007/s11434-006-2052-x
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DOI: https://doi.org/10.1007/s11434-006-2052-x