Abstract
This paper is concerned with the optimal control of a class of nonlinear time-delay systems affected by external persistent disturbances. A feedforward and feedback optimal control (FFOC) law, consisting of analytical linear feedforward and feedback terms and the limit of a compensation sequence, is obtained by a successive approximation approach (SAA). In order to obtain a physically realizable feedforward control, a disturbance observer is introduced in the exosystem. Simulation results demonstrate the validity of the SAA and the robustness of the FFOC.
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BANKS, S. P., and MHANA, K. J., Optimal Control and Stabilization for Nonlinear Systems, IMA Journal of Mathematical Control and Information, Vol. 9, pp. 179–196, 1992.
AGANOVIC, Z., and GAJIC, Z., The Successive Approximation Procedure for Finite-Time Optimal Control of Bilinear Systems, IEEE Transactions on Automatic Control, Vol. 39, pp. 1932–1935, 1994.
MRACEK, C. P., and CLOUTIER, J. R., Control Designs for the Nonlinear Benchmark Problem via the State-Dependent Riccati Equation Method, International Journal of Robust and Nonlinear Control, Vol. 8, pp. 401–433, 1998.
TANG, G. Y., Suboptimal Control for Nonlinear Systems: A Successive Approximation Approach, Systems and Control Letters, Vol. 54, pp. 429–434, 2005.
BANKS, S. P., and McCaffrey, D., Lie Algebras, Structure of Nonlinear Systems, and Chaotic Motion, International Journal of Bifurcation and Chaos, Vol. 8, pp. 1437–1462, 1998.
BANKS, S. P., and DINESH, K., Approximate Optimal Control and Stability of Nonlinear Finite and Infinite-Dimensional Systems, Annals of Operations Research, Vol. 98, pp. 19–44, 2000.
BANKS, S. P., Exact Boundary Controllability and Optimal Control for a Generalized Korteweg-De Vries Equation, International Journal of Nonlinear Analysis, Methods, and Applications, Vol. 47, pp. 5537–5546, 2001.
CIMEN, T., and BANKS, S. P., Global Optimal Feedback Control for General Nonlinear Systems with Nonquadratic Performance Criteria, Systems and Control Letters, Vol. 53, pp. 327–346, 2004.
CAI, G., HUANG, J., and YANG, S. X., An Optimal Control Method for Linear Systems with Time Delay, Computers and Structures, Vol. 81, pp. 1539–1546, 2003.
BITTANTI, S., LORITO, F., and STRADA, S., An LQ Approach to Active Control of Vibrations in Helicopters, ASME Journal on Dynamic Systems, Measurement, and Control, Vol. 118, pp. 482–488, 1996.
MA, H., TANG, G. Y., and ZHAO, Y. D., Feedforward and Feedback Optimal Control for Offshore Structures Subjected to Irregular Wave Forces, Ocean Engineering, (in press).
TANG, G. Y., Feedforward and Feedback Optimal Control for Linear Systems with Sinusoidal Disturbances, High Technology Letters, Vol. 7, pp. 16–19, 2001.
MARINO, R., SANTOSUOSSO, G. L., and TOMEI, P., Robust Adaptive Compensation of Biased Sinusoidal Disturbances with Unknown Frequency, Automatica, Vol. 39, pp. 1755–1761, 2003.
BROWN, L. J., and ZHANG, Q., Periodic Disturbance Cancellation with Uncertain Frequency, Automatica, Vol. 40, pp. 631–637, 2004.
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Communicated by Q. C. Zhao
This work was supported by the National Natural Science Foundation of China, Grant 60574023 and the Natural Science Foundation of Qingdao City of China, Grant 05-1-JC-94.
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Tang, G.Y., Zhao, Y.D. Optimal Control of Nonlinear Time-Delay Systems with Persistent Disturbances. J Optim Theory Appl 132, 307–320 (2007). https://doi.org/10.1007/s10957-006-9131-7
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DOI: https://doi.org/10.1007/s10957-006-9131-7