Abstract
A recurrent neural network is introduced for the N-stage optimal control problem. The new neural network is based on a reformulation of the original optimal control problem and the gradient method. The simulation results on two examples indicate that the new neural network is quite effective.
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Balakrishnan, S. N. and Biega, V.: Adaptive-critic-based neural networks for aircraft optimal control, J. Guid. Control Dyn. 19 (1996), 893–898.
Bryson, A. E. and Ho, Y.-C.: Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere, New York, 1975.
Cai, B.: Neural networks, fuzzy logic, and optimal control for vehicle active systems with fourwheel steering and active suspension, Ph.D. Thesis, Fachbereich Elektrotechnik, Universitäet der Bundeswehr Müenchen, Neubiberg, 1993.
Chua, L.O. and Lin, G.-N.: Nonlinear programming without computation, IEEE Trans. Circuits Syst. CAS-31 (1984), 182–188.
Hopfield, J. J. and Tank, D. W.: Neural computation of decisions in optimization problems, Biol. Cybern. 52 (1985), 141–152.
Jacobson, D. H. and Mayne, D. Q.: Differential Dynamic Programming, Elsevier Sci. Publ.: New York, 1970.
Liao, L.-Z. and Shoemaker, C. A.: Convergence in unconstrained discrete-time differential dynamic programming, IEEE Trans. Automat. Contr. 36 (1991), 692–706.
Pantoja, J. F. A. De O.: Differential dynamic programming and Newton's method, Int. J. Control 47 (1988), 1539–1553.
Parisini, T. and Zoppoli, R.: Neural networks for the solution of N-stage optimal control problems, In: T. Kohonen, K. Mäkisara, O. Simula, and J. Kangas (eds.), Artificial Neural Networks, Elsevier Science Publ. B.V., North-Holland, 1991, pp. 333–338.
Toomarian, N. B. and Barhen, J.: Learning a trajectory using adjoint functions and teacher forcing, Neural Network 5 (1992), 473–484.
White, D. A. and Sofge, D. A.: Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, Van Nostrand Reinhold, New York, 1992.
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Liao, LZ. A Recurrent Neural Network for N-Stage Optimal Control Problems. Neural Processing Letters 10, 195–200 (1999). https://doi.org/10.1023/A:1018776323513
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DOI: https://doi.org/10.1023/A:1018776323513