Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin

By Ya. Z. Tsypkin

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Middleton, D . (1960). ” McGrawHill, New York. F. (1962). ” Wiley (Interscience), New York. L. (1966). ” Sovyetskoe Radio, Moscow. 2. (1 966). Adaptation, learning and self-learning in automatic systems, Automat. Remote Contr. 27 ( l) , 23-61. A. (1958). , IRE Trm7s. Inform. Theory IT-4 (l), 3. 1 Introduction In this chapter we shall consider recursive algorithmic methods of solving optimization problems. These methods encompass various iterative procedures related to the application of sequential approximations.

T h e Theory of Matrices,” 2 Vols. Chelsea, New York. V. (1962). ” Chelsea, New York. S. (1961). ” Gosenergoizdat, Moscow. R. (1956). ” Tokyo. W. (1960). ” Pergamon Press, New York. Kalman, R. (1961). On the general theory of optimal control, “Proceedings of the First IFAC, Automatic and Remote Control,” Vol. 1, pp. 481-492. Butterworths, London. Kalman, R. (1964). When is a linear control system optimal? Trans. A S M E 86D. A. (1963). ” Fizmatgiz, Moscow. K. (1964). ” MIT Press, Cambridge, Mass.

30) This is Slater's regularity condition which is well-known in the theory of nonlinear programming. , > 0, then 6, = g,(c*) = 0. 14) on the optimal value of the vector. It should be noticed that the Kuhn-Tucker theorem provides the necessary and sufficient conditions of optimality if the functionals f ( c ) and g,(c) (v = I , . . , M , ) are convex. 31) The block diagram of the system which corresponds to this algorithm is shown in Fig. 8. The half-wave rectifier in this scheme is introduced to realize the inequality constraints.

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