By C. T. Leonides

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**Extra resources for Advances in Algorithms and Computational Techniques in Dynamic Systems Control Part 1 of 3: Advances in Theory and Applications**

**Example text**

69) The optimal stochastic control problem is now reduced to the optimal deterministic control problem of minimizing J x subject to the dynamic constraint of P. Use of the matrix maximum principle is one way of deriving a solution. Thus, let the Hamiltonian of the system be given by: — — _T T T T H = tr(QP) + tr(AP + PA + CPC + DPD + EE )S, (70) where S is the n x n symmetric costate matrix. 5 11 S= T 5 12 S 12 S 22 Then 3H _ _T -T -T S = - — = - ( Q + A S + SA + C SC + D SD) ap (71) with atr[HPCD]=5 ΘΡ(Τ) P(0) = P 0 .

BROCKETT, Stochastic bilinear models. Proc. J. Autom. , 1979, pp. 1420-1422 (1979). -K. NG, Optimal linear nonanticipative control of partially observable bilinear systems. IEEE Trans. Autom. Control AC-29, 271-274 (1984). C. BRUNI, G. DIPILLO, and G. KOCH, Mathematical models and identification of bilinear systems. In "Theory and Applications of Variable Structures Systems" (R. R. Mohler and R. ), pp. 137-152, Academic Press, New York, 1972. C. S. KUBRUSLY and O. L. COSTA, Mean -square stability conditions for discrete stochastic bilinear systems.

KOCH, Mathematical models and identification of bilinear systems. In "Theory and Applications of Variable Structures Systems" (R. R. Mohler and R. ), pp. 137-152, Academic Press, New York, 1972. C. S. KUBRUSLY and O. L. COSTA, Mean -square stability conditions for discrete stochastic bilinear systems. IEEE Trans. Autom. Control AC-30(11), 1082-1087 (1985). K. , Springer-Verlag, Berlin and New York, 1974. CONTROL AND DYNAMIC SYSTEMS COMPUTATIONAL TECHNIQUES FOR THE MATRIX PSEUDOINVERSE IN MINIMUM VARIANCE REDUCED-ORDER FILTERING AND CONTROL THOMAS H.