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By H. Jerome Keisler

ISBN-10: 0821822977

ISBN-13: 9780821822975

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Structural feedback control of discrete linear stochastic systems with quadratic cost. IEEE Trans. Automatic Control, AC-22(1977): 232-236. 22. , N. Nichols, and P. Van Douren. Robust pole assignment in linear state feedback. Int. J. Control, 41 (1985): 1129-1155. 23. Khalil, H. Multi-model design of a Nash strategy. J. Optimization Theory and Applications, 31( 1980): 553-564. 24. Khalil, H. and P. Kokotovic. Control strategies for decision makers using different models of the same system. IEEE Trans.

If estimates of the noise statistics are needed, they can be obtained either in a second step after identifying the system parameters, or simultaneously by a combined second and fourth order statistics based method. C u m u l a n t S t a t i s t i c s : In the sequel we will use higher order cumulant statistics of an error signal. It is therefore useful to recall certain results from [23] and [24] that we will use later. The (joint) fourth cumulant of the zero-mean random variables f ( t l ) , f(t2), f(t3) and f ( t 4 ) i s given by cum4{f(tl), f(t2), f(t3), f(t4)} - E { f ( t l ) f ( t 2 ) f ( t 3 ) f ( t 4 ) } -E{f(tl)f(t2)}E{f(ta)y(t4)}- -E( f(t ) f(t, E{f(tl)f(ta)}E{f(t2)y(t4)} f(t )} (II-lO) provided the appropriate moments exist.

And K. Furuta. On the bilinear transformation of Riccati equations. IEEE Trans. Automatic Control, AC-31(1986): 50-54. 29. Kwakernaak, H. and R. Sivan, Linear Optimal Control Systems, Wiley Interscience, New York, 1972. 30. Lewis, F. Optimal Control, Wiley, New York, 1986. 31. Mahmoud, M. A quantitative comparison between two decentralized control approaches. Int. J. Control, 28(1978): 261-275. 32. Medanic, J. Geometric properties and invariant manifolds of the Riccati equation. IEEE Trans. Automatic Control, AC-27(1982): 670--677.

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An Infinitesimal Approach to Stochastic Analysis by H. Jerome Keisler

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