Learning, Control and Hybrid Systems: Festschrift in Honor by Yutaka Yamamoto, Shinji Hara

By Yutaka Yamamoto, Shinji Hara

This quantity covers a wide selection of papers on studying, regulate and hybrid platforms. The papers are the lawsuits of the Bangalore Workshop held in January 1998, that honoured the fiftieth birthdays of Mathukumalli Vidyasagar and Bruce Allen Francis. The 27 papers, written via foreign experts within the box, hide various pursuits. The editors have grouped those into the next four different types: a) studying and Computational matters b) Hybrid structures c) Modeling, id and Estimation d) strong keep an eye on. The study components are varied and entire, giving the reader a distinct chance to discover various fields during which control/system theorists could be . particular themes contain: studying in dynamical platforms, randomized algorithms in strong keep watch over layout, identity of platforms, electronic sign processing, strong and H-infinity keep watch over, regulate of hybrid platforms and supervisory regulate. This booklet also will offer readers with an perception into destiny instructions on top of things and method conception, as they're envisioned through specialists from worldwide. Readers also will reap the benefits of having the ability proportion with the members within the fascinating new methods to regulate and method idea that have been mentioned on the workshop. destiny instructions are estimated via specialists from worldwide.

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Then the condition p(w) > 0 Vw is satisfied if and only if r(8) has exactly n~ zeros in the left half-plane and exactly n~ zeros in the right half-plane. ), there 2Strictly speaking, we should write -~(c < 1) instead of c = 1. Vidyasagar 22 are exactly n~ negative determinants. This is a Boolean formula in these determinants. Moreover, each of these determinants is a rational function of x, y, c, and the maximum degree of any determinant with respect to y and c is 2~vn~. Since none of these rational functions has any poles in X x Y x [0, 1), it is possible to clear the denominators and to express the conditions in terms of 2n,~ polynomial inequalities in x,y,c.

The inherent complexity of some of the most elementary problems in systems and control points to the necessity of using alternative approximate techniques to deal with problems that are unsolvable or intractable when exact solutions are sought. We survey some of the decidability and complexity results available for three classes of discrete time nonlinear systems. In each case, we draw the line between the problems that are unsolvable, those that are NP-hard, and those for which polynomial time algorithms are known.

For convenience, let nc := as + f~s denote the McMillan degree of the closedloop transfer function, and let n,~ denote the McMillan degree of the weighted closed-loop transfer function W(1 + GK) -1. Define the symbols gu(-) and G as before. T h e o r e m 5 With all symbols as above, we have P-dim(G) <_ 2(l + 1)lg[8el3un~(2nc + 2n~ + 1)]. ) function. Thus the bounds given above will be rather small even for high-order control systems. However, the integer l, representing the number of "degrees of freedom" in the parameter y, appears linearly in the upper bound.

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