By Ronald R. Mohler
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Extra resources for Bilinear Control Processes: With Applications to Engineering, Ecology, and Medicine
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In his theory on thermodynamics, he presented the concept of controllability and studied the reachable zones of nonlinear thermodynamic processes with multiplicative control. There are numerous degrees of state controllability and output controllability that are formally defined in the literature. These are discussed in detail by Hsu and Meyer [2], Athans and Falb [3], and Lee and Markus [4]. In this book, controllability will refer to state controllability unless otherwise specified. This is the most common convention.
REFERENCES 1. Weed, L. ” Case-Western Res. Univ. Press, Cleveland, Ohio, 1964. Davis, R. , Communication for the medical community-a prototype of a special interest audience. Proc. AIAA Annu. Meeting, 6th, Anaheim, California, October 20-24, 1969, Paper No. 69-1072. 3. Interdisciplinary research topics in urban engineering. Rep. Urban Engrg. Study Committee. Amer. Engrg. , 1969. 4. Future fields of control application. NASA Symp. MIT, Cambridge, Massachusetts, February 10-11,1969. Available through Sci.
8), there are several conclusions that can be derived directly from linear system theory. 8) is not completely controllable if and only if (A, C) and (ByC) are not completely controllable. 8) to be completely controllable. 9) can be completely controllable even if (A, C) and (ByC) are not completely controllable. 3 Sufficient Conditions for Complete Controllability 27 where v E Rm-a,u E Ra, and the other terms are as defined in Eq. 9). Also, u, v are bounded and measurable controls on [0, co). The main result for this system, based on the theory of Lie groups as given by Chevalley [8], is to define the set of attainable points in state space by a so-called maximal integral manifold.