Control of Complex Systems: Methods and Technology by H. Abou-Kandil, M. Drouin, M. Mariton

By H. Abou-Kandil, M. Drouin, M. Mariton

Since the begining of the sixties, keep watch over theorists have constructed a wide physique of information relating advanced or large-scale platforms thought. utilizing the nation area procedure, their function used to be to increase easy methods to deal with the more and more subtle automation wishes of artificial platforms. regardless of a number of amazing contributions, and a few winning functions, it may be acknowledged that this idea has now not but develop into an engineering device. however, the emergence of inexpensive and trustworthy microprocessors has profoundly remodeled business instrumentation and keep watch over structures. approach keep watch over gear is equipped in multilevel dispensed constructions, heavily concerning the strategies brought by way of advanced platforms keep watch over concept. This similarity should still prefer a fruitful intersection for sensible purposes. although, a spot nonetheless exists among the literature on keep an eye on concept and the area of technological achievements. within the many books on advanced platforms, few have given recognition to the technological elements of a realistic keep an eye on challenge. the current e-book is an try and fill this hole. to do that, it regularly displays the viewpoints that: - idea and expertise are indivisible points of an identical challenge. -On-line implementation for actual time purposes is the last word aim of a keep an eye on study.

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This direction was pioneered by Bauman (1971) and Mesarovic et al. g. in Singh and Titli (1978), Singh and Hassan (1976), and Wassel and Wend (1979). A decomposition-coordination method is based on the following principle: - The initial optimization problem is decomposed into a set of sub-problems that are individually easier to solve. The obtained simplification can be for example a size reduction. Decomposition is attained through the parameterization of some variables, say A.. - The sub-problems are coordinated so that the concatenation of their solutions defines the overall solution.

For discrete-time systems and under the assumption that the control appears linearly in the state equations, the discrete TPBVP may be solved by first transforming it into an equivalent summation equation by a Green's function method (Falb and De Jong 1969, Halme et al. 1974). The main difficulty when applying such method arise from the dimensionality problem (the calculations are done using vectors of twice the system's dimension); also for practical reasons only a few terms in the series are used to determine the control law, which may lead to very poor results.

19) will be easier to manipulate for our purpose in this section. I U·lk (3 ' 1' 21) where the subsystems weighting matrices Q; and R; are respectively semi-positive definite and positive definite. As usual the global system (A, B, C) will be supposed observable and controllable. 2) K-1 N L L=L. k=O i=1 1 T 1 T {-2 X1·k Q,. lk + BII.. lk "" A.. 19). lk + w. lk + B II.. lk+1 k=O N "" T + P;k Z;k - ( £.... 24) To make the sub-Lagrangians independent, some variables are parameterized. Several choices are possible (Singh and Titli 1978), but it is only the interaction prediction approach that yields a mixed control structure.

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