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In a Confucian tributary system, order was different from the Hobbesian jungle where men were equal but because of survival had to be hostile to each other, nor was it the same as in a Lockean society where people were equal but they had to be competitive to stay ahead of one another, and it was not a Kantian culture in which people were equal and friendly to each other.
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By using standard Hankels norm approximation technique, the system order is reduced from 27 to 11th order by retaining the dominant dynamic characteristics of the system.
It will be a valuable tool for identification of physiological and engineering systems in conditions where the system order is unknown and its parameters change with a SV.
Three issues, namely uncertainty, temporal behaviour, unknown system order, are however uncharted by any existing McSLMs and all McSLMs in the literature are designed for classification problems.
In addition, these methods assume the system order is known a priori, which is not necessarily true in practice.
Checking for the number of principal (dominant) singular values clearly indicates that the system order is N = 4.
Note that when the system order is unknown, different standard techniques, available in the literature [2], can be employed to estimate the order.
Specifically, researches have shown that chaos is achievable when the system order is less than 3, whereas hyperchaos can be obtained when the system order is less than 4. Referring to synchronization, studies have shown that chaotic fractional-order systems can also be synchronized [27].
This result verifies that the identification of system order is reliable regardless of the value of i as long as it is chosen to be larger than N.
Note that due to the Cayley-Hamilton theorem, an exponent larger than M−1, with M denoting the system order, is not required [28].
In fact, correctly identifying the system order is essential to ensure that subsequent parameter estimation will yield a well-defined set of model coefficient estimates.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com