Optimal approximation of linear systems by artificial immune response. (English) Zbl 1107.93005
Summary: This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proved that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one shows that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.
MSC:
| 93A30 | Mathematical modelling of systems (MSC2010) |
| 93B40 | Computational methods in systems theory (MSC2010) |
| 92C50 | Medical applications (general) |
Keywords:
approximation of linear systems; artificial immune systems; immune response; clonal selection; immunological memoryReferences:
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