Recursive Immuno-Inspired Algorithm for Time Variant Discrete Multivariable Dynamic System State Space Identification

Abstract

In this paper a recursive immuno inspired algorithm is proposed to identify time variant discrete multivariable dynamic systems. The main contribution of this paper has as starting point the idea that a multivariable dynamic system state space model can be seen as a point in a space defined by all possible matrices quadruples that define a state space model. With this in mind, the time variant discrete multivariable dynamic system modeling is transformed in an optimization problem and this problem is solved with an immuno inspired algorithm. To do that the inputs given to the system and the resulting outputs are divided in small sets containing data from small time intervals. These sets are defined as time windows, and for each window an immuno inspired optimization algorithm is applied to find the state space model that better represents the system at that time interval. The initial candidate solutions of each time interval are the ones of the last interval. The immuno inspired algorithm proposed in this paper has some modifications to the original Opt-AINet algorithm to deal with the constraints that are natural from the system identification problem and these modifications are also contributions of this paper. The method proposed in this paper was applied to identify a time variant benchmark system, resulting in a time variant model. The outputs estimated with this model are closer to the benchmark system outputs than the outputs estimated with models obtained by other known identification methods. The Markov parameters of the variant benchmark system are also reproduced by the time variant model found with the new method.