State space model calculation method, system and equipment of multivariate fractional order system

Abstract

The invention discloses a state space model calculation method, system and device for a multivariate fractional order system, and the method comprises the steps: obtaining a rational transfer matrix of the multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix; extracting a polynomial transfer vector of the polynomial transfer matrix; constructing a directed graph meeting a preset condition according to the polynomial transfer vector; determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset construction vector, the polynomial transfer vector, a preset first relational expression and a preset corresponding relation; determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix; and determining a state space model corresponding to the rational transfer matrix according to the second model parameter, a preset operation rule and a preset model relational expression. According to the method, the state space model of which the internal dimension is much lower than that of an existing method can be generated.

Description

Technical field [0001] The present invention relates to the technical field of model prediction, in particular to a multivariate fractional order system state space model calculation methods, systems and equipment. Background [0002] Fractional-order calculus belongs to a mathematical tool-based, in terms of control science, fractional calculus equations can be used to make a good mathematical description of the fractional order control system, and on this basis for the dynamic and stable performance analysis of the system, fractional calculus is like a new language, with its unique logic and grammar rules. Among them, multivariate fractional order systems have been widely used in various fields, such as industrial automation, economics, and anomalous diffusion in semi-infinite waves. [0003] A basic problem of the multivariate fractional order system is the implementation of the state space model, that is, the state space model is established by the transfer matrix, because t...

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Problems solved by technology

However, unlike the traditional integer case, obtaining a minimal state-space model of a multivariate fractional order system is often very difficult

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