Identification and Control of MIMO Linear Systems under Sufficient and Insufficient Excitation

In closed-loop identification of unknown control systems, stability is a major concern. Particularly, when the system does not proceed with sufficient excitation. In this paper, a closed-loop identification strategy for Multi-Input Multi-Output (MIMO) linear systems is intended via a robust adaptive control law based on Sliding Mode Control (SMC). Under both sufficient and insufficient excitation of the system, Evolving Linear Models (ELMs) are deployed to identify and control the system. It is explained that under insufficient excitation, linear correlations between input and output signals and their derivatives can be removed. An equivalent reduced-order model of the original system results which can be identified as an ELM. Defining the control law based on the SMC and using appropriate adaptation rules for parameters of the model, the tracking errors converge to zero and the stability of the system is guaranteed. Meanwhile, the parameters of the model converge to their true values. Simulation results demonstrate the efficacy of the proposed approach.