A robust decentralized model reference adaptive control for non-minimum-phase interconnected systems
Discrete time, single-input, single-output, scalar interconnected systems of the following form are considered: \[ Y_i(t) = \phi_i^{\ast}(t-1) \theta_i^{\ast} + \sum_{j=1, j\not=i}^N C_{ij}(q^{-1}) + \xi_i(t), \qquad i=1,\ldots,N \] where \(C_{ij}(q^{-1})\) are polynomials in the shift \(q^{-1}\), \(\phi_i^{\ast}(t-1)\) denotes the regression vector of inputs \(U_I(\cdot)\) and outputs \(Y_i(\cdot)\), \(\theta_i^{\ast}\) contains the unknown parameters of the nominal subsystem, and \(\xi_i(t)\) represents the unmodelled response. The control objective is to stabilise the global system with no information exchange between the subsystems. This is achieved by a decentralised model reference adaptive control law, which does not use the \(\sum C_{ij}(q^{-1}) + \xi_i(t)\), and relies on robust parameter estimation (a combination of adaptive data filtering and recursive least-square algorithm). Known upper bounds of the system order and time delays, and bounds of \(\|\theta^{\ast}_i\|\) are (beside other conditions) required.
scientific article; zbMATH DE number 1348270