Direct adaptive control using an adaptive reference model

Decentralized adaptive control of systems with uncertain interconnections, plant-model mismatch and actuator failures

“…In this case, the columns b i f ∈ R ni , (f = 1, 2, ..., m i ) of the known B i ∈ R ni×mi matrix are parallel to the reference model input matrix b mi ∈ R ni , b i f = b mi /α i f for some known α i f 's. The result can be easily extended for the case of unknown α i f (see [9]). The actuator failures are modeled in this paper as…”

“…Therefore, the nominal plant satisfies the matching condition. But the plant-model matching conditions could be violated due to abnormal changes in the plant or incorrect knowledge of the plant's mathematical structure [9]. In comparison to the previous results on decentralized adaptive control, dynamic systems consisting of interconnected subsystems with unknown interconnections are considered in this paper such that a plantmodel mismatch exists between the individual subsystems and their respective reference models.…”

“…That is, V (t) is bounded for all t, and standard stability analysis arguments [9] can be used to show that all signals and estimates are bounded, and lim t→∞ (x i (t) − x mi (t)) = 0, (i = 1, 2, ..., N ).…”

“…For simplicity of presentation, we shall assume that δa i (t) remains within the quadratic stability bounds, however, as is common in literature, a simple parameter projection algorithm [9], [10] can be used to ensure that this condition is met. Theorem 1: For the system given by (1), (10), the adaptive controller (6) with the gain adaptive lawṡ…”

“…This is feasible because of the availability of highly efficient numerical algorithms and the trend toward rapidly accelerating computational capability. To further ensure that the mismatch estimates remain within the permissible bounds, a projection algorithm (e.g., [9]) can be used.…”