Extreme properties of an adaptive control system with identification (application of identifiability equations). I. A one control input—one output plant

The impact is discussed of process non-identifiability on extreme (as the timeincreases) properties of the adaptive control system with identification. The set of process non-identifiability is described in an extreme adaptive system; sufficient conditions of process identifiability are reported; the controller optimality and system stability are analyzed for a non-identifiable process. The algorithm for computing the estimates of unknown process parameters is not described in detail but the estimates are assumed to converge in some probabilistic sense. To solve the problem by identifiability equations, only the knowledge of the process and controller structures is used.