Adaptive controllers with explicit and implicit reference models and stochastic self tuning regulators-eqivalence and duality aspects
It is shown in this paper that : 1) The Minimum Variance Self Tuning Regulators and a configuration of Adaptive Controllers with Implicit (or Explicit) Reference Model feature an asymptotic duality character which extends the duality existing in the linear case with known parameters between the minimum variance control and the modal control. 2) Adaptive Control with an Explicit Reference Model is equivalent to an Adaptive Control with an Implicit Reference Model using an intermediate adaptive predictor, if the adaptive predictor plus the control behave like the explicit reference model. 3) The result of 1) is generalized by considering the asymptotic duality between Model Reference Adaptive Controllers and the class of Stochastic self Tuning Regulators which contains the self tuning minimum variance regulator as a particular case.
The specification of non-functional requirements, e. g., on timing forms an essential part of modern system design. Modeling languages such as MARTE/CCSL provide dedicated description means enabling engineers to formally define the ticking of the clocks to be implemented in terms of clock constraints and the actually intended timing behavior in terms of instant relations. But thus far, instant relations have only been utilized in order to monitor the correct execution of the clock constraints. In this work, we propose a methodology which, for the first time, verifies clock constraints against the given instant relations. To this end, the timing behavior is represented in terms of an automaton followed by its verification through satisfiability solvers. A case study illustrates the application of the proposed methodology.