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Modeling and Verification using Different Notations for CPSs: The One-Water-Tank Case Study

Staroletov Sergey, Schulte Horst, Baar Thomas, Konyukhov Ivan, Shilov Nikolay, Rozov Andrei, Liakh Tatiana, Zyubin Vladimir

Annals of Computer Science and Information Systems

2021

Vol. 25

485--488

The choice of an adequate notation and subsequent system formalization are the crucial points for the design of cyber-physical systems (CPSs). Here, an appropriate notation allows an explicit specification of the deterministic system behavior for specified initial states and inputs. We base our study on an industrial example (water tank) that comprises nominal as well as safety-critical states, and focus on the notation’s support to validate/verify crucial safety properties. Several industrial notations (e.g. Matlab/Simulink©) to design and simulate such a hybrid system have been tried based on our physical model. In addition, we remodel our example using the well-founded mathematical formalism of hybrid automata. It enables us to formally express and verify important safety properties using the theorem prover KeYmaera

Fractional order tube model reference adaptive control for a class of fractional order linear systems

Balaska Hanane, Ladaci Samir, Djouambi Abdelbaki, Schulte Horst, Bourouba Bachir

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 3

501--515

We introduce a novel fractional order adaptive control design based on the tube model reference adaptive control (TMRAC) scheme for a class of fractional order linear systems. By considering an adaptive state feedback control configuration, the main idea is to replace the classical reference model with a single predetermined trajectory by a fractional order performance tube guidance model allowing a set of admissible trajectories. Besides, an optimization problem is formulated to compute an on-line correction control signal within specified bounds in order to update the system performance while minimizing a control cost criterion. The asymptotic stability of the closed loop fractional order control system is demonstrated using an extension of the Lyapunov direct method. The dynamical performance of the fractional order tube model reference adaptive control (FOTMRAC) is compared with the standard fractional order model reference adaptive control (FOMRAC) strategy, and the simulation results show the effectiveness of the proposed control method.