témavezető: Tar József
helyszín (magyar oldal): Óbudai Egyetem helyszín rövidítés: ÓE
A kutatási téma leírása:
In the practice, precise and efficient control is needed for certain state variables of multiple variable physical systems in which the number of the independent control variables is less than that of the independent state variables. In such cases, either the propagation of certain state variables is completely abandoned or the concept of the Model Predictive Control (MPC) is applied in which the model of the controlled system is embedded into the mathematical framework of the Optimal Controllers. This approach uses a cost function that summarizes the contributions of the frequently contradictory requirements. By minimizing this cost a kind of "compromise" is achieved. Whenever approximate and/or incomplete system models are available, the use of this controller is justified only for short time-intervals. The only way to reduce the accumulation of the effects of the modeling errors is the frequent re-design of the time horizon from the actual state as initial state that is done by the Receding Horizon Controllers [1]. The more sophisticated Adaptive Controllers are designed by the use of Lyapunov’s "Direct Method" [2] that has a complicated mathematical framework that cannot easily be combined with that of the optimal controllers. As a potential competitor of the Lyapunov function-based adaptive controllers a Fixed Point Transformation-based approach can be suggested [3] that in the first step transforms the the problem of computing the control signal into the task of finding an appropriate fixed point of a contractive map. The fixed point can be found by iteration in which the iterative sequence is generated by this contracting map [4]. This method can be used for contradiction resolution without the minimization of any cost function by tracking the observable state components with time-sharing on a rotary basis.
An alternative approach may be the modification of the Classic Receding Horizon Controller in which, following the finite horizon design made by the use of the available approximate dinamic model, instead exerting the so calculated control signals the modification of the nominal trajectory is adaptively tracked by the Fixed Point Transformation-based method.
In the research making comparative simulation investigations are planned. Depending on the complexity of the available dynamic models and cost functions, besides the classic LQR controller [5] and the use of the Riccati equations [6] the application of Nonlinear Programming is expected, too.
References
[1] J. Richalet, A. Rault, J.L. Testud, and J. Papon. Model predictive heuristic control: Applications to industrial processes. Automatica, 14(5):413–428, 1978.
[2] A.M. Lyapunov. Stability of motion. Academic Press, New-York and London,1966.
[3] J.K. Tar. Towards Replacing Lyapunov’s ”Direct” Method in Adaptive Control of Nonlinear Systems (invited plenary lecture at the Mathematical Methods in Engineering Intl. Symp. (MME), 21-24 October 2010, Coimbra, Portugal), chapter in Mathematical Methods in Engineering (Eds.: N.M. Fonseca Ferreira & J.A. Tenreiro Machado). Springer Dordrecht, Heidelberg, New York, London, 2014.
[4] S. Banach. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (About the Operations in the Abstract Sets and Their Application to Integral Equations). Fund. Math., 3:133–181, 1922.
[5] Brian D.O. Anderson and John B. Moore. Optimal Control: Linear Quadratic Methods. Prentice – Hall International, Inc., A Division of Simon & Schuster, Englewood Cliffs, NJ 07632, 1989.
[6] [14] Tayfun Cimen. State-dependent Riccati equation in nonlinear optimal control synthesis. In the Proc. of the Special International Conference on Complex Systems: Synergy of Control, Communications and Computing - COSY 2011, Hotel Metropol Resort, Ohrid, Republic of Macedonia, September, 16 – 20, 2011, pages 321–332, 2011.
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