témavezető: Tar József
helyszín (magyar oldal): Óbudai Egyetem helyszín rövidítés: ÓE
A kutatási téma leírása:
In the field of model-based control or Model Predictive Control (MPC) in the practice various problems used to occur as
1) The imprecision and incompleteness of the available system models;
2) The lack of possibility for measuring each state variable;
3) In many cases the state variables depend on the directly measurable quantities through functions of uncertain parameters that show great variability;
4) The high complexity, often too high order of the available models;
5) Limitations in the possible control actions;
6) Often we have strongly underactuated systems that means that it is impossible to precisely control each state variable simultaneously;
7) In many cases between the observations and the control action some time-delay is present.
Depending on the circumstances the extent of the delay can be known in advance as a fixed value or it may be uncertain.
For instance, in the description of the illness of Diabetes Mellitus, various models are developed for the same phenomenon. For instance the “Minimal Model” by Bergman that has only a few state variables [1] and the more complex, 10 compartment model by Dalla Man et al. [2], try to describe the same glucose-insulin system. In the anaesthesia models a "fictitious" state variable is applied in the model that does not cover some real part of the human body: its role is to describe some time-delay effects (e.g. [3, 4]). The sensitivity of the patients are related to the measurable signals as the “Bispectral Index” [5], or the EEG signals of the central nervous system processed by wavelet analysis [6]; this relation is described by the strongly nonlinear Hill curve with parameters of great interpatient standard deviations.
The basic idea of the novel approach here suggested is the strict separation of the kinetic (kinematic) and dynamic aspects in the control by using an incomplete and approximate inverse dynamic model of the system under control to estimate the necessary "control forces" that can result in the kinematically prescribed "system response". If the so calculated "forces" would be exerted on the controlled system without any modification, due to the modeling errors, the obtained and observed response would be different to the prescribed one. Instead trying to "learn" the precise model of the controlled system the method generates an iterative sequence in real time so that this sequence converges to the solution of the control task. In the case of a digital controller in each control cycle there is possibility to make only one step in the iteration. The iterative sequence is generated by a contractive map according to Banach’s Theorem [7]. For the generation of the contractive map various novel functions were suggested recently. This method ab ovo works with time-delays: the controller learns from the past data.
The structure of this novel approach is far more simple and versatile than that of the Lyapunov-Krasovskii functionals-based methods are. If it is known that the response immediately appears (as e.g. in Classical Mechanics the acceleration immediately appears with the appearance of the action force), then exactly the same delay times (the cycle length of the digital controller) must be applied for the past control action and for its effect. If we have some information according to which it can be expected that the response is delayed with respect to the action we have possibility to apply asymmetric delay times without extra mathematical difficulties. We also can see that too long delays may cause learning from a more or less obsolete information that may degrade the precision of the control.
The planned research mainly aims at theoretical considerations and for illustration of the results, numerical simulations. Consequently it can be realized by simple and already existing tools as laptops working under WINDOWS or LINUX operating systems, the freely applicable SCILAB – XCOS simulation package and TEX-type word processors, or the Atom - Julia softwares with the Python’s graphical library (MATPLOTLIB) – also freely accessible.
References
[1] R.N. Bergman, Y.Z. Ider, C.R. Bowden, and C. Cobelli. Quantitative estimation of insulin sensitivity. Am. J. Physiol. Endocrinol. Metab., 236:E667–E677, 1979.
[2] C. Dalla Man, R.A. Rizza, and C. Cobelli. Meal simulation model of glucose-insulin system. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 54(10):1740–1749, 2007.
[3] C.M. Ionescu, R. De Keyser, B.C. Torrico, T.D. Smet, M.M.R.F. Struys, and J.E. Normey-Rico. Robust predictive control strategy applied for Propofol dosing using BIS as a controlled variable during anesthesia. IEEE Transactions on Biomedical Engineering, 55(9):2161–2170, 2008.
[4] I. Nascu, R. Oberdieck, and E.N. Pistikopoulos. Offset-free explicit hybrid model predictive control of intravenous anaesthesia. In: Proc. of the of the 2015 IEEE International Conference on Systems, Man, and Cybernetics, October 9-13, 2015, Hong Kong, pages 2475–2480, 2015.
[5] M.M.R.F. Struys, H. Vereecke, A. Moerman, E.W. Jensen, D. Verhaegen, N. De Neve, F.J.E. Dumortier, and E.P. Mortier. Ability of the Bispectral Index, autoregressive modelling with exogenous input-derived auditory evoked potentials, and predicted Propofol concentrations to measure patient responsiveness during anesthesia with Propofol and Remifentanil. Anesthesiology, 99(4):802–812, 2003.
[6] T. Zikov, S. Bibian, G.A. Dumont, M. Huzmezan, and C.R. Ries. Quantifying cortical activity during general anesthesia using wavelet analysis. IEEE Transactions on Biomedical Engineering, 53(4):617–632, 2006.
[7] 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.
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