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STABILIZING THE PERIODIC ORBITS IN A CHAOTIC MAPPING DESCRIBING THE DISCRETE HEALTH SYSTEMS VIA PREDICTION-BASED CONTROL

In the paper the problem of location and stabilization of unstable periodic orbits (UPOs) in discrete systems is investigated via the prediction-based control (PBC). It involves using the state of the free system one period ahead as reference for the control signal. Two types of control gains are tested, the first requiring the knowledge of the UPO to be stabilized and the second depending only on the actual state of the trajectory. The effectiveness of PBC is demonstrated on a chaotic mapping describing the malignant tumor growth. When the results obtained with the two control laws are compared with each other, it is found that the second variant is qualitatively superior, both in terms of convergence and the number of stabilized UPOs, especially for long-period orbits.