Dynamical processes resulting from the interaction of conti nuous and discrete dynamics are often encountered in living organisms. T ime evolutions of such processes constitute continuous variables that ar e subject to instant changes at discrete points of time. Usually\, these discrete events cannot be observed directly and have to be reconstructe d from the accessible for measurement continuous variables.

\n\nTh us\, the problem of hybrid state estimation from measurements of continu ous outputs is important to and naturally arises in life sciences but\, so far\, scarcely covered in the existing literature.

\n\nThis the sis deals with a special class of hybrid systems\, where the continuous linear part is controlled by an intrinsic impulsive feedback that contri butes discrete dynamics. The impacting pulsatile feedback signal is not available for measurement and\, therefore\, has to be reconstructed. To estimate all the elements of the hybrid state vector\, an observation pr oblem is considered.

\n\nThe focus of the work is on a state obser vation problem for an analytically tractable example of a hybrid oscilla tor with rich nonlinear dynamics including\, e.g.\, monostable and bista ble high-periodic and quasiperiodic solutions as well as deterministic c haos. At the same time\, the three-dimensional case of the considered hy brid oscillator constitutes a mathematical model of testosterone regulat ion in the male validated through system identification on human endocri ne data. In a pulsatile endocrine regulation loop\, one of the hormones (releasing hormone) is secreted in pulses from neurons in the hypothalam us of the brain. Thus a direct measurement of the concentration of this hormone in the human is not possible for ethical reasons and it has to b e estimated in some manner from the available data\, for instance by app lying an observer.

\n\nIt is desirable for an observer to guarante e asymptotic convergence of the state estimate to that of the observable plant from all feasible initial conditions at a highest possible rate. When the state estimation error is zero\, the hybrid observer is in a sy nchronous mode characterized by the firings of the impulses in the obser ver feedback and those of the plant occurring simultaneously.

\n\nTherefore\, the observer design problem can be formulated as synchroniza tion of the plant states with those of the observer. This approach does not formally demand observability of the hybrid plant solution. Further\ , since the dynamics of the oscillator are highly nonlinear\, the state estimation problem is considered with respect to particular solutions of the observed system\, whose characteristics are assumed to be known\, b ut not the initial conditions. The observer design problem for the impul sive Goodwin'\;s oscillator consists of the selection of the observer structure and of assigning desired properties to a discrete map that ca ptures the observer state transitions from one impulse firing to another through manipulating the degrees of freedom of the observer. \;

\n DESCRIPTION:This thesis deals with a special class of hybrid systems\, wh ere the continuous linear part is controlled by an intrinsic impulsive f eedback that contributes discrete dynamics. SUMMARY:Hybrid observers for systems with intrinsic pulse-modulated feedb ack LOCATION:2446\, ITC\, Lägerhyddsvägen 2\, Uppsala TZID:Europe/Stockholm DTSTART:20190614T091500 DTEND:20190614T235900 UID:20190614T091500-45474@uu.se END:VEVENT END:VCALENDAR