Accession Number : ADA506882


Title :   Switching Systems: Controllability and Control Design


Descriptive Note : Final rept. 1 May 2008-25 Apr 2009


Corporate Author : HUNGARIAN ACADEMY OF SCIENCES BUDAPEST HUNGARY COMPUTER AND AUTOMATION RESEARCH INST


Personal Author(s) : Bokor, Jozsef ; Gaspar, Peter ; Szabo, Zoltan


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a506882.pdf


Report Date : 25 Apr 2009


Pagination or Media Count : 54


Abstract : We consider two classes of switches: switches-on-time and switches-on-state. Switching-on-time is the simplest of the two and it can be considered as an intrinsic (or endogenous) switching scheme in the sense that it involves only changes in the tangent space (switching from one element to another one of the family of vector fields) without need to check what happens on the flow of the solution. In endogenous switching one assumes to have complete control over the time of switch, i.e., the time instant in which the switching occurs, and over the switching pattern, i.e., which of the systems is activated (selected) in the switching event. This type of switching is called open-loop switching. Switching-on-state is more complicated: it requires a check on the integral curve of the system in order to decide when to pass from a dynamic mode to another one (exogenous switching). It is an important observation that any switching-on-state path has a unique corresponding switching-on-time path, however these switching times and switching patterns depend on the state. Controllability of switching systems has been investigated mostly for the linear case, i.e., when the dynamics in the given modes are linear time invariant (LTI) and the case when arbitrary switching is possible (open--loop switching). By using geometric methods and imbedding linear switching systems in the class of the linear parameter varying systems (LPV) we have obtained controllability results. In contrast, bimodal systems are special classes of switching systems, where the switch from one mode to the other one depends on the state (closed-loop switching). In the simplest case the switching condition is described by a hypersurface in the state space.


Descriptors :   *CONTROL THEORY , *LINEAR SYSTEMS , *ALGORITHMS , ALGEBRAIC FUNCTIONS , CLOSED LOOP SYSTEMS , DWELL TIME , SWITCHES , THEOREMS , HUNGARY , VECTOR SPACES , FEEDBACK , STABILIZATION , OPEN LOOP SYSTEMS


Subject Categories : Numerical Mathematics
      Cybernetics


Distribution Statement : APPROVED FOR PUBLIC RELEASE