 Electrical and Electronic Engineering  Research Publications
Electrical and Electronic Engineering  Research Publications
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ItemPointwise extremum seeking control scheme under repeatable control environmentTan, Y ; Mareels, I ; Nešić, D ; Xu, JX (IEEE, 20070101)

ItemExtremum Seeking From 1922 To 2010Tan, Y ; Moase, WH ; Manzie, C ; Nesic, D ; Mareels, IMY ; Chen, J (IEEE, 20100101)Extremum seeking is a form of adaptive control where the steadystate inputoutput characteristic is optimized, without requiring any explicit knowledge about this inputoutput characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and timescale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.

ItemOn the use of switched linear controllers for stabilizability of implicit recursive equationsNesic, D (IEEE, 19980101)Stabilizability of implicit recursive equations is investigated. These equations arise naturally in the context of output deadbeat control for systems described by NARMAX models. Due to nonuniqueness of the solutions of these equations a special kind of a constrained stabilizability problem is considered. We take a hybrid switching control approach in testing the existence of a locally stabilizing controller. A method for the design of a stabilizing switching controller is also presented.

ItemStability of high order polynomial dynamics and minimum phase discretetime systemsNešić, D ; Mareels, IMY (IEEE, 19970408)The definition of a minimum phase nonlinear system, as usually found in the literature, is not general enough to be used for some classes of systems. The nonlinearity may yield a variety of different behaviors that are not addressed and analyzed in the literature. We provide a constructive method to test several different minimum phase properties for classes of explicit and implicit discretetime polynomial systems. The method is based on a symbolic computation package called QEPCAD. Our results can also be interpreted as a constructive approach to stability and stabilizability of explicit and implicit discretetime polynomial systems.

ItemAn output dead beat controllability test for a class of odd polynomial systemsNešić, D ; Mareels, IMY (IEEE, 19970408)An output dead beat controllability test that stops after finitely many rational operations is presented for a class of odd polynomial systems. The test is based on the Gröbner basis method but it needs to be facilitated in general with the QEPCAD symbolic computation package. Geometric properties due to which output dead beat controllability may be lost are identified and analysed. The computational requirements are smaller when compared with the known output dead beat controllability tests.

ItemOn some triangular structures and the state deadbeat problem for polynomial systemsNesic, D ; Mareels, IMY (I E E E, 19970101)QEPCAD based controllability testing for polynomial discretetime systems is computationally very expensive and it may lead to nonterminating algorithms. We identify the structure of a large class of polynomial discretetime systems, which reduces the computational cost associated with the deadbeat controllability test and which may lead to finite time controllability tests. For this purpose we use QEPCAD and the Grobner basis method. The structure which we identify encompases several classes of systems for which deadbeat controllability tests exist.

ItemAnalysis of minimum phase properties for nonaffine nonlinear systemsNesic, D ; Skafidas, E ; Mareels, IMY ; Evans, RJ (IEEE, 19970101)A system can be termed nonminimum phase according to some definitions available in the literature and yet the same system may exhibit stable zero output constrained dynamics. We show that for nonaffine nonlinear systems there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are stable, whereas a discontinuous controller which achieves this exists. We give conditions for existence and present a method for design of discontinuous switching controllers which yield stable zero dynamics. In this sense, the results of this paper enlarge the class of nonaffine nonlinear systems that can be termed minimumphase.

ItemNecessary and sufficient conditions for output dead beat controllability for a class of polynomial systemsNesic, D ; Mareels, I ; Bastin, G ; Mahoney, R (I E E E, 19950101)Output dead beat control for a class of non linear discrete time systems, which are described by a single inputoutput polynomial difference equation, is considered. Necessary and sufficient conditions for the existence of output dead beat control (or output controllability in finite time) are presented. A tractable output dead beat controllability test is obtained.

ItemA note on the control of a spherical inverted pendulumLiu, G ; Mareels, I ; Nešić, D (IFAC, 20070101)We carry out extensive numerical simulations of a spherical inverted pendulum with various controllers to verify our theoretical developments. The simulations are useful in quantitatively understanding the operation of the system with different controllers and checking that the theoretical results are consistent with the numerical results. Using the numerical simulations, we also discuss in some detail various important aspects of the performance of the closed loop systems in order to compare the controllers.

ItemOn automatic seeking of optimal steadystates in biochemical processesBastin, G ; Nešić, D ; Tan, Y ; Mareels, I (IFAC, 20070101)It is discussed how the automatic seeking of optimal steady states biochemical reactors can be achieved by using nonmodel based extremumseeking control with semiglobal practical stability and convergence properties. A special attention is paid to processes with multiple steadystates and multivalued cost functions.
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