Electrical and Electronic Engineering - Research Publications
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ItemMinimum phase properties for input nonaffine nonlinear systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-04)For input nonaffine nonlinear control systems, the minimum phase property of the system in general depends on the control law. Switching or discontinuous controllers may offer advantages in this context. In particular, 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 locally stable, whereas a discontinuous controller which achieves this exists. For single-input/single-output input nonaffine nonlinear systems we give sufficient conditions for existence and present a method for the design of discontinuous switching controllers which yield locally stable zero dynamics.
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ItemControllability of structured polynomial systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-04)Two algorithms, based on the Grobner basis method, which facilitate the controllability analysis for a class of polynomial systems are presented. The authors combine these algorithms with some recent results on output dead-beat controllability in order to obtain sufficient, as well as necessary, conditions for complete and state dead-beat controllability for a surprisingly large class of polynomial systems. Our results are generically applicable to the class of polynomial systems in strict feedback form.
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ItemStabilisability and stability for explicit and implicit polynomial systems: A symbolic computation approach(SPRINGER-VERLAG LONDON LTD, 1999)Stabilisability and stability for a large class of discrete-time polynomial systems can be decided using symbolic computation packages for quantifier elimination in the first order theory of real closed fields. A large class of constraints on states of the system and control inputs can be treated in the same way. Stability of a system can be checked by constructing a Lyapunov function, which is assumed to belong to a class of polynomial positive definite functions. Moreover, we show that stability/stabilisability can be decided directly from the ε-δ definition.
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ItemDead-beat control of simple Hammerstein models(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1998-08)Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonminimum-time state dead-beat controllers are given for certain classes of simple Hammerstein systems. A general minimum-time state dead-beat controller is presented for a class of simple Hammerstein systems. A design for a family of minimum-time control laws is provided. This enables, to a certain extent, shaping of transient response via choosing an appropriate control law. Finally, the authors design an output dead-beat controller for a class of Hammerstein systems that are not necessarily state dead-beat controllable.
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ItemDead beat controllability of polynomial systems: Symbolic computation approaches(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1998-02)State and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the Quantifier Elimination by Partial Cylindrical Algebraic Decomposition (QEPCAD) symbolic computation program. The method is unified for a very large class of systems and can handle one- or two-sided control constraints. Families of minimum time state/output dead beat controllers are obtained. The computational complexity of the test is prohibitive for general polynomial systems, but by constraining the structure of the system we may beat the curse of complexity. A computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented. Necessary and sufficient conditions are given. They are still very difficult to check. Therefore, a number of easier-to-check sufficient conditions are also provided. The latter are based on the Gröbner basis method and QEPCAD. It is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system.
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ItemOutput dead beat control for a class of planar polynomial systems(SIAM PUBLICATIONS, 1998-01)Output dead beat control for a class of nonlinear discrete time systems, which are described by a single input-output (I-O) polynomial difference equation, is considered. The class of systems considered is restricted to systems with a two-dimensional state space description. It is assumed that the highest degree with which the present input appears in the equation is odd. Necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented. We also design a minimum time output dead beat control algorithm (feedback controller) which yields stable zero dynamics, whenever this is feasible. A number of interesting phenomena are discussed and illustrated with examples.
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ItemInvariant Sets and Output Dead Beat Controllability for Odd Polynomial Systems: The Gröbner Basis Method(Elsevier BV, 1996)An algebraic test for output dead beat controllability for a class of odd polynomial systems is presented. Necessary and sufficient conditions are given. They are in general very difficult to check. Therefore, a number of easier-to-check sufficient conditions are also provided. The tests can be automatized using symbolic manipulation software packages and are based on the Gröbner basis method. Some examples are presented.