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126 Systems combining linearity and saturations, and relations to “neural nets”
Abstracts
896
123 Software Development for Programmable Logic Controllers - A Methodology and a System J.P. Estlma de Oliveira, J.L. Azevedo, J.A. Ferreira, P.J. Ferreira, pp 233-238 A universal methodology and a system to program PLCs are presented. The system front end is a Graphical User Interface (GUI), supporting the relay ladder language and a simulator. The GUI is a user-friendly environment with menus, icons and a point-and-click interface. After
the GUI, an Intermediate Literal Language (ILL) implements a virtual PLC. ILL file.s are then used by specific parser-drivers (developed with lex and yacc utilities), to translate ILL det'mitions into real PLC statements. Object-oriented programming techniques, based on C++, are used, along with Blaise Win++ class library. The system runs as a Microsoft Windows application.
Abstracts in this section are from papers presented at: IFAC SYMPOSIUM ON NONLINEAR CONTROL SYSTEMS DESIGN Bordeaux, France, 24-26 June 1992 Full papers appear in the Proceedings volume to which the page numbers relate, published by IFAC and available from Pergamon Press. (ISBN: 0 08 041901 1)
124 Recent Advances in the Stabilization Problem for Low Dimensional Systems W.P. Dayawansa, pp 1-8 This paper surveys recent advances on the stabilization for two- and three-dimensional, single-input, affine nonlinear systems. Among the new results given here is a theorem which states that a generic, single-input, threedimensional, homogeneous polynomial system of a fixed odd degree p can be asymptotically stabilized by using homogeneous feedback of degree p.
125 Nonlinear/-/lq Control and Hamilton-Jacobt Inequalities A. van der Schaft, pp 9-14 Although the linear HIq control problem was originally formulated in the frequency domain, its translation to the time-domain has a clear interpretation which naturally extends to nonlinear systems. The H]q optimal control problem can be formulated as the optimal attenuation of the L2-gain from unknown disturbances entering the system to a set of to-be-controlled variables; it can therefore be centred around the classical Bounded Real Lemma in the linear case, and in the nonlinear case to generalizations of this lemma. The paper surveys previous work and makes some new observations. Nonlinear H]q control appears to be an area where modem nonlinear control theory can be fruitfully combined with more-classical theory.
126 Systems Combining Linearity and Saturations, and Relations to "Neural Nets" E.D. Sontag, pp 15-21 This paper deals with control systems consisting of linearly interconnected integrators (or delay lines) and scalar nonlinearities. For linear systems with saturating sensors, results on observability and minimal realization are mentioned. When saturations appear in actuators, questions of control become of interest, and stabilization techniques are described in the paper. If there are
feedback loops containing the nonlinearities, "recurrent neural nets" are obtained, and various issues relating to their computational power and identifiability of parameters are discussed.
127 A Dynamical Systems Approach to Control
F. Colonius, W. Kliemann, pp 23-29 Control systems can be viewed as dynamical systems over (infinite) dimensional state spaces. From this point of view the long-term behaviour of control systems, such as limit sets, Morse sets, approximations on the entire time axis, ergodicity, Lyapunov exponents, stable and unstable manifolds, etc., becomes accessible. This paper presents some of the underlying theory, as well as applications to the global characterization of control systems with bounded control ranges that are not completely controllable, to control of chaotic systems, and to exponential stability of uncertain systems.
128 Dynamical Discontinuous Feedback Control of Non-Linear systems H. Sira-Ramirez, pp 31-36 Discontinuous feedback stabilization of nonlinear systems, expressed in generalized state represen-tation form, is accomplished by zeroing of a suitable inputdependent manifold. Pulse frequen-cy modulation, pulse width modulation and sampled sliding mode control strategies are treated from a unified viewpoint which naturally arises from fundamental results of the differential algebraic approach to systems dynamics and control. The approach leads naturally to dynamical discontinuous feedback policies resulting in (chatteringfree) smoothed constrained linearization and induced robust asymptotic output error stabilization. The results are applicable in a variety of nonlinear control problems, including stabilization, tracking, and model matching. Illustrative examples from non-traditional application areas are presented with simulations.
896
123 Software Development for Programmable Logic Controllers - A Methodology and a System J.P. Estlma de Oliveira, J.L. Azevedo, J.A. Ferreira, P.J. Ferreira, pp 233-238 A universal methodology and a system to program PLCs are presented. The system front end is a Graphical User Interface (GUI), supporting the relay ladder language and a simulator. The GUI is a user-friendly environment with menus, icons and a point-and-click interface. After
the GUI, an Intermediate Literal Language (ILL) implements a virtual PLC. ILL file.s are then used by specific parser-drivers (developed with lex and yacc utilities), to translate ILL det'mitions into real PLC statements. Object-oriented programming techniques, based on C++, are used, along with Blaise Win++ class library. The system runs as a Microsoft Windows application.
Abstracts in this section are from papers presented at: IFAC SYMPOSIUM ON NONLINEAR CONTROL SYSTEMS DESIGN Bordeaux, France, 24-26 June 1992 Full papers appear in the Proceedings volume to which the page numbers relate, published by IFAC and available from Pergamon Press. (ISBN: 0 08 041901 1)
124 Recent Advances in the Stabilization Problem for Low Dimensional Systems W.P. Dayawansa, pp 1-8 This paper surveys recent advances on the stabilization for two- and three-dimensional, single-input, affine nonlinear systems. Among the new results given here is a theorem which states that a generic, single-input, threedimensional, homogeneous polynomial system of a fixed odd degree p can be asymptotically stabilized by using homogeneous feedback of degree p.
125 Nonlinear/-/lq Control and Hamilton-Jacobt Inequalities A. van der Schaft, pp 9-14 Although the linear HIq control problem was originally formulated in the frequency domain, its translation to the time-domain has a clear interpretation which naturally extends to nonlinear systems. The H]q optimal control problem can be formulated as the optimal attenuation of the L2-gain from unknown disturbances entering the system to a set of to-be-controlled variables; it can therefore be centred around the classical Bounded Real Lemma in the linear case, and in the nonlinear case to generalizations of this lemma. The paper surveys previous work and makes some new observations. Nonlinear H]q control appears to be an area where modem nonlinear control theory can be fruitfully combined with more-classical theory.
126 Systems Combining Linearity and Saturations, and Relations to "Neural Nets" E.D. Sontag, pp 15-21 This paper deals with control systems consisting of linearly interconnected integrators (or delay lines) and scalar nonlinearities. For linear systems with saturating sensors, results on observability and minimal realization are mentioned. When saturations appear in actuators, questions of control become of interest, and stabilization techniques are described in the paper. If there are
feedback loops containing the nonlinearities, "recurrent neural nets" are obtained, and various issues relating to their computational power and identifiability of parameters are discussed.
127 A Dynamical Systems Approach to Control
F. Colonius, W. Kliemann, pp 23-29 Control systems can be viewed as dynamical systems over (infinite) dimensional state spaces. From this point of view the long-term behaviour of control systems, such as limit sets, Morse sets, approximations on the entire time axis, ergodicity, Lyapunov exponents, stable and unstable manifolds, etc., becomes accessible. This paper presents some of the underlying theory, as well as applications to the global characterization of control systems with bounded control ranges that are not completely controllable, to control of chaotic systems, and to exponential stability of uncertain systems.
128 Dynamical Discontinuous Feedback Control of Non-Linear systems H. Sira-Ramirez, pp 31-36 Discontinuous feedback stabilization of nonlinear systems, expressed in generalized state represen-tation form, is accomplished by zeroing of a suitable inputdependent manifold. Pulse frequen-cy modulation, pulse width modulation and sampled sliding mode control strategies are treated from a unified viewpoint which naturally arises from fundamental results of the differential algebraic approach to systems dynamics and control. The approach leads naturally to dynamical discontinuous feedback policies resulting in (chatteringfree) smoothed constrained linearization and induced robust asymptotic output error stabilization. The results are applicable in a variety of nonlinear control problems, including stabilization, tracking, and model matching. Illustrative examples from non-traditional application areas are presented with simulations.