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149 On differentially flat nonlinear systems
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Abstracts for equivalence (weak equivalence) of a system to a linear controllable system.
147 Generalized State Space Descriptions and Digital Implementation S.T. Glad, pp 149-152 Discrete-time approximations of a nonlinear differential equation in the input and output are considered. A certain approximation is shown to approximate with arbitrary accuracy, provided the sampling interval tends to zero. The coefficients are shown to be bounded as the sampling interval tends to zero, provided certain conditions are met by the powers of the derivatives.
148 Rational System Equivalence, and Generalized Realization Theory S. Diop, pp 153-158 Assuming that two irreducible (differential algebraic) systems are rationally equivalent if their associated differential fields are differentially isomorphic, the authors provide a necessary and sufficient condition for a system to be rationally realizable, in the sense that it is rationally equivalent to a system in generalized state form. Input derivatives may be present. If two systems are rationally equivalent then one is observable if and only if the other one is so. Rational observability is a necessary and sufficient condition for a system to be rationally equivalent to its external behaviour. Finally, the problem of minimality of a realization is shown to be trivial in this approach.
149 On Differentially Fiat Nonlinear Systems M. Flless, J. L~vine, P. Martin, P. Rouchon, pp 159-163 A differential field characterization of a class of dynamic feedback linearizable systems is given via the notion of differentially flat systems. For such systems, the linearizing dynamic feedback is obtained as an endogeneous dynamic feedback. Examples of flat systems are often encountered in practice.
150 Links Between Local Controllability and Local Continuous Stabilization J.-M. Coron, pp 165-171 The paper proves that a control system which satisfies well-known sufficient conditions for small-time local controllability - for example the Hermes Condition - can be dynamically locally asymptotically stabilized by means of a continuous time-varying feedback law. For special systems (including systems without drift) local stabilization in finite time is obtained by means of a continuous time-varying feedback law.
151 Strong Dynamic Input-Output Decoupling: from Linearity to Nonlinearity H j . C . Huijberts, H. Nijmeijer, pp 173-178 The paper is concerned with the strong dynamic inputoutput decoupling problem (SDIODP) for nonlinear systems. It is shown that, given a generically satisfied assumption, the solvability of the SDIODP around an equilibrium point is equivalent to the solvability of the same problem for the linearization of the system around this equilibrium point. The Singh compensator, a dynamic state feedback of minimal order that solves the SDIODP, is introduced. It is shown that, given the assumption mentioned above, the linearization of the
Singh compensator around an equilibrium point is a Singh compensator for the linearization of the original nonlinear system around this equilibrium point.
152 An Algebraic Interpretation of the Structure Algorithm with an Application to Feedback Decoupllng E. Delaleau, M. Fiiess, pp 179-184 The main result given in this paper states that right invertible linear and nonlinear systems can be decoupled via a quasi-static state feedback, which does not require the integration of any differential equation. The authors' method relies on the translation of the structure algorithm into the algebraic language of filtrations.
153 Moving Horizon Observers H. Mlchalska, D.Q. Mayne, pp 185-190 A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The observer produces an estimate of the state of the nonlinear system at time t, by minimizing, or approximately minimizing, a cost function over the interval (horizon) [t - T,t]; as t advances, so does the horizon. Two forms of the estimator are described. In the first, the cost is a function of the unknown state. In the second, an observer with control injection is employed, the injection v being obtained by the (approximate) solution of an optimal control problem. Global convergence of the estimators is established.
154 Dynamic Forms and Their Application to Control G. Meyer, pp 191-195 The rigid body model plays a basic role in both modeling and control of many systems including aircraft flight control. The distinctive feature of the rigid body is that its motion evolves on a curved space. Consequently, the designer must take into account the deterioration of chosen co-ordinatizations near their singularities, where the control actions, and the sensitivity to modeling and sensor errors, become unacceptable. The various dynamic forms described in the paper provide an effective means for the necessary co-ordinate patching and control law implementation. The utility of these forms is illustrated by means of several applications to flight control.
155 Observer Design in the Tracking Control Problem of Robots H. Berghuis, H. Nijmeijer, P. L6hnberg, pp 197-202 Full state feedback is the starting point for the majority of currently available control methods for rigid robots, an assumption that can hardly be realized in practice due to the poor quality of velocity measurements. This paper considers the tracking control problem of robots using only position measurements. Some known state feedback controllers are modified by integrating a velocity observer in the loop, thereby yielding an exponentially stable closed-loop system without the need for high gain assumptions. The removed requirement for velocity measurements, and consequently for expensive velocity data-acquisition hardware, makes the presented control methods interesting, particularly from an economic point of view.
Abstracts for equivalence (weak equivalence) of a system to a linear controllable system.
147 Generalized State Space Descriptions and Digital Implementation S.T. Glad, pp 149-152 Discrete-time approximations of a nonlinear differential equation in the input and output are considered. A certain approximation is shown to approximate with arbitrary accuracy, provided the sampling interval tends to zero. The coefficients are shown to be bounded as the sampling interval tends to zero, provided certain conditions are met by the powers of the derivatives.
148 Rational System Equivalence, and Generalized Realization Theory S. Diop, pp 153-158 Assuming that two irreducible (differential algebraic) systems are rationally equivalent if their associated differential fields are differentially isomorphic, the authors provide a necessary and sufficient condition for a system to be rationally realizable, in the sense that it is rationally equivalent to a system in generalized state form. Input derivatives may be present. If two systems are rationally equivalent then one is observable if and only if the other one is so. Rational observability is a necessary and sufficient condition for a system to be rationally equivalent to its external behaviour. Finally, the problem of minimality of a realization is shown to be trivial in this approach.
149 On Differentially Fiat Nonlinear Systems M. Flless, J. L~vine, P. Martin, P. Rouchon, pp 159-163 A differential field characterization of a class of dynamic feedback linearizable systems is given via the notion of differentially flat systems. For such systems, the linearizing dynamic feedback is obtained as an endogeneous dynamic feedback. Examples of flat systems are often encountered in practice.
150 Links Between Local Controllability and Local Continuous Stabilization J.-M. Coron, pp 165-171 The paper proves that a control system which satisfies well-known sufficient conditions for small-time local controllability - for example the Hermes Condition - can be dynamically locally asymptotically stabilized by means of a continuous time-varying feedback law. For special systems (including systems without drift) local stabilization in finite time is obtained by means of a continuous time-varying feedback law.
151 Strong Dynamic Input-Output Decoupling: from Linearity to Nonlinearity H j . C . Huijberts, H. Nijmeijer, pp 173-178 The paper is concerned with the strong dynamic inputoutput decoupling problem (SDIODP) for nonlinear systems. It is shown that, given a generically satisfied assumption, the solvability of the SDIODP around an equilibrium point is equivalent to the solvability of the same problem for the linearization of the system around this equilibrium point. The Singh compensator, a dynamic state feedback of minimal order that solves the SDIODP, is introduced. It is shown that, given the assumption mentioned above, the linearization of the
Singh compensator around an equilibrium point is a Singh compensator for the linearization of the original nonlinear system around this equilibrium point.
152 An Algebraic Interpretation of the Structure Algorithm with an Application to Feedback Decoupllng E. Delaleau, M. Fiiess, pp 179-184 The main result given in this paper states that right invertible linear and nonlinear systems can be decoupled via a quasi-static state feedback, which does not require the integration of any differential equation. The authors' method relies on the translation of the structure algorithm into the algebraic language of filtrations.
153 Moving Horizon Observers H. Mlchalska, D.Q. Mayne, pp 185-190 A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The observer produces an estimate of the state of the nonlinear system at time t, by minimizing, or approximately minimizing, a cost function over the interval (horizon) [t - T,t]; as t advances, so does the horizon. Two forms of the estimator are described. In the first, the cost is a function of the unknown state. In the second, an observer with control injection is employed, the injection v being obtained by the (approximate) solution of an optimal control problem. Global convergence of the estimators is established.
154 Dynamic Forms and Their Application to Control G. Meyer, pp 191-195 The rigid body model plays a basic role in both modeling and control of many systems including aircraft flight control. The distinctive feature of the rigid body is that its motion evolves on a curved space. Consequently, the designer must take into account the deterioration of chosen co-ordinatizations near their singularities, where the control actions, and the sensitivity to modeling and sensor errors, become unacceptable. The various dynamic forms described in the paper provide an effective means for the necessary co-ordinate patching and control law implementation. The utility of these forms is illustrated by means of several applications to flight control.
155 Observer Design in the Tracking Control Problem of Robots H. Berghuis, H. Nijmeijer, P. L6hnberg, pp 197-202 Full state feedback is the starting point for the majority of currently available control methods for rigid robots, an assumption that can hardly be realized in practice due to the poor quality of velocity measurements. This paper considers the tracking control problem of robots using only position measurements. Some known state feedback controllers are modified by integrating a velocity observer in the loop, thereby yielding an exponentially stable closed-loop system without the need for high gain assumptions. The removed requirement for velocity measurements, and consequently for expensive velocity data-acquisition hardware, makes the presented control methods interesting, particularly from an economic point of view.