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Full-Text Articles in Control Theory
Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall
Linearizable Feedforward Systems: A Special Class, Issa Amadou Tall
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We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow …
On Linearizability Of Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
On Linearizability Of Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
In this paper we address the problem of linearizability of systems in strict feedforward form. We provide an algorithm, along with explicit transformations, that linearizes a system by change of coordinates when some easily checkable conditions are met. Those conditions turn out to be necessary and sufficient, that is, if one fails the system is not linearizable. We revisit type I and type II classes of linearizable strict feedforward systems provided by Krstic in [6] and illustrate our algorithm by various examples mostly taken from [5], [6].
Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek
Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek
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We show that any symmetry of a smooth strict feedforward system is conjugated to a scaling translation and any 1-parameter family of symmetries to a family of scaling translations along the first variable. We compute explicitly those symmetries by finding the conjugating diffeomorphism. We deduce, in accordance with our previous work, that a smooth system is feedback equivalent to a strict feedforward form if and only if it gives rise to a sequence of systems, such that each element of the sequence, firstly, possesses an infinitesimal symmetry whose flow is conjugated to a 1- parameter families of scaling translations and, …
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
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Recently we proved that any smooth (resp. analytic) strict feedforward system can be brought into its normal form via a smooth (resp. analytic) feedback transformation. This will allow us to identify a subclass of strict feedforward systems, called systems in special strict feedforward form, shortly (SSFF), possessing a canonical form which is an analytic counterpart of the formal canonical form. For (SSFF)-systems, the step-by-step normalization procedure of Kang and Krener leads to smooth (resp. convergent analytic) normalizing feedback transformations. We illustrate the class of (SSFF)-systems by a model of an inverted pendulum on a cart.
Strict Feedforward Form And Symmetries Of Nonlinear Control Systems, Witold Respondek, Issa Amadou Tall
Strict Feedforward Form And Symmetries Of Nonlinear Control Systems, Witold Respondek, Issa Amadou Tall
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We establish a relation between strict feedforward form and symmetries of nonlinear control systems. We prove that a system is feedback equivalent to the strict feedforward form if and only if it gives rise to a sequence of systems, such that each element of the sequence, firstly, possesses an infinitesimal symmetry and, secondly, it is the factor system of the preceding one, i.e., is reduced from the preceding one by its symmetry. We also propose a strict feedforward normal form and prove that a smooth strict feedforward system can be smoothly brought to that form.
Weighted Canonical Forms Of Nonlinear Single-Input Control Systems With Noncontrollable Linearization, Issa Amadou Tall, Witold Respondek
Weighted Canonical Forms Of Nonlinear Single-Input Control Systems With Noncontrollable Linearization, Issa Amadou Tall, Witold Respondek
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We propose a weighted canonical form for single-input systems with noncontrollable first order approximation under the action of formal feedback transformations. This weighted canonical form is based on associating different weights to the linearly controllable and linearly noncontrollable parts of the system. We prove that two systems are formally feedback equivalent if and only if their weighted canonical forms coincide up to a diffeomorphism whose restriction to the linearly controllable part is identity.
Normal Forms For Nonlinear Discrete Time Control Systems, Boumediene Hamzi, Issa Amadou Tall
Normal Forms For Nonlinear Discrete Time Control Systems, Boumediene Hamzi, Issa Amadou Tall
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We study the feedback classification of discrete-time control systems whose linear approximation around an equilibrium is controllable. We provide a normal form for systems under investigation.
Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek
Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek
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We study the feedback group action on two-inputs non-linear control systems. We follow an approach proposed by Kang and Krener which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes that obtained in the single-input case. We also give homogeneous m-invariants of the action of the group of homogeneous transformations on the homogeneous systems of the same degree. We illustrate our results by analyzing the normal form and invariants of homogeneous systems of degree two.
How Many Symmetries Does Admit A Nonlinear Single-Input Control System Around An Equilibrium?, Witold Respondek, Issa Amadou Tall
How Many Symmetries Does Admit A Nonlinear Single-Input Control System Around An Equilibrium?, Witold Respondek, Issa Amadou Tall
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We describe all symmetries of a single-input nonlinear control system, that is not feedback linearizable and whose first order approximation is controllable, around an equilibrium point. For a system such that a feedback transformation, bringing it to the canonical form, is analytic we prove that the set of all local symmetries of the system is exhausted by exactly two 1-parameter families of symmetries, if the system is odd, and by exactly one 1-parameter family otherwise. We also prove that the form of the set of symmetries is completely described by the canonical form of the system: possessing a nonstationary symmetry, …
Normal Forms, Canonical Forms, And Invariants Of Single Input Nonlinear Systems Under Feedback, Issa Amadou Tall, Witold Respondek
Normal Forms, Canonical Forms, And Invariants Of Single Input Nonlinear Systems Under Feedback, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analysing, step by step, the action of homogeneous transformations on the homogeneous part of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms coincide. We give an explicit construction of transformations bringing the system to its normal, dual normal, and canonical form.