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Full-Text Articles in Control Theory
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
Miscellaneous (presentations, translations, interviews, etc)
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
Miscellaneous (presentations, translations, interviews, etc)
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.