Approximate and local linearizability of non-linear discrete-time systems

Lee, Hong-Gi; Marcus, Solomon

doi:10.1080/00207178608933653

Cited by 60 publications

(1 citation statement)

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“…Before studying opacity for systems of this kind, we take a brief detour to make note of some of the relevant literature. In a series of papers, the authors of [42], [43], and [44] derived conditions under which a DTNLS could be equivalently represented as a discrete-time linear system. A geometric analysis of controllability of DTNLSs in terms of Lie algebras of vector fields was presented in [45].…”

Section: Opacity For Nonlinear Systemsmentioning

confidence: 99%

Notions of Centralized and Decentralized Opacity in Linear Systems

Ramasubramanian

Cleaveland

Marcus

2020

IEEE Trans. Automat. Contr.

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We formulate notions of opacity for cyberphysical systems modeled as discrete-time linear timeinvariant systems. A set of secret states is k-ISO with respect to a set of nonsecret states if, starting from these sets at time 0, the outputs at time k are indistinguishable to an adversarial observer. Necessary and sufficient conditions to ensure that a secret specification is k-ISO are established in terms of sets of reachable states. We also show how to adapt techniques for computing underapproximations and over-approximations of the set of reachable states of dynamical systems in order to soundly approximate k-ISO. Further, we provide a condition for output controllability, if k-ISO holds, and show that the converse holds under an additional assumption.We extend the theory of opacity for single-adversary systems to the case of multiple adversaries and develop several notions of decentralized opacity. We study the following scenarios: i) the presence or lack of a centralized coordinator, and ii) the presence or absence of collusion among adversaries. In the case of colluding adversaries, we derive a condition for nonopacity that depends on the structure of the directed graph representing the communication between adversaries.Finally, we relax the condition that the outputs be indistinguishable and define a notion of -opacity, and also provide an extension to the case of nonlinear systems.

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Section: Opacity For Nonlinear Systemsmentioning

confidence: 99%

Notions of Centralized and Decentralized Opacity in Linear Systems

Ramasubramanian

Cleaveland

Marcus

2020

IEEE Trans. Automat. Contr.

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On the effect of perturbations on the stability of input-output linearizing controllers for a class of discrete-time nonlinear systems

Cruz-Hernández¹,

Álvarez²,

Castro‐Linares

1998

Int. J. Robust Nonlinear Control

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An analysis of the effect of parameter perturbations on the stability of input–output linearizing controllers for a class of MIMO discrete‐time nonlinear systems is presented. A static‐state feedback is designed to input–output linearize a system without perturbations, and it is applied to the same system with an uncertain parameter vector, thus introducing an uncertain parameter term in the nominal input–output linearized system. It is shown that the state trajectories of the closed‐loop perturbed system are ultimately bounded provided the closed‐loop nominal system is exponentially stable and some conditions on the bounds of the perturbation terms are satisfied. © 1998 John Wiley & Sons, Ltd.

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Discrete-Time Nonlinear Control Systems

Nijmeijer

Schaft

1990

Nonlinear Dynamical Control Systems

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Approximate and local linearizability of non-linear discrete-time systems

Cited by 60 publications

References 10 publications

Notions of Centralized and Decentralized Opacity in Linear Systems

Notions of Centralized and Decentralized Opacity in Linear Systems

On the effect of perturbations on the stability of input-output linearizing controllers for a class of discrete-time nonlinear systems

Discrete-Time Nonlinear Control Systems

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