Discrete time immersion and invariance adaptive control via partial state feedback for systems in block strict feedback form

Yalçın, Yaprak

doi:10.1016/j.ejcon.2015.05.002

Cited by 8 publications

(3 citation statements)

References 28 publications

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“…Global exponential [11,17,18,26,32,35,36] Global asymptotic [3,33,34,38] Local exponential [10,18,27,28] Local asymptotic [2,6,8,12,25] Finite-time [13,18] Table 1 Systems/observers satisfying Definition 1 in the literature.…”

Section: Referencesmentioning

confidence: 99%

A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

Yang¹,

Murguia²,

Kuijper³

et al. 2019

Preprint

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We address the problem of state estimation and attack isolation for general discrete-time nonlinear systems when sensors are corrupted by (potentially unbounded) attack signals. For a large class of nonlinear plants and observers, we provide a general estimation scheme, built around the idea of sensor redundancy and multi-observer, capable of reconstructing the system state in spite of sensor attacks and noise. This scheme has been proposed by others for linear systems/observers and here we propose a unifying framework for a much larger class of nonlinear systems/observers. Using the proposed estimator, we provide an isolation algorithm to pinpoint attacks on sensors during sliding time windows. Simulation results are presented to illustrate the performance of our tools.

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Section: Referencesmentioning

confidence: 99%

A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

Yang¹,

Murguia²,

Kuijper³

et al. 2019

Preprint

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show abstract

“…In Hu and Zhang (2015), control of rigid-body under constant disturbance is considered and I & I approach is used for both estimation of angular velocity and the disturbance in continuous-time domain. In discrete-time setting (Yalc and Astolfi, 2012), a full state feedback adaptive control design for nonlinear systems in strict feedback form and in (Yalçın, 2015) a partial feedback adaptive control together with I & I state-estimation for nonlinear system in block strict feedback is presented. Note that, we did not encounter with a study that utilizes I & I approach for disturbance attenuation in the discrete-time control.…”

Section: Introductionmentioning

confidence: 99%

Discrete-time backstepping control with nonlinear adaptive disturbance attenuation for the inverted-pendulum system

Adıgüzel

Yalçın

2019

Transactions of the Institute of Measurement and Control

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A discrete-time backstepping controller with an active disturbance attenuation property for the Inverted-Pendulum system is constructed in this paper. The main purpose of this study is to show that Immersion and Invariance (I & I) approach can be used to design a nonlinear observer for disturbance estimation and demonstrate its effectiveness considering a nonlinear system with an unstable equilibrium point, namely Inverted-Pendulum system, by utilizing the estimated values in backstepping control design. All designs are directly performed in discrete-time domain to obtain directly implementable observer and controller in discrete processors with superior performance compared to emulators. The Inverted-Pendulum system is not in strict feedback form therefore backstepping procedure cannot be directly applied. In order to enable backstepping construction, firstly a partial feedback linearization is performed and afterwards a novel discrete-time coordinate transformation is proposed. Prior to the construction of partial feedback linearizing and backstepping controller, a nonlinear disturbance estimator design is proposed with Immersion and Invariance approach. The estimated disturbance values used in the partial feedback linearization and construction of the backstepping controller. The global asymptotic stability of the estimator and local asymptotic stability of overall closed loop system are proved in the sense of Lyapunov. Performance of proposed direct discrete-time backstepping control with discrete I & I observer is compared with a backstepping sliding mode controller with another nonlinear disturbance observer (NDO) by simulations.

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“…That is why this approach is favored by many researchers and numerous research results are emerging in recent years. Based on Astolfi and Ortega 20 and Astolfi et al, 21 and by construction of a monotone function, a new framework to design I&I adaptive controllers for nonlinearly parameterized systems was proposed in Liu et al 22 and Wang et al 23 The I&I adaptive control method was extended to the nonlinear discrete systems case in Yalçın 24 and Yalçın and Astolfi. 25 In addition to being continuously improved in theory, this adaptive method has also be successfully applied in practice, such as single-machine infinite-bus power system with a static var compensator, 26 the underactuated quadrotor unmanned aerial vehicle, and 27 nonlinear aeroelastic system.…”

Section: Introductionmentioning

confidence: 99%

Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems

Lou

Zhao

2017

Intl J Robust & Nonlinear

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SummaryThis paper presents a novel framework to asymptotically adaptively stabilize a class of switched nonlinear systems with constant linearly parameterized uncertainty. By exploiting the generalized multiple Lyapunov functions method and the recently developed immersion and invariance (I&I) technique, which does not invoke certainty equivalence, we design the error estimator, continuous state feedback controllers for subsystems, and a switching law to ensure boundedness of all closed-loop signals and global asymptotical regulation of the states, where the solvability of the I&I adaptive stabilization problem for individual subsystems is not required. Then, along with the backstepping method, the proposed design technique is further applied to a class of switched nonlinear systems in strict-feedback form with an unknown constant parameter so that the I&I adaptive stabilization controllers for the system is developed. Finally, simulation results are also provided to demonstrate the effectiveness of the proposed design method.

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Discrete time immersion and invariance adaptive control via partial state feedback for systems in block strict feedback form

Cited by 8 publications

References 28 publications

A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

Discrete-time backstepping control with nonlinear adaptive disturbance attenuation for the inverted-pendulum system

Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems

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