Simultaneous compensation of input and state delays for nonlinear systems

Bekiaris-Liberis, Nikolaos

doi:10.1016/j.sysconle.2014.08.014

Cited by 27 publications

(5 citation statements)

References 41 publications

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“…The stability proof is based on an equivalent representation of plant (1), using transport PDEs for the actuator states, and on an equivalent PDE representation of the predictor states (3)- (5). We present the alternative representations for the plant and the predictor states before stating and proving the main result of this section, since the reader might find the alternative formalisms helpful in better digesting the design and analysis ideas of our methodology.…”

Section: Assumptionmentioning

confidence: 99%

“…a) Background and Motivation: Despite the recent outburst in the development of predictor-based control laws for nonlinear systems with input delays [5], [6], [7], [8], [9], [10], [11], [13], [14], [15], [16], [17], [26], [27], [28], [29], [30], [31], [32], [35], [36], [37], [42], [43], [44], [45], [46], the problem of the systematic predictor-feedback stabilization of multi-input nonlinear systems with, potentially different, in each individual input channel, long input delays, has remained, heretofore, untackled, although the problem was solved in the linear case in the early 1980s [4] (see also [41]). In this article, we address the problem of stabilization of multi-input nonlinear systems with distinct input delays of arbitrary length and develop a nonlinear version of the prediction-based control laws developed in [4] and recently in [53], [54] for the compensation of input delays in multi-input linear systems.…”

Section: Introductionmentioning

confidence: 99%

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Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

Bekiaris-Liberis

Krstić

2017

IEEE Trans. Automat. Contr.

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We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different time instants, the key design challenge, which we resolve, is the construction of the predictors of the plant's state over distinct prediction horizons such that the corresponding input delays are compensated. Global asymptotic stability of the closed-loop system is established by utilizing arguments based on Lyapunov functionals or estimates on solutions. We specialize our methodology to linear systems for which the predictor-feedback control laws are available explicitly and for which global exponential stability is achievable. A detailed example is provided dealing with the stabilization of the nonholonomic unicycle, subject to two different input delays affecting the speed and turning rate, for the illustration of our methodology.

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Section: Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

Bekiaris-Liberis

Krstić

2017

IEEE Trans. Automat. Contr.

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“…(5) and the constant mismatch in the inertia matrix of the spacecraft, simultaneously. All simulation parameters are selected the same as the first simulation except the actual time delay, which is assumed here to be τ = 634 ms.…”

Section: Uncertainty Scenariomentioning

confidence: 99%

“…Generally speaking, these works can be divided into three categories. The first class of the control algorithms is utilized predictor-based feedback control law to compensate delay effects (see, for example [5,6,13,[24][25][26]). This method is essentially a nonlinear version of the Smith predictor [25] which was extended to nonlinear systems in [25] by Krstic. In the second group of control algorithms, the controller is firstly designed by neglecting delay.…”

Section: Introductionmentioning

confidence: 99%

Global attitude stabilization of rigid spacecraft with unknown input delay

et al. 2015

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Global attitude stabilization of a rigid spacecraft with unknown actuator delay time is an important problem that has rarely been studied. In this paper, first we investigate a Lyapunov-based controller for attitude regulation of a rigid spacecraft with delayed inputs. Simple conditions for global asymptotical stability are obtained by assuming that the true delay value is unknown, but approximation of its upper bound is available. It is also shown that a proper design of the controller prevents the unwinding phenomenon. Then, we extend the results for the system while taking disturbance effects into account. Based on LyapunovKrasovskii methodology, it is proven that the proposed controller can drive the closed-loop trajectories to a small region in the neighborhood of the origin in the presence of external disturbances and model uncertainties. Various numerical simulations are carried out to illustrate the effectiveness of the proposed control system.

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“…Although in recent years the control problem of SISO nonlinear systems with input delay is frequently considered, such as Bekiaris-Liberis (2014) and Khazaee et al (2015), a few studies have been performed in the field of interconnected systems with input delays (Bakule et al, 2016; Zhu et al, 2010). Bakule et al (2016) designed an LMI-based decentralized H ∞ state feedbback controller for linear interconnected systems with uncertainties and input delays.…”

Section: Introductionmentioning

confidence: 99%

Adaptive decentralized fuzzy output feedback tracking control for a class of nonlinear large-scale systems with input delays

Baigzadehnoe

Rafiee

Khosravi

et al. 2017

Transactions of the Institute of Measurement and Control

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In this paper, the decentralized tracking control problem of nonlinear large-scale systems with immeasurable states and unknown nonlinearities in each subsystem and their interconnections subject to input delays is proposed. Based on the universal approximation properties of fuzzy systems, a fuzzy observer is designed to estimate the inaccessible states of the system. Subsequently, by defining the appropriate change of coordinates and employing the backstepping technique, an adaptive fuzzy backstepping output feedback control scheme is proposed for nonlinear interconnected systems subject to input delays. Owing to the problem of so-called explosion of complexity that inherently arises in the design procedures of the traditional backstepping technique, an adaptive fuzzy dynamic surface output feedback control approach is also presented for this class of large-scale systems. Moreover, it is shown that the two proposed adaptive decentralized fuzzy observer-based control approaches ensure all the signals of the closed loop system uniformly ultimately bounded and the norms of the tracking errors as well as the norms of the observation errors can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are carried out on the chemical reactor recycle system to illustrate and compare the effectiveness of the two proposed approaches.

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Simultaneous compensation of input and state delays for nonlinear systems

Cited by 27 publications

References 41 publications

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

Predictor-Feedback Stabilization of Multi-Input Nonlinear Systems

Global attitude stabilization of rigid spacecraft with unknown input delay

Adaptive decentralized fuzzy output feedback tracking control for a class of nonlinear large-scale systems with input delays

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