Backstepping control of linear time-varying systems with known and unknown parameters

Zhang, Youping; Fi̇dan, Barış; Ioannou, Pétros

doi:10.1109/tac.2003.819074

Cited by 109 publications

(5 citation statements)

References 33 publications

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“…For a class of nonlinear MIMO systems given in form in (21), meeting the matching condition requirement in Equation 24, a nonlinear SBC is given by:…”

Section: Theoremmentioning

confidence: 99%

“…Numerous variations of backstepping control can be found in the literature. Specific formulations exist for nonlinear systems with time delays [19], systems with structural obstacles in obtaining continuous feedback laws [20], time-varying systems [21], nonlinear systems with block structures [22], plants with unknown backlash nonlinearities [23], nonholonomic systems with strong nonlinear drifts [24], systems with unknown dead-zone non-linearity [25], nonlinear systems with delay of neutral type [26], and so on. The backstepping method is also used to assist in design for fuzzy control [27][28][29], neural network control [25,[30][31][32][33][34], and wavelet adaptive control [35,36].…”

Section: Introductionmentioning

confidence: 99%

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Sliding Mode Control in Backstepping Framework for a Class of Nonlinear Systems

Shen

Iorio

2019

JMSE

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Both backstepping control (BC) and sliding mode control (SMC) have been studied extensively over the past few decades, and many variations of controller designs based on them can be found in the literature. In this paper, sliding mode control in a backstepping framework (SBC) for a class of nonlinear systems is proposed and its connections to SMC studied. SMC is shown to be a special case of SBC. Without losing generality, the regulation control problem is studied, while tracking control is achieved by replacing the states with the difference between the states and their desired values. The SBCs are designed for nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) systems with the presence of bounded uncertainties from unmodeled dynamics, parametric variations, disturbances, and measurement noise, and the closed loop systems are proven to be asymptotically stable using the Lyapunov stability theory. The comparison of SBC to SMC from the design process, chattering effects, and chatter reduction are also discussed. SBC inherits the merits of backstepping control in choosing gains independently, while leveraging useful nonlinear dynamics for controller design simplification. Hence, it provides more flexibility in controller design in the sense of controlling coverage speed and making use of useful nonlinearities in the dynamics. To demonstrate the effectiveness of SBC, an application on cruise tracking control of an autonomous underwater vehicle was studied.

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“…For a class of nonlinear MIMO systems given in form in (21), meeting the matching condition requirement in Equation 24, a nonlinear SBC is given by:…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sliding Mode Control in Backstepping Framework for a Class of Nonlinear Systems

Shen

Iorio

2019

JMSE

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“…Construction of a high-quality automated adaptive system for the optimization of the operation mode of a control object under modern conditions is solved using a systems approach [5]. From the perspective of this approach, solution to the problems on minimization (optimization) of the CG cooling temperature mode and on increasing economic efficiency of production requires creation of a mathematical model of the evaporator.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Identification of heat exchange process in the evaporators of absorption refrigerating units under conditions of uncertainty

Babichenko

Kravchenko

et al. 2018

EEJET

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“…This method can achieve asymptotic stabilization/tracking only if the derivatives of time‐varying parameters are

{\mathcal{L}}_1

. Another approach is switching

\sigma

‐modification, 21‐23 which adds leakages to parameter update laws if parameter estimates drift out of a prespecified region to ensure the boundedness of parameter estimates. However, this approach cannot achieve asymptotic stabilization/tracking when unknown parameters are persistently varying.…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

Adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties

Chu,

Liu

2023

Intl J Robust & Nonlinear

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The paper considers adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties. The time‐varying uncertainties do not need to be differentiable, but their variation amplitudes are required to be known. Such uncertainties appear not only in the system nonlinearities but also as the control coefficient. We pursue a tight design scheme by combining tuning functions and the congelation of variables method, thereby avoiding the overuse of dominations and obtaining a less conservative controller. In view of the essence of the control problem, we don't design a continuous controller first and then search for a complex and suitable event‐triggering mechanism, as emulation methods done in the literature. In contrast, we adopt a simple event‐triggering mechanism with the relative threshold, while seeking a complex and appropriate adaptive controller which contains the new adaptive treatment for execution error due to the unknown time‐varying control coefficient. Note that there are three parameter dynamic compensators in the adaptive controller, and one is specialized to the execution error, which is not required in the continuous feedback context. It is shown that with the proposed adaptive event‐triggered controller, all the closed‐loop signals are bounded, the system state converges to zero, and no Zeno behavior occurs. A comparative simulation is provided to verify the theoretical results.

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Backstepping control of linear time-varying systems with known and unknown parameters

Abstract: NOMENCLATUREThe following notation is used throughout this paper, unless otherwise stated.th element of vector . th coordinate column vector in . th row of matrix .

Cited by 109 publications

References 33 publications

Sliding Mode Control in Backstepping Framework for a Class of Nonlinear Systems

Sliding Mode Control in Backstepping Framework for a Class of Nonlinear Systems

Identification of heat exchange process in the evaporators of absorption refrigerating units under conditions of uncertainty

Adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties

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