Distributed consensus with unknown control coefficients and unknown Lipschitz nonlinearity

Abstract The paper investigates the control problem for a class of lower-triangular nonlinear uncertain systems with mismatched uncertainties and unknown values of control coefficients. Based on the signs of control coefficients rather than the nominal values or the approximative mathematical expressions, a new active disturbance rejection control is proposed. The design procedure can be concluded by three steps: determining the equivalent integrators chain form, constructing the extended state observer to estimate the total disturbance, and designing a dynamical system to let the actual input track the ideal input. Then under a mild assumption for mismatched uncertainties and unknown control coefficients, the paper rigorously analyzes the bounds of tracking error, estimating error and the error between the actual and ideal inputs. The presented theoretical results reveal the strong robustness of the proposed method to mismatched uncertainties and uncertain control input coefficients. Moreover, the tuning law of observer parameter and the parameter of dynamical input design is theoretically shown.

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Adaptive tracking control for uncertain nonlinear systems subject to unknown control coefficients, state constraints, and input saturation

10.21203/rs.3.rs-745797/v1 ◽

2021 ◽

Author(s):

Chunxiao Wang ◽

Lu Qi ◽

Yan Zhao ◽

Jiali Yu

Keyword(s):

Tracking Control ◽

State Constraints ◽

Input Saturation ◽

Approximation Error ◽

Tracking Performance ◽

Dynamic Surface ◽

Unknown Control Coefficients ◽

Unknown Control ◽

Control Direction ◽

Control Coefficients

Abstract This article is committed to studying the tracking control problem for a class of uncertain nonlinear system with unknown control coefficients. The system is subject to full state constraints, input saturation constraint, and external disturbances simultaneously. By introducing a hyperbolic tangent function to approximate the saturated input function, the sharp corner caused by the input saturation is avoided. In the meanwhile, an auxiliary system is constructed to compensate the resulting approximation error. By using the barrier Lyapunov function (BLF) based adaptive backsteping control, the Nussbaum-type adaptive controllers are constructed for the augmented system with unknown control direction. It not only ensures the system states are always within the constrained range, but also guarantees the tracking performance of the system, no matter whether the control direction of the system is known or not. Meanwhile, dynamic surface control (DSC) is used in the controller design, which avoids ”computation explosion” caused by the repeated derivation of virtual control law. Aiming at the nonparametric uncertainty of the system, a common adaptive law is designed by combining the unknown constant bounds of the external disturbance with the error term caused by input saturation estimation. It improves the tracking performance of the system and reduces the burden of the controller greatly. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme in three scenarios.

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Bounded Analysis and Practical Tracking Control of Complex Stochastic Nonlinear Systems with Unknown Control Coefficients

Complexity ◽

10.1155/2020/1502065 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Long-Chuan Guo ◽

Xiang-Kun Fang

Keyword(s):

Nonlinear Systems ◽

Tracking Error ◽

Upper And Lower Bounds ◽

Design Parameters ◽

Stochastic Nonlinear Systems ◽

Tracking Controller ◽

Unknown Control Coefficients ◽

Unknown Control ◽

Theoretical Results ◽

Control Coefficients

This paper mainly focuses on the output practical tracking controller design for a class of complex stochastic nonlinear systems with unknown control coefficients. In the existing research results, most of the complex systems are controlled in a certain direction, which leads to the disconnection between theoretical results and practical applications. The authors introduce unknown control coefficients, and the values of the upper and lower bounds of the control coefficients are generalized by constants to allow arbitrary values to be arbitrarily large or arbitrarily small. In the control design program, the design problem of the controller is transformed into a parameter construction problem by introducing appropriate coordinate transformation. Moreover, we construct an output feedback practical tracking controller based on the dynamic and static phase combined by Ito stochastic differential theory and selection of appropriate design parameters, ensuring that the system tracking error can be made arbitrarily small after some large enough time. Finally, a simulation example is provided to illustrate the efficiency of the theoretical results.

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