Delay-dependent robust and reliable H∞ fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems

doi:10.1016/j.fss.2009.10.017

Fuzzy Sets and Systems

Volume 161, Issue 6, 16 March 2010, Pages 872-892

https://doi.org/10.1016/j.fss.2009.10.017 Get rights and content

Abstract

This paper develops the delay-dependent robust and reliable $H_{\infty}$ fuzzy hyperbolic control for nonlinear large-scale interconnected systems with parameter uncertainties. Firstly, the modeling method of fuzzy hyperbolic model (FHM) is given for the general large-scale interconnected systems. The main advantages of using FHM over T–S fuzzy model are that neither premise structure identification nor completeness design of premise variables space is needed. Therefore the required computational effort is less than that of using T–S fuzzy model, especially when a lot of fuzzy rules are needed to model complex nonlinear systems. Then according to the Lyapunov direct method and the decentralized control theory of large-scale interconnected systems, linear matrix inequality (LMI)-based conditions with some free weighting matrices are derived, which guarantee the closed-loop interconnected systems to be robustly stable with the $H_{\infty}$ performance even in the presence of some possible actuator failures. Moreover, precise failure parameters of actuators are not required, and the only requirements are the lower and upper bounds of failure parameters. The restriction that the derivative of the time-varying delay is smaller than one is removed. Therefore, the results obtained are less conservative. Three simulation examples are provided to show the effectiveness of the proposed approach.

References (23)

B.S. Chen et al.
A systematic molecular circuit design method for gene networks under biochemical time delays and molecular noises
BMC Systems Biology
(2008)
L. Li et al.
New approaches on $H_{\infty}$ control of T–S fuzzy systems with interval time-varying delay
Fuzzy Sets and Systems
(2009)
Y.Z. Wang et al.
Robust $H_{\infty}$ control based on fuzzy hyperbolic model with time-delay
Progress in Natural Science
(2008)
H.N. Wu et al.
Reliable mixed $L_{2} / H_{\infty}$ fuzzy static output feedback control for nonlinear systems with sensor faults
Automatica
(2005)
H.G. Zhang et al.
Delay-dependent robust $H_{\infty}$ control for uncertain fuzzy hyperbolic systems with multiple delays
Progress in Natural Science
(2008)
M.S. Bazaraa et al.
Linear Programming and Network Flows
(1977)
Y. He et al.
Further improvement of free-weighting matrices technique for system with time-varying delay
IEEE Transactions on Automatic Control
(2007)
F.H. Hsiao et al.
Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control
IEEE Transactions on Fuzzy Systems
(2005)
Z.Z. Hu
Decentralized stabilization of large scale interconnected systems with delays
IEEE Transactions on Automatic Control
(1994)
C.G. Li et al.
Stability analysis of fuzzy large-scale systems with time delays in interconnections
International Journal of General Systems
(2004)

S.X. Lun et al.

Delay-independent fuzzy hyperbolic guaranteed cost control design for a class of nonlinear continuous-time system with uncertainties

Acta Automatica Sinica

(2005)

Cited by (16)

Decentralized direct adaptive fuzzy control scheme for state-constrained interconnected systems
2023, Fuzzy Sets and Systems
This paper focuses on the problem of decentralized adaptive fuzzy tracking control for state-constrained interconnected systems. However, feasibility conditions on virtual controllers are imposed by barrier Lyapunov function (BLF) based approaches. To remove it, a nonlinear state-dependent barrier function (NSBF) is proposed, based on which the constrained interconnected system is equivalently transformed into a non-constrained one. Nonlinear interactions and uncertainties are approximated by fuzzy logic systems (FLS). A decentralized direct adaptive fuzzy control (DAFC) scheme is developed, in which a class of reduced-order smooth functions is fused with backstepping control design procedures, and only one adaptive law is used in each decentralized controller. With the proposed control scheme, not only the feasibility conditions but also the partial-derivative terms are not involved in virtual controllers, and the time derivative of the Lyapunov function is ensured negative semi-definite. It is shown that the proposed control scheme guarantees that the state constraints are not violated, and the tracking error converges to a predefined interval asymptotically. Two simulation examples confirm the effectiveness of the proposed control scheme.
Interval type-2 generalized fuzzy hyperbolic modelling and control of nonlinear systems[Formula presented]
2022, Applied Soft Computing
Generalized Fuzzy Hyperbolic Models (GFHMs) offer a simpler structure and less computational complexity than the typical fuzzy systems. Type-2 fuzzy systems, in contrast, have better handling of uncertainty but at the cost of higher computational complexity. Here, we propose a synergistic hybrid framework of interval type-2 fuzzy systems and GFHMs for a better uncertainty handling and simpler computational structure in the modelling and control of nonlinear systems. For this purpose, we first extend the GFHM to a computational model with various width and subsequently propose interval type-2 generalized fuzzy hyperbolic systems (IT2-GFHS) as a computational framework for nonlinear systems modelling. We then employ this IT2-GFHS in a general sliding-based robust nonlinear controller. Theoretical Lyapunov analysis reveals the overall asymptotic stability of the resulting closed-loop system. The numerical simulations for system modelling and identification on two nonlinear benchmark problems also reveal higher accuracy, lower computation time, and fewer adjustable parameters for the proposed IT2-GFHS models. Furthermore, applications to two nonlinear benchmark control problems show similar performance in terms of robustness to noise and disturbances compared with type-2 fuzzy systems, with the IT2-GFHS-based nonlinear controller having considerably fewer computations and floating-point operations. Finally, the proposed approach is experimentally implemented to control a 3-Prismatic-Series-Prismatic (3-PSP) parallel robot. Experimental results also confirm the improved tracking performance of the proposed method compared with interval type-2 and type-1 fuzzy systems, while also requiring fewer adjustable parameters.
Stability analysis and stabilization for fuzzy hyperbolic time-delay system based on delay partitioning approach
2016, Neurocomputing
This paper investigates the problems of stability analysis and stabilization for a class of fuzzy hyperbolic time-delay systems. A generalization of the fuzzy hyperbolic time-delay model is firstly proposed, which is more effective in representing nonlinear control systems. By means of the delay-partitioning method, a novel basis-dependent Lyapunov–Krasovskii function is constructed to reduce the conservatism of stability conditions. Those conditions are converted to finite linear matrix inequalities, which can be readily solved by standard numerical software. Using this result, the problem of stabilization is also solved. Then, both the stability and stabilization results are further extended to fuzzy hyperbolic time-delay systems with parameter uncertainties. Finally, three illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed methods.
Decentralized guaranteed cost stabilization of time-delay large-scale systems based on reduced-order observers
2011, Journal of the Franklin Institute
Citation Excerpt :
In fact, time delays are sometimes inherent in large-scale systems due to information transmission among distributed subsystems. With this in mind, some results on decentralized stabilization of time-delay large-scale system are reported (see e.g. [2–4,7–9,18]). To date, however, very little attention has been drawn to select a particular controller amongst all the admissible stabilizing controllers.
This paper addresses the problem of decentralized guaranteed cost stabilization (DGCS) of large-scale systems with delays both in the isolated subsystems and interconnections based on reduced-order observers. Sufficient conditions for the existence of delay-independent decentralized guaranteed cost controller (DGCC) are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMIs constraints is formulated to design the optimal DGCC which minimizes the guaranteed cost of the closed-loop large-scale systems. Finally, a simulation is performed to show the effectiveness of the proposed control scheme.
A survey on control for Takagi-Sugeno fuzzy systems subject to engineering-oriented complexities
2021, Systems Science and Control Engineering
A novel stability criterion for fuzzy hyperbolic time-delay system based on dynamic delay partitioning approach
2017, 2017 IEEE Symposium Series on Computational Intelligence, SSCI 2017 - Proceedings

View all citing articles on Scopus

View full text

Delay-dependent robust and reliable H∞ fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems

Abstract

BMC Systems Biology

Fuzzy Sets and Systems

Progress in Natural Science

Automatica

Progress in Natural Science

Linear Programming and Network Flows

Further improvement of free-weighting matrices technique for system with time-varying delay

IEEE Transactions on Automatic Control

Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control

IEEE Transactions on Fuzzy Systems

Decentralized stabilization of large scale interconnected systems with delays

IEEE Transactions on Automatic Control

Stability analysis of fuzzy large-scale systems with time delays in interconnections

International Journal of General Systems

Delay-independent fuzzy hyperbolic guaranteed cost control design for a class of nonlinear continuous-time system with uncertainties

Acta Automatica Sinica

Delay-dependent robust and reliable $H_{\infty}$ fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems