Robust tracking control design for fractional-order interval type-2 fuzzy systems

Nonlinear Dynamics - This paper is concerned with an uncertainty and disturbance estimator-based tracking control problem for a class of interval type-2 fractional-order Takagi-Sugeno fuzzy systems...     

Quantization-based tracking control for fuzzy singularly perturbed Markov jump systems with incomplete transition information and packet dropout

In this article, the tracking control problem for discrete-time singularly perturbed systems with a piecewise-homogeneous Markov chain subject to the effect of quantization and packet dropout is addressed based on Takagi–Sugeno (T–S) fuzzy-approximation. Firstly, the stochastic variation of mode transition probabilities with time-varying peculiarities is considered in a finite set, which is dominated by a higher-level homogeneous Markov chain. Moreover, partially unknown information in higher-level transition probabilities (HTPs) matrix is resolved by constructing a unified framework, which covers the stochastic switching and arbitrary switching as special cases, simultaneously. Secondly, considering the burden of network communication between components, the quantization impact and packet dropout caused by network network-induced constraints are integrated into the co-design of fuzzy tracking controller, which is mode-dependent and variation-dependent. Several criteria for the stochastic stability and \({\mathcal {H}}_{\infty }\) performance of the augmented system are deduced by establishing a series of linear matrix inequalities. Ultimately, two simulation examples are given to verify the practicability and effectiveness of the proposed control design schemes.

     

Dynamic output-feedback control for singular Markovian jump systems with partly unknown transition rates

Nonlinear Dynamics - This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with partly unknown transition rates. First of all, for the...     

Output-feedback control for singular Markovian jump systems with input saturation

This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with input saturation. The stabilization and set invariance conditions are first formulated in terms of non-convex matrix inequalities which is not linear matrix inequalities (LMIs). This paper, however, successfully derives the necessary and sufficient conditions for the non-convex inequalities in terms of LMIs. Also, an optimization problem is formulated to find the largest contractively invariant set in mean square sense of the closed-loop systems. Two numerical examples show the validity of the derived results.     

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy controllers to verify the effectiveness of the proposed method.     

Security control of interval type-2 fuzzy system with two-terminal deception attacks under premise mismatch

Nonlinear Dynamics - This paper focuses on security control of nonlinear networked control systems with parameter uncertainties. Interval type-2 T–S fuzzy model is used to represent the...     

Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays

Nonlinear Dynamics - This paper addresses the problem of finite-time observer-based control for continuous-time nonlinear Markovian jump systems with time-varying delays. The existing studies about...     

Stability of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities

In this paper, stochastic stability for a class of discrete-time Markovian jump delay systems with delayed impulses and partly unknown transition probabilities is investigated. Some new results are given based on stochastic Lyapunov functionals. It is shown that an unstable discrete-time Markovian jump delay system can be stochastically stable under certain stabilizing impulses. It is also shown that, when the nearest impulsive time interval is appropriately large, a stable discrete-time Markovian jump delay system can retain its stochastic stability property even with destabilizing impulses. Numerical examples together with their simulations are provided to demonstrate the effectiveness of the derived results.     

Observer-based fractional-order adaptive type-2 fuzzy backstepping control of uncertain nonlinear MIMO systems with unknown dead-zone

Nonlinear Dynamics - A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input...     

Adaptive type-2 neural fuzzy sliding mode control of a class of nonlinear systems

Nonlinear Dynamics - The objective of this study is to design an optimal control scheme for the control of a class of nonlinear flexible multi-body systems with extremely coupled dynamics and...     

Hybrid-triggered control for fuzzy Markov jump systems under input saturation

Nonlinear Dynamics - This article investigates the issue of hybrid-triggered control for fuzzy Markov jump system under input saturation. First, a hybrid-triggered control scheme is presented,...     

Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays

This paper studies the problem of the robustly exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays. The contribution of this paper is two-fold. Firstly, by constructing a modified Lyapunov functional and using free-weighting matrices technique, some delay-dependent robustly exponential stability criteria of such systems are obtained in terms of linear matrix inequalities (LMIs), which are less conservative than some existing ones. Secondly, a state feedback controller is designed, which can guarantee the robustly exponential stability of the uncertain closed-loop systems. Some illustrative numerical examples are given to demonstrate the reduced conservatism and applicability of the obtained results.     

Dynamic event-triggered and asynchronous sliding mode control for T-S fuzzy Markov jump systems

Nonlinear Dynamics - In this paper, the motion of a smart rigid-flexible satellite considering large deflections for its flexible appendages in general planar motion is modeled. Also, the satellite...     

Synchronization of complex networks with nonhomogeneous Markov jump topology

The problem of synchronization of complex networks with nonhomogeneous Markov jump topology and time-varying coupling delay is investigated in this paper. The Markov process in the underlying complex networks is finite piecewise homogeneous, which is a special case of nonhomogeneous Markov process. Based on the Lyapunov functional approach, an exponential stability condition is derived for the error system in terms of the linear matrix inequality method. Based on the condition, the design method of the desired controller is given. An example is given to show the effectiveness of the proposed technique.     

Linear control systems with fuzzy parameter

We consider linear control systems with undetermined parameters that are elements of a fuzzy set. For this system, we introduce the notion of pencil of trajectories and establish some of its properties. We also introduce the notion of fuzzy reachable set and prove that it is convex and compact. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 61–67, January–March, 2006.     

Dissipative control of switched nonlinear systems with sliding mode: an event-triggered control scheme

This paper introduces the event-triggered scheme to study the problems of dissipative control and dissipativity-based sliding mode control (SMC) for switched nonlinear systems. Firstly, based on a designed event-triggered scheme, a piecewise continuous state feedback controller is constructed; sufficient conditions for \(\left( Q,S,R\right) \)-\(\alpha \)-dissipativity of the resulting system are derived by the approaches of a switched Lyapunov function and an average dwell time. Secondly, these two methods are extended to the study of \(H_\infty \) performance and passive performance; the corresponding sufficient conditions are provided. Thirdly, the dissipative control problem is solved by introducing an event-triggered scheme into SMC method. Sufficient conditions for dissipativity of the resulting system are derived, and an SMC law is designed to guarantee the reachability. At the end of this paper, the correctness of the proposed methods is proved by two numerical examples.