A criterion of robustness intelligent nonlinear control for multiple time-delay systems based on fuzzy Lyapunov methods

A control system with state feedback controllers, in which the fuzzy Lyapunov approach is developed for the stability criterion, is studied. The proposed intelligent design provides a systematic and effective framework for the control systems. The global nonlinear controller is constructed based on T–S (Takagi–Sugeno) fuzzy controller design techniques, blending all such local state feedback controllers. Based on this design, the stability conditions of a multiple time-delay system are derived in terms of the fuzzy Lyapunov theory. The effectiveness and the feasibility of the proposed controller design method are demonstrated through numerical simulations.     

Control Problems for Systems with Uncertainty

A review is made of the results obtained at the S. P. Timoshenko Institute of Mechanics in synthesis of robust controllers for linear stationary and periodic systems with uncertainty. The emphasis is on algorithms for construction of the Lyapunov function by solving the matrix Riccati equation and linear matrix inequalities. To illustrate the algorithms proposed, stabilization systems with uncertainty are synthesized for an A4D aircraft and a hopping vehicle. The numerical implementation of the algorithms involves no difficulties, since they are oriented toward standard MATLAB routines     

Pragmatical adaptive synchronization of different orders chaotic systems with all uncertain parameters via nonlinear control

A new adaptive synchronization scheme by pragmatical asymptotically stability theorem is proposed in this paper. Based on this theorem and nonlinear control theory, a new adaptive synchronization scheme to design controllers can be obtained and especially the constraints for minimum values of feedback gain K in controllers can be derived. This new strategy shows that the constraint values of feedback gain K are related to the error of unknown and estimated parameters if the goal system is given. Through this new strategy, an appropriate feedback gain K can be always decided easily to obtain controllers achieving adaptive synchronization. Two identical Lorenz systems with different initial conditions and two completely different nonlinear systems with different orders, augmented R?ssler??s system and Mathieu?Cvan der Pol system, are used for illustrations to demonstrate the efficiency and effectiveness of the new adaptive scheme in numerical simulation results.     

Low-energy impact of adaptive cylindrical piezoelectric–composite shells

A theoretical framework for analyzing low-energy impacts of laminated shells with active and sensory piezoelectric layers is presented, including impactor dynamics and contact law. The formulation encompasses a coupled piezoelectric shell theory mixing first order shear displacement assumptions and layerwise variation of electric potential. An exact in-plane Ritz solution for the impact of open cylindrical piezoelectric–composite shells is developed and solved numerically using an explicit time integration scheme. The active impact control problem of adaptive cylindrical shells with distributed curved piezoelectric actuators is addressed. The cases of optimized state feedback controllers and output feedback controllers using piezoelectric sensors are analyzed. Numerical results quantify the impact response of cylindrical shells of various curvatures including the signal of curved piezoelectric sensors. Additional numerical studies quantify the impact response of adaptive cylindrical panels and investigate the feasibility of actively reducing the impact force.     

Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques

In this paper, recursive and active backstepping nonlinear techniques are employed to design control functions for the respective, control, and synchronization of the new hyperchaotic Liu system. The designed recursive backstepping nonlinear controllers are capable of stabilizing the hyperchaotic Liu system at any position as well as controlling it to track any trajectory that is a smooth function of time. The designed active backstepping nonlinear controllers are effective in globally synchronizing two identical hyperchaotic Liu systems evolving from different initial conditions. The results are all validated by numerical simulations.     

Pinning synchronization of complex network with non-derivative and derivative coupling

This paper investigates synchronization of a complex network with non-derivative and derivative coupling. For achieving the pinning synchronization, the corresponding controllers are designed and applied to only a small fraction of nodes. Both linear and adaptive feedback control methods are used to design controllers. Based on Lyapunov stability theory, several simple and useful criteria for pinning synchronization are derived. Finally, numerical simulations are given to verify the effectiveness of the derived results.     

Modeling and control of a nonlinear half-vehicle suspension system: a hybrid fuzzy logic approach

Modeling and control of vehicle suspension system are high noteworthy from safety to comfort. In this paper, an analytical nonlinear half-vehicle model which is included quadratic tire stiffness, cubic suspension stiffness, and coulomb friction is derived based on fundamental physics. A hybrid fuzzy logic approach which combines fuzzy logic and PID controllers is designed for reducing the vibration levels of passenger seat and vehicle body. Performances of designed controllers have been evaluated by numerical simulations. Comparisons with classical PID control, Fuzzy Logic Control (FLC) and Hybrid Fuzzy-PID control (HFPID) have also been provided. Results of numerical simulations are evaluated in terms of time histories of displacement and acceleration responses and ride index comparison. A good performance for the Hybrid Fuzzy-PID controller with coupled rules (HFPIDCR) is achieved in simulation studies despite the nonlinearities.     

PI/PID controller stabilizing sets of uncertain nonlinear systems: an efficient surrogate model-based approach

Nonlinear Dynamics - Closed forms of stabilizing sets are generally only available for linearized systems. An innovative numerical strategy to estimate stabilizing sets of PI or PID controllers...     

Cluster oscillatory synchronization of networked Lagrangian systems with the distributed adaptive observers

This paper investigates cluster synchronization problem for uncertain networked Lagrangian systems with nonidentical oscillatory leaders. Firstly, in the case of positive couplings and in the case of positive and negative couplings, we propose two different distributed adaptive observers. Based on these adaptive observers, two adaptive controllers are developed. Then, some cluster synchronization criteria are given to ensure that the desired cluster synchronization scheme can be arrived. Due to introduction of these two adaptive observers, it is no longer necessary for each follower to obtain the frequency information of the corresponding leader system. Finally, the performance and effective of the provided controllers are verified by some numerical examples.     

Adaptive nonsingular terminal sliding mode control for synchronization of identical Φ 6 oscillators

The main goal of this paper is to propose the adaptive nonsingular terminal sliding mode controllers for complete synchronization (CS) and anti-synchronization (AS) between two identical ?? ⁶ Van der Pol or Duffing oscillators with presentations of system uncertainties and external disturbances. Unlike directly eliminating the nonlinear items of synchronized error system for sliding mode control schemes in the literature, the proposed adaptive controllers can tackle the nonlinear dynamics without active cancellation. The controllers can be implemented without known bounds of system uncertainties and external disturbances. Meanwhile, the feedback gains are not determined in advance but updated by the adaptive rules. Sufficient conditions are given based on the Lyapunov stability theorem and numerical simulations are performed to verify the effectiveness of presented schemes. The results show that the chaotic synchronization can be achieved accurately by the chattering free control.     

Observer-based synchronization of memristive systems with multiple networked input and output delays

This paper investigates the synchronization problem of memristive systems with multiple networked input and output delays via observer-based control. A memristive system is set up, and the fuzzy method has been employed to linearize the dynamical system of the memristive system; the networked input and output delays are considered in the synchronization problem of this system. A truncated predictor feedback approach is employed to design the observers. Under certain restrictions, a class of finite-dimensional observer-based output feedback controllers is designed. A numerical example is carried out to demonstrate the effectiveness of the proposed methods.     

Chaos synchronization of Rikitake chaotic attractor using the passive control technique

Chaos synchronization of Rikitake system applying the passive control method is investigated in this paper. Based on the passive technique, the passive controllers are designed. The nonlinear controller for the synchronization of two identical Rikitake systems or two different chaotic systems is simple and convenient to realize. Both theoretical analysis and numerical results show the effectiveness of the proposed method.     

A Nonlinear Vibration Absorber for Flexible Structures

An approach for implementing an active nonlinear vibration absorber for flexible structures is presented. The technique exploits the saturation phenomenon exhibited by multidegree-of-freedom systems with quadratic nonlinearities possessing two-to-one autoparametric resonances. The strategy consists of introducing second-order controllers and coupling each of them with the plant through a sensor and an actuator, where both the feedback and control signals are quadratic. Once the structure is forced near its resonances, the oscillatory response is suppressed through the saturation phenomenon. We present theoretical and experimental results of the application of the proposed vibration absorber. The structure consists of a cantilever beam, the feedback signal is generated by a strain gage, and the actuation is achieved through piezoceramic patches. The equations of motion are developed and analyzed through perturbation techniques and numerical simulation. Then, the strategy is tested by assembling the controllers in electronic components and suppressing the vibrations of the first and second modes of two beams.     

Control and synchronization for a class of new chaotic systems via linear feedback

This paper presents a class of new chaotic systems containing two system parameters and a nonlinear term. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and spectrum of Lyapunov exponents. Based on Lyapunov stability criteria, the simple sufficient conditions for the design of appropriate linear state feedback controllers to stabilize and synchronize globally the new chaotic systems are presented.     

On the sliding mode control of a Ball on a Beam system

This paper investigates the sliding mode control of the Ball on a Beam system. A static and a dynamic sliding-mode controllers are designed using a simplified model of the system; the simplified model renders the system feedback linearizable. Then, a static and a dynamic sliding-mode controllers are designed using the complete model of the Ball on a Beam system. Simulation results indicate that the proposed controllers work well. The four proposed controllers are implemented using an experimental setup. Implementation results indicate that the proposed control schemes work well. As expected, it is found that the proposed two controllers which are designed using the complete model of the system gave better performance than the ones designed using the simplified model of the system. In addition, the experimental results indicate the two dynamic controllers greatly reduce the chattering usually associated with sliding-mode controllers.     

A fuzzy wavelet neural network-based approach to hypersonic flight vehicle direct nonaffine hybrid control

A direct nonaffine hybrid control methodology is proposed for a generic hypersonic flight models based on fuzzy wavelet neural networks (FWNNs). The addressed strategy extends the previous indirect nonaffine control approaches stemming from simplified models of affine formulations. To cope with nonaffine effects on control design, analytically invertible models are constructed and then novel hybrid controllers are developed directly using nonaffine models. Furthermore, by employing FWNNs to devise adaptive terms, inversion errors are canceled via fuzzy neural approximations. In addition, robust terms are designed to achieve larger stable region in comparison with earlier work using Lyapunov synthesis. Finally, numerical simulation results from a hypersonic flight vehicle model are given to clarify the efficiency of the proposed direct nonaffine control scheme in the presence of parametric uncertainties.     

Anti-synchronization of Liu system and Lorenz system with known or unknown parameters

This work is concerned with anti-synchronization of Liu system and Lorenz system. Based on Lyapunov stability theory, different controllers are designed to anti-synchronize the two non-identical chaotic systems, active control is used when parameters are known, while the adaptive control law and the parameter update rule are derived via adaptive control when parameters are uncertain. Moreover, the convergence speeds of the scheme can be adjusted by changing the control coefficients. Finally, numerical simulations are also shown to verify the results.     

Projective synchronization of hyperchaotic Lü system and Liu system

This work is concerned with projective synchronization of hyperchaotic Lü system and Liu system by add-order method. Different controllers are designed to projective-synchronize the two nonidentical chaotic systems, active control is used when parameters are known, while the adaptive control law and the parameter update rule are derived via adaptive control when parameters are uncertain. Moreover, the convergence rates of the scheme can be adjusted by changing the control coefficients. Finally, numerical simulations are also shown to verify the results.     

Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control

This paper investigates the issue of almost sure cluster synchronization in nonlinearly coupled complex networks with nonidentical nodes and time-varying delay. These networks are modulated by a continuous-time Markov chain and disturbed by a Brownian movement. The decentralized adaptive update law and pinning control protocol are employed in designing controllers for guaranteeing almost sure cluster synchronization. By constructing a novel stochastic Lyapunov–Krasovskii function and using the stochastic Lasalle-type invariance theorem, some sufficient conditions for almost sure cluster synchronization of the networks are derived. Finally, a numerical example is given to testify the effectiveness of the theoretical results.     

Control of the nonlinear oscillator bifurcation under a superharmonic resonance

A weakly nonlinear oscillator is modeled by a differential equation. A superharmonic resonance system can have a saddle-node bifurcation, with a jumping transition from one state to another. To control the jumping phenomena and the unstable region of the nonlinear oscillator, a combination of feedback controllers is designed. Bifurcation control equations are derived by using the method of multiple scales. Furthermore, by performing numerical simulations and by comparing the responses of the uncontrolled system and the controlled system, we clarify that a good controller can be obtained by changing the feedback control gain. Also, it is found that the linear feedback gain can delay the occurrence of saddle-node bifurcations, while the nonlinear feedback gain can eliminate saddle-node bifurcations. Feasible ways of further research of saddle-node bifurcations are provided. Finally, we show that an appropriate nonlinear feedback control gain can suppress the amplitude of the steady-state response.