Decentralized control of uncertain nonlinear stochastic systems based on DSC

In this paper, the decentralized stabilization control approach based on the dynamic surface control (DSC) is proposed for a class of large-scale interconnected stochastic nonlinear systems. The proposed approach combined the existing dynamic surface control (DSC) with back-stepping technique. This approach can overcome the problem of “explosion of complexity” inherent in the back-stepping method. Thus, the proposed control approach is simpler than the traditional back-stepping control method for the large-scale interconnected stochastic nonlinear systems. The stability analysis shows that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Direct adaptive neural control for strict-feedback stochastic nonlinear systems

This note considers the problem of direct adaptive neural control for a class of nonlinear single-input/single-output (SISO) strict-feedback stochastic systems. The variable separation technique is introduced to decompose the coefficient functions of the diffusion term. Radical basis function (RBF) neural networks are used to approximate unknown and desired control signals, then a novel direct adaptive neural controller is constructed via backstepping. The proposed adaptive neural controller guarantees that all the signals in the closed-loop system remain bounded in probability. A main advantage of the proposed controller is that it contains only one adaptive parameter needed to be updated online. Simulation results demonstrate the effectiveness of the proposed approach.     

Event-triggered-based fixed-time adaptive neural fault-tolerant control for stochastic nonlinear systems under actuator and sensor faults

Nonlinear Dynamics - In this paper, the problem of adaptive fault-tolerant control with event-triggered scheme is studied for a class of uncertain stochastic nonlinear systems with the actuator and...     

Adaptive neural output feedback control of nonlinear discrete-time systems

In this paper, a nonautonomous impulsive neutral-type neural network with delays is considered. By establishing a singular impulsive delay differential inequality and employing contraction mapping principle, several sufficient conditions ensuring the existence and global exponential stability of the periodic solution for the impulsive neutral-type neural network with delays are obtained. Our results can extend and improve earlier publications. An example is given to illustrate the theory.     

Adaptive neural tracking control for a class of perturbed pure-feedback nonlinear systems

This paper focuses on the problem of the adaptive neural control for a class of a perturbed pure-feedback nonlinear system. Based on radial basis function (RBF) neural networks’ universal approximation capability, an adaptive neural controller is developed via the backstepping technique. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood around the origin. The main advantage of this note lies in that a control strategy is presented for a class of pure-feedback nonlinear systems with external disturbances being bounded by functions of all state variables. A numerical example is provided to illustrate the effectiveness of the suggested approach.     

Adaptive fuzzy finite-time control of stochastic nonlinear systems with actuator faults

Nonlinear Dynamics - This paper considers the finite-time control problem for a class of nonlinear stochastic systems with actuator faults/failure. A fast convergence feedback control algorithm...     

Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients

Nonlinear Dynamics - This paper is devoted to the adaptive finite-time prescribed performance control (FTPPC) for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs),...     

Adaptive dynamic surface neural network control for nonstrict-feedback uncertain nonlinear systems with constraints

This paper presents an adaptive dynamic surface neural network control for a class of nonstrict-feedback uncertain nonlinear systems subjected to input saturation, dead zone and output constraint. The problem of input saturation is solved by designing an anti-windup compensator, and the issue of output constraint is addressed by introducing tan-type Barrier Lyapunov function. Furthermore, based on adaptive backstepping technique, a series of novel stabilizing functions are derived. First-order sliding mode differentiator is introduced into backstepping design to obtain the first-order derivative of virtual control. The real control input is obtained using dead-zone inverse method. It is proved that the proposed control scheme can achieve finite time convergence of the output tracking error into a small neighbor of the origin and guarantee all the closed-loop signals are bounded. Simulation results demonstrate the effectiveness of the proposed control scheme.     

Adaptive smooth control for nonlinear uncertain systems

Nonlinear Dynamics - This paper presents an adaptive smooth controller for a class of nonlinear dynamical systems in the presence of bounded uncertainties with unknown bounds. Motivated by the...     

Adaptive intelligence learning for nonlinear chaotic systems

In this paper, a reinforcement learning algorithm is proposed for a class of nonlinear differential chaotic systems. The nonlinear function of the chaotic systems is assumed to be bounded but the bounds are unknown. The unknown bounds need to be on-line adjusted. An adaptive optimal (or near optimal) control input with the reinforcement signal can be obtained compared with the current adaptive control for chaotic systems. The reinforcement signal is approximated by the neural networks. Based on Lyapunov analysis theory and by using Young’s inequalities, the closed-loop system is guaranteed to be stable. Finally, the simulation results are given to illustrate the effectiveness of the approach.     

Lyapunov function construction for nonlinear stochastic dynamical systems

Though the Lyapunov function method is more efficient than the largest Lyapunov exponent method in evaluating the stochastic stability of multi-degree-of-freedom (MDOF) systems, the construction of Lyapunov function is a challenging task. In this paper, a specific linear combination of subsystems’ energies is proposed as Lyapunov function for MDOF nonlinear stochastic dynamical systems, and the corresponding sufficient condition for the asymptotic Lyapunov stability with probability one is then determined. The proposed procedure to construct Lyapunov function is illustrated and validated with several representative examples, where the influence of coupled/uncoupled dampings and excitation intensities on stochastic stability is also investigated.     

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...     

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.     

Adaptive impulsive synchronization of nonlinear chaotic systems

In this paper, an adaptive impulse control with only one restriction criterion is derived to achieve synchronization of nonlinear chaotic systems in the exponential rate of convergence. It is assumed that the system satisfies the local Lipschitz condition and the Lipschitz constant is estimated by an augmented adaptation equation. The significance of the related control parameters in the criterion is also discussed in detail. The Duffing and the Lorenz systems have been simulated to illustrate the theoretical analysis.     

Event-triggered optimal control for nonlinear stochastic systems via adaptive dynamic programming

Nonlinear Dynamics - For nonlinear Itô-type stochastic systems, the problem of event-triggered optimal control (ETOC) is studied in this paper, and the adaptive dynamic programming (ADP)...     

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructi...     

Almost sure state estimation for nonlinear stochastic systems with Markovian switching

In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic systems with Markovian switching. A nonlinear state estimator with Markovian switching is first proposed, and then, a sufficient condition is given, which guarantees the almost sure asymptotic stability of the dynamics of the estimation error. Based on this condition, some simplified criteria are deduced by taking special forms of Lyapunov functions. Subsequently, an easy-to-verify procedure is put forward for the state estimation problem of the linear stochastic system with Markovian switching. Finally, two numerical examples are used to illustrate the effectiveness of the main results.