T–S fuzzy affine model based non-synchronized state estimation for nonlinear Itô stochastic systems

Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

In this study, we investigate multi-player noncooperative minmax H∞ target tracking game strategy with conflicting target strategies and cooperative H∞ target tracking game strategy with common target strategy of nonlinear mean-field stochastic jump diffusion (MFSJD) system with external disturbance. Due to the nonlinear terms and mean-field (average) behaviors in the stochastic nonlinear MFSJD system and minmax H∞ payoff function, the multi-player noncooperative and cooperative minmax H∞ mean-field game strategy of nonlinear MFSJD system are more difficult than the linear MFSJD system and conventional nonlinear stochastic system. To avoid solving complex Hamilton Jacobi Isaacs inequalities (HJIIs) of multi-player noncooperative minmax H∞ mean-field target tracking game strategy of nonlinear MFSJD system, the nonlinear MFSJD system is interpolated by a set of local linearized MFSJD system through smoothing functions by the global linearization method. Then the multi-player noncooperative minmax H∞ nonlinear mean-field target tracking game strategy design can be transformed to a linear matrix inequalities (LMIs)-constrained multi-objective optimization problem (MOP). The LMIs-constrained MOP could be efficiently solved by the help of the proposed LMIs-constrained multi-objective evolution algorithm (MOEA). We can prove that the Pareto optimal solution of LMIs-constrained MOP is the Nash equilibrium solution of noncooperative minmax H∞ mean-field target tracking strategy of nonlinear mean-field MFSJD system. Further, the cooperative minmax H∞ mean-field common target tracking strategy of nonlinear mean-field stochastic system is reduced to an LMIs-constrained single-objective optimization problem (SOP). Finally, two simulation examples of cyber-financial mean-field systems are given to illustrate the design procedure and compare the efficacies of the proposed noncooperative and cooperative minmax H∞ mean-field target tracking strategy of nonlinear MFSJD systems.

In this paper, robust constrained model predictive control of uncertain fuzzy affine systems is considered. Based on piecewise quadratic Lyapunov functions, highly efficient robust constrained predictive control approaches are developed so that the closed-loop stability is guaranteed, and the transient control performance is improved even under input or state constraints. Moreover, by using approximate ellipsoid and S -procedure, the solution to the fuzzy affine model based predictive control can be cast as a convex optimization problem subject to some linear matrix inequalities, rather than a nonconvex problem via bilinear matrix inequalities as in conventional fuzzy affine model-based control. The proposed controllers are thus easier for real-time implementation in industry. Simulation results on the fluidized bed combustion plant have demonstrated the performance of the proposed approaches.

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method.

This manuscript considers the finite time adaptive neural tracking control problem for a class of the nonstrict-feedback stochastic nonlinear systems with Bouc-Wen hysteresis input. During the design process, a Bouc-Wen model is first adopted to obtain the input hysteresis phenomenon. By fusion with the backstepping technique and the neural network approximation capability, the unknown nonlinearities are coped with, a constructive finite time adaptive neural network control strategy is proposed. Furthermore, the finite-time mean square stability of stochastic nonlinear systems is proved, and at last the effectiveness of the proposed control strategy is validated by the simulations.

In this paper, the dynamic surface control (DSC) algorithm is proposed for a class of stochastic nonlinear systems with nonminimum phase and the standard output-feedback form. The proposed algorithm is a stochastic vision by combining the traditional back-stepping together with the DSC technique, which can overcome the problem of ‘explosion of complexity’ in the back-stepping designing procedure for the stochastic nonlinear systems. Thus, it can reduce the computation complexity and is easy to be used in the actual implementation. It is shown that all the signals of the resulting closed-loop system are uniformly ultimately bounded.

A novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure-feedback form

Fixed-time adaptive neural self-triggered decentralized control for stochastic nonlinear systems with strong interconnections

This paper investigates the stabilization problem for a class of discrete‐time stochastic non‐affine nonlinear systems based on T‐S fuzzy models. Based on the function approximation capability of a class of stochastic T‐S fuzzy models, it is shown that the stabilization problem of a stochastic non‐affine nonlinear system can be solved as a robust stabilization problem of the stochastic T‐S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non‐affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

This paper investigates an improved fixed-time stability theory together with a state feedback controller for a class of nonlinear stochastic systems. First, a delicate transformation is performed, and next, a Gamma function is utilized to directly derive the value of the integral function, which ultimately yields a fixed-time stabilization theorem with a higher precision upper bound for the settling time. Unlike the existing estimation process of amplifying twice, we only performed one amplification, which weakens the effect of amplification. Then, a state feedback controller is constructed for stochastic systems by the method of adding a power integrator. Utilizing the proposed stochastic fixed-time stability theory, simulations show that the intended controller ensures that the trivial solution of the suggested system is fixed-time stable in probability. The results of the simulation demonstrate that the suggested control scheme is meaningful.

Stabilization for T–S model based uncertain stochastic systems

This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.

In this work, an adaptive neural network (NN) optimized output-feedback control problem is studied for a class of stochastic nonlinear systems with unknown nonlinear dynamics, input saturation, and state constraints. A nonlinear state observer is designed to estimate the unmeasured states, and the NNs are used to approximate the unknown nonlinear functions. Under the framework of the backstepping technique, the virtual and actual optimal controllers are developed by employing the actor-critic architecture. Meanwhile, the tan-type Barrier optimal performance index functions are developed to prevent the nonlinear systems from the state constraints, and all the states are confined within the preselected compact sets all the time. It is worth mentioning that the proposed optimized control is clearly simple since the reinforcement learning (RL) algorithm is derived based on the negative gradient of a simple positive function. Furthermore, the proposed optimal control strategy ensures that all the signals in the closed-loop system are bounded. Finally, a practical simulation example is carried out to further illustrate the effectiveness of the proposed optimal control method.

This paper put forward a piecewise quadratic Lyapunov functions approach combined with time information to analysis hybrid systems' stability issues. The piecewise quadratic Lyapunov functions can be continuous or discontinuous, and with the aid of time information, we can let the piecewise quadratic Lyapunov functions increase to some extent. The search of piecewise quadratic Lyapunov functions are finished by linear matrix inequalities. Two examples are showed to demonstrate the effectiveness of the approach.