Constrained controllability of nonlinear stochastic impulsive systems

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

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

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.

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.

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

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.

Stabilization of a class of nonlinear stochastic systems

Involves formulation of some problems arising in the analysis and control of a class of discrete-time nonlinear stochastic systems in terms of linear matrix inequalities. This allows one to utilize a wide variety of numerical techniques available for tackling both the feasibility problem and the actual numerical solution in an efficient manner.

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.

In this paper, the covariance control algorithm for nonlinear stochastic systems using covariance feedback is studied. Covariance control of nonlinear systems scenario involves the theory of covariance control based on the idea of the covariance feedback. Therefore, the proposed covariance control algorithm is derived for our case, firstly by applying the covariance control method and linear approximation of nonlinear systems, and then it is achieved by adopting this method for a class of nonlinear stochastic systems by using feedback linearization idea and a covariance feedback controller. The effectiveness of the proposed covariance feedback algorithm is studied using numerous simulations concerning different nonlinear case studies.

This paper studies the infinite horizonH∞control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean squareH∞control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.

Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

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

This paper discusses the multi-player non-cooperative game of nonlinear stochastic time-varying systems described by Itô-type differential equations in a finite time interval. Multi-player non-cooperative game problems are represented by multi-objective Pareto (MOP) control problems to describe the fact that each player has their own goals. By applying Hamilton–Jacobi inequalities (HJIs), the criterion of upper bounds of the MOP boundary is obtained for nonlinear stochastic systems, and the corresponding strategies are designed for such games, so the MOP problem is transformed into a HJI-constrained MOP problem. In order to overcome the difficulty of solving HJIs, a global linearization method is proposed to approximate the nonlinear systems. By the proposed global linearization method, multi-player non-cooperative game problems are transformed into Riccati equation-constrained MOP problems, and the approximate solutions of HJI-constrained MOP problems are obtained. Finally, a practical example is given to illustrate the effectiveness of the proposed method.

This paper extends H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control theory to a more general class of stochastic nonlinear systems with dynamic uncertainties. From the view of stochastic dissipation, we investigate the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> robust performance rule design for this general class of systems. Under some mild assumptions on the unmodeled dynamics, we establish the relationship between the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gain of the dynamic uncertain stochastic nonlinear systems and the solution to a certain HJI inequality. Furthermore, for some systems satisfying some proper matching conditions, we discuss the methods of acquiring the control laws without solving HJI inequality.