Finite-time Stabilization and Robust Control of Stochastic Nonlinear System Based on Hamiltonian Realization

This article takes a fast finite-time control of stochastic nonlinear systems into account. The presence of unknown stochastic disturbance terms makes the traditional fast finite-time control approaches unavailable. To deal with this difficulty, by establishing an auxiliary function and using Jensen's inequality, in Lemma 6, a new criterion of fast finite-time stability is first established for the uncertain stochastic system. Based on the approximation ability of neural networks (NNs), an innovative fast finite-time strategy is put forward for stochastic nonlinear systems. Furthermore, by adopting the presented fast finite-time stability criterion, the stability of the stochastic systems is confirmed. Finally, two simulations are implemented to validate the feasibility of the presented NN control strategy.

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

In this article, the problem of event‐triggered adaptive asymptotic tracking control (ATC) for stochastic nonlinear systems with unknown control directions (UCDs) and full state constraints is concerned. It must be said that the controller design and system analysis is more complex and difficult since the existence of stochastic disturbances, UCDs and full state constraints simultaneously. By introducing the lower bound of the UCDs into the barrier Lyapunov functions, an event‐triggered adaptive MTN ATC scheme is proposed based on the boundary estimation method and a new event‐triggered control (ETC) strategy, which can achieve satisfactory asymptotic tracking performance and control performance of the system, while reduce the occupation of network resources. The simulation results not only verify the effectiveness of the proposed control scheme, but also present different tracking performances between three ETC strategies for comparison, further confirming the superiority of the proposed ETC strategy in achieving asymptotic tracking performance.

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.

In this paper we consider finite-time stabilization and finite-time boundedness control problems for time-varying discrete-time systems. We give a set of sufficient conditions, in terms of differen...

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.

Traditional Lyapunov stability theory cannot directly apply to constrained stochastic nonlinear systems when using barrier Lyapunov functions due to their inherent lack of radial unboundedness. This article presents a novel approach to establishing finite-time stability for such systems by employing Lyapunov functions. The proposed stability analysis relies on a time-varying gain function that remains uniformly bounded. This approach ensures that the system achieves finite-time stability with an arbitrarily prescribed upper bound on the settling time, thereby effectively avoiding the unbounded controller gain problem. The resulting stability is further extended to the finite-time state-feedback control for strict-feedback stochastic nonlinear systems with output constraints. Simulation studies validate the effectiveness of the proposed control scheme.

In this paper, we consider the problem of decentralized adaptive output‐feedback regulation for stochastic nonlinear interconnected systems with unknown virtual control coefficients, stochastic unmodeled dynamic interactions. The main contributions of the paper are as follows: (1) This paper presents the first result on decentralized output‐feedback control for stochastic nonlinear systems with unknown virtual control coefficients; (2) For stochastic interconnected systems with stochastic integral input‐to‐state stable unmodeled dynamics, and more general nonlinear uncertain interconnections which depend upon the outputs of subsystems and the stochastic unmodeled dynamics, a decentralized output‐feedback controller is designed to drive the outputs and states to the origin almost surely. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Fuzzy model-based control of nonlinear stochastic systems with time-delay

This article investigates the event-triggered optimized tracking control problem for stochastic nonlinear systems based on reinforcement learning (RL). By using the backstepping strategy, an adaptive RL algorithm is performed under the identifier-critic-actor architecture to achieve event-triggered optimized control (ETOC). Moreover, a novel dynamically adjustable event-triggered mechanism is delicately designed, which adjusts the triggering threshold online to economize communication resources and reduce the computation burden. To overcome the difficulty that the virtual control signals are discontinuous due to the state-triggering, the virtual controllers are designed with the continuous sampling states signals, and the actual optimal controller is redesigned by using the triggered states in the last step. Furthermore, the proposed ETOC in this paper has significant advantages in terms of saving network resources because the event-triggered mechanism is employed in the sensor-to-controller channel and the event-sampled states are utilized to directly activate the control actions. Finally, it can be guaranteed that all signals of the stochastic system are bounded under the presented ETOC method. A simulation example is carried out to illustrate the effectiveness of the proposed ETOC algorithm.

This paper provides finite-time and fixed-time stabilization control strategy for delayed memristive neural networks. Considering that the parameters in the memristive model are state-dependent, which may contain unexpected parameter mismatch when different initial conditions are chosen, in this case, the traditional robust control and analytical methods cannot be carried out directly. To overcome this problem, a brand new robust control strategy was designed under the framework of Filippov solution. Based on the designed discontinuous controller, numerically testable conditions are proposed to stabilize the states of the target system in finite time and fixed time. Moreover, the upper bound of the settling time for stabilization is estimated. Finally, numerical examples are exhibited to explain our findings.

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.

SummaryThis article is mainly concentrated on the predefined‐time adaptive fuzzy control of stochastic nonlinear systems. To handle nonlinear functions that are uncertain, fuzzy logic systems (FLSs) are used to approximate them. Compared with the existing studies, a Lyapunov‐type criterion for practically predefined‐time stochastic stabilization (PPSS) is put forward to guarantee the stabilization of the system. The stabilization time is merely dependent on one design parameter, which means the parameter can be adjusted to set the stability time.

This paper considers the output-feedback control problem for a class of stochastic nonlinear systems with unknown control directions and perturbations. By using radial basis function neural network (RBF NN) approximation approach, the tuning function method and backstepping technique, an adaptive output-feedback controller is successfully constructed to guarantee the closed-loop system to be mean square semi-globally uniformly ultimately bounded (M-SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.

This paper proposes an adaptive learning algorithm for stochastic nonlinear systems with dead-zone characteristics and state constraints. First, the approximation capability of neural networks is utilized to model the unknown nonlinear dynamics, and an adaptive neural network controller is designed based on the backstepping control technique. Second, a dynamic event-triggering mechanism is developed, where the triggering condition dynamically adjusts over time based on system information and internal variables. Meanwhile, the auxiliary system is utilized to counteract the dead-zone nonlinearity, and the state constraints are handled by designing a barrier Lyapunov function. The proposed event-triggered dynamic surface control strategy not only ensures the semi-global uniform ultimate boundedness of the stochastic nonlinear system but also effectively eliminates the Zeno behavior. Finally, simulation experiments demonstrate the feasibility of the proposed learning strategy.