scholarly journals Stabilization of a Class of Stochastic Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Valiollah Ghaffari ◽  
Hamid Reza Karimi ◽  
Navid Noroozi ◽  
S. Vahid Naghavi
Keyword(s):  
Nonlinear Systems ◽  
Stochastic Systems ◽  
Adaptive Controller ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Closed Loop Systems ◽  
Time Control ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability

This paper addresses two control schemes for stochastic nonlinear systems. Firstly, an adaptive controller is designed for a class of motion equations. Then, a robust finite-time control scheme is proposed to stabilize a class of nonlinear stochastic systems. The stability of the closed-loop systems is established based on stochastic Lyapunov stability theorems. Links between these two methods are given. The efficiency of the control schemes is evaluated using numerical simulations.

Adaptive finite-time control for stochastic nonlinear systems using multi-dimensional Taylor network

2021 ◽  
pp. 014233122110396
Author(s):  
Shan-Liang Zhu ◽  
Ming-Xin Wang ◽  
Yu-Qun Han
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Lyapunov Stability Theory ◽  
Loop System ◽  
Stochastic Nonlinear Systems ◽  
Time Control ◽  
Control Scheme ◽  
The Stability

In this paper, the problem of adaptive finite-time multi-dimensional Taylor network (MTN) control for a class of stochastic nonlinear systems is investigated. By combining the MTN-based approximate method and adaptive backstepping technique, a novel adaptive finite-time MTN control scheme is proposed. In this scheme, the MTNs are used to approximate the unknown nonlinear functions of the systems. The finite-time Lyapunov stability theory is utilized to prove the stability of the close-loop system. The proposed scheme can ensure that all signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood of the origin in a finite time. Three simulation examples are presented to show the effectiveness of the control scheme. It should be pointed that the adaptive MTN controller proposed in this paper has the advantages of fast computational speed and good real-time performance thanks to the simple structure of the MTN.

scholarly journals Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 963
Author(s):  
Yang Li ◽  
Jianhua Zhang ◽  
Xiaoyun Ye ◽  
Cheng Siong Chin
Keyword(s):  
Nonlinear Systems ◽  
Fixed Time ◽  
High Order ◽  
Convergence Time ◽  
Feedback Form ◽  
Time Control ◽  
Control Scheme ◽  
Lyapunov Stability Criterion ◽  
The Stability ◽  
Strict Feedback

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

scholarly journals Forecasting COVID-19 with Importance-Sampling and Path-Integrals

2020 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Simulated Annealing ◽  
Nonlinear Systems ◽  
Financial Markets ◽  
Path Integral ◽  
Stochastic Systems ◽  
Path Integrals ◽  
Strong Support ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Adaptive Simulated Annealing

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

scholarly journals Forecasting COVID-19 with Importance-Sampling and Path-Integrals

2021 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Simulated Annealing ◽  
Nonlinear Systems ◽  
Financial Markets ◽  
Path Integral ◽  
Stochastic Systems ◽  
Path Integrals ◽  
Strong Support ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Adaptive Simulated Annealing

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

scholarly journals Forecasting with Importance-Sampling and Path-Integrals

2020 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Simulated Annealing ◽  
Nonlinear Systems ◽  
Financial Markets ◽  
Path Integral ◽  
Stochastic Systems ◽  
Path Integrals ◽  
Strong Support ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Adaptive Simulated Annealing

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are described as being useful to detail such systems. Method: ASA and PATHINT/PATHTREE have been demonstrated as being effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Results: Not only can selected systems in these three disciplines be aptly modeled, but results of detailed calculations have led to new results and insights not previously obtained. Conclusion: While optimization and path-integral algorithms are now quite well-known (at least to many scientists), these applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

scholarly journals Forecasting with Importance-Sampling and Path-Integrals: Applications to COVID-19

2020 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Simulated Annealing ◽  
Nonlinear Systems ◽  
Financial Markets ◽  
Path Integral ◽  
Stochastic Systems ◽  
Path Integrals ◽  
Strong Support ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Adaptive Simulated Annealing

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

scholarly journals Forecasting with Importance-Sampling and Path-Integrals: Applications to COVID-19

2020 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Simulated Annealing ◽  
Nonlinear Systems ◽  
Financial Markets ◽  
Path Integral ◽  
Stochastic Systems ◽  
Path Integrals ◽  
Strong Support ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Stochastic Systems ◽  
Adaptive Simulated Annealing

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are described as being useful to detail such systems. Method: ASA and PATHINT/PATHTREE have been demonstrated as being effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Not only can selected systems in these three disciplines be aptly modeled, but results of detailed calculations have led to new results and insights not previously obtained. Conclusion: While optimization and path-integral algorithms are now quite well-known (at least to many scientists), these applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

A Design Method of LS-SVM Based Stable Adaptive Controller for a Class of Nonlinear Systems

2011 ◽  
Vol 48-49 ◽  
pp. 17-20
Author(s):  
Chun Li Xie ◽  
Tao Zhang ◽  
Dan Dan Zhao ◽  
Cheng Shao
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Nonlinear Function ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Control Law ◽  
Continuous Systems ◽  
Control Schemes ◽  
Closed Systems ◽  
Simulation Results

A design method of LS-SVM based stable adaptive controller is proposed for a class of nonlinear continuous systems with unknown nonlinear function in this paper. Due to the fact that the control law is derived based on the Lyapunov stability theory, the scheme can not only solve the tracking problem of this class of nonlinear systems, but also it can guarantee the asymptotic stability of the closed systems, which is superior to many LS-SVM based control schemes. The effectiveness of the proposed scheme is demonstrated by simulation results.

Robust fault-tolerant tracking control for a class of nonlinear systems based on position measurements only

2016 ◽  
Vol 230 (6) ◽  
pp. 486-497 ◽  
Author(s):  
Gang Shen ◽  
Zhen-Cai Zhu ◽  
Xiang Li ◽  
Qiang Meng ◽  
Yu Tang ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Fault Tolerant ◽  
Tracking System ◽  
High Quality ◽  
Differential Signal ◽  
Time Dynamic ◽  
Closed Loop Systems ◽  
Controlled Systems ◽  
Attitude Tracking ◽  
Control Scheme

The problem of trajectory tracking for a class of nonlinear systems in the presence of un-modeled dynamics, parameter variations and even the actuator faults is investigated in this paper. A novel fault-tolerant control scheme is proposed by combining the nominal model-based controller and time-delay controller, which are adopted to achieve the real-time dynamic compensation and guarantee the robust stability of the controlled systems, respectively. Moreover, high-quality differential signals are unavailable in the presence of disturbances and measurement noise, which limit the performance of closed-loop systems in practice. Therefore, an extended state observer (ESO) is introduced to obtain high-quality differential signal estimations based on position measurements only. Furthermore, the effectiveness of the proposed novel control scheme is verified by testing in the spacecraft attitude tracking system.

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