scholarly journals A Covariance Feedback Approach to Covariance Control of Nonlinear Stochastic Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Salman Baroumand ◽  
Amir Reza Zaman ◽  
Mohammad Reza Mahmoudi
Keyword(s):  
Nonlinear Systems ◽  
Linear Approximation ◽  
Feedback Linearization ◽  
Control Algorithm ◽  
Stochastic Systems ◽  
Control Method ◽  
Nonlinear Case ◽  
Nonlinear Stochastic Systems ◽  
Covariance Control ◽  
Feedback Algorithm

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.

scholarly journals Composite Antidisturbance Control for a Class of Nonlinear Stochastic Systems via Disturbance Observer

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yunlong Liu ◽  
Yumin Zhang ◽  
Xiuming Yao
Keyword(s):  
Disturbance Observer ◽  
Stochastic Systems ◽  
Control Method ◽  
The Other ◽  
Stabilization Problem ◽  
Nonlinear Stochastic Systems ◽  
Stochastic Disturbance ◽  
Harmonic Signals ◽  
Unknown Phase ◽  
Dynamic Performances

The stabilization problem is investigated in this paper for a class of nonlinear systems with disturbances. The disturbances are supposed to be classified into two types. One type in the input channel is generated by an exogenous system, which can represent the constant or harmonic signals with unknown phase and magnitude. The other type is stochastic disturbance. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. By integrating the disturbance observers with conventional control method, the first type of disturbances can be estimated and rejected. Simultaneously, the desired dynamic performances can be guaranteed. An example is given to show the effectiveness of the proposed scheme.

A Covariance Controller Design Incorporating Optimal Estimation for Nonlinear Stochastic Systems

1996 ◽  
Vol 118 (2) ◽  
pp. 346-349 ◽  
Author(s):  
Wen-Jer Chang ◽  
Hung-Yuan Chung
Keyword(s):  
Cost Function ◽  
Stochastic Systems ◽  
Controller Design ◽  
Optimal Estimation ◽  
Nonlinear Stochastic Systems ◽  
Numerical Example ◽  
Describing Functions ◽  
Covariance Control ◽  
Variance Design

This note addresses the problem of constrained variance design with minimizing LQG cost function via the method of covariance control incorporating the optimal estimation for nonlinear stochastic systems. The nonlinear stochastic systems are first linearized and then are examined by way of the technique of describing functions. Finally, an application of this approach to a position servomechanism is illustrated by a numerical example.

scholarly journals Robust Tracking Control of Robot Manipulators Using Only Joint Position Measurements

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ancai Zhang ◽  
Jinhua She ◽  
Xuzhi Lai ◽  
Min Wu ◽  
Jianlong Qiu ◽  
...  
Keyword(s):  
Tracking Control ◽  
Feedback Linearization ◽  
Control Algorithm ◽  
Control Method ◽  
Robot Manipulator ◽  
Joint Position ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Nominal Model ◽  
Simulation Results

This paper concerns the tracking control of a robot manipulator with unknown uncertainties and disturbances. It presents a new control method that uses only joint position measurements to design a tracking controller. The controller has two parts. One is based on a feedback linearization technique; it makes the nominal model of a manipulator asymptotically track a desired trajectory. The other is based on the idea of equivalent input disturbance (EID); it compensates for uncertainties and disturbances. Together they enable a robot manipulator to precisely track the desired trajectory. The new control algorithm is applied to a two-link robot manipulator, and simulation results demonstrate the validity of this method.

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

2020 ◽  
Vol 392 ◽  
pp. 195-209
Author(s):  
Rui Wang ◽  
Yanjun Liu ◽  
Fusheng Yu ◽  
Jiayin Wang ◽  
Xiao Wang ◽  
...  
Keyword(s):  
Fuzzy Control ◽  
Control Algorithm ◽  
Stochastic Systems ◽  
Feedback Form ◽  
Nonlinear Stochastic Systems ◽  
Fuzzy Control Algorithm

A Variational Method for Approximating the Response of Nonlinear Stochastic Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 353-357
Author(s):  
L. D. Zirkle ◽  
L. G. Clark
Keyword(s):  
Approximate Solution ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Variational Method ◽  
Variational Methods ◽  
Stochastic Systems ◽  
Random Variables ◽  
Nonlinear Stochastic Systems ◽  
Non Gaussian

A method is introduced for determining approximate properties of the response of nonlinear stochastic systems. The method is based in concept on the variational methods of mechanics and allows the consideration of classes of systems not readily subject to analysis by existing techniques. Three examples are presented illustrating the application to nonlinear systems with non-stationary inputs, non-Gaussian inputs and with time delay. The main limitation of the technique is the necessity for assuming a meaningful form for the approximate solution in terms of arbitrary random variables.

scholarly journals A novel adaptive control design method for stochastic nonlinear systems using neural network

2021 ◽  
Author(s):  
Mohammad Mahdi Aghajary ◽  
Arash Gharehbaghi
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Stochastic Systems ◽  
Control Method ◽  
Dead Zone ◽  
Stochastic Nonlinear Systems ◽  
Adaptation Period ◽  
Dynamic Surface ◽  
Actuator Nonlinearity

AbstractThis paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.

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.

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