scholarly journals Adaptive State-Feedback Stabilization for Stochastic Nonholonomic Mobile Robots with Unknown Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenli Feng ◽  
Qingli Sun ◽  
Zhijun Cao ◽  
Dongkai Zhang ◽  
Hua Chen
Keyword(s):  
Mobile Robots ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Unknown Parameters ◽  
Nonholonomic Mobile Robots ◽  
Stabilizing Controllers ◽  
Stochastic Case ◽  
Switching Control Strategy ◽  
Zero Equilibrium

The stabilizing problem of stochastic nonholonomic mobile robots with uncertain parameters is addressed in this paper. The nonholonomic mobile robots with kinematic unknown parameters are extended to the stochastic case. Based on backstepping technique, adaptive state-feedback stabilizing controllers are designed for nonholonomic mobile robots with kinematic unknown parameters whose linear velocity and angular velocity are subject to some stochastic disturbances simultaneously. A switching control strategy for the original system is presented. The proposed controllers that guarantee the states of closed-loop system are asymptotically stabilized at the zero equilibrium point in probability.

scholarly journals Asymptotic Stabilization by State Feedback for a Class of Stochastic Nonlinear Systems with Time-Varying Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Wang ◽  
Wuquan Li ◽  
Xiuhong Wang
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Original System ◽  
Feedback Stabilization ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Control Coefficients

This paper investigates the problem of state-feedback stabilization for a class of upper-triangular stochastic nonlinear systems with time-varying control coefficients. By introducing effective coordinates, the original system is transformed into an equivalent one with tunable gain. After that, by using the low gain homogeneous domination technique and choosing the low gain parameter skillfully, the closed-loop system can be proved to be globally asymptotically stable in probability. The efficiency of the state-feedback controller is demonstrated by a simulation example.

scholarly journals Adaptive Synchronization and Antisynchronization of a Hyperchaotic Complex Chen System with Unknown Parameters Based on Passive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Weiwei Cai ◽  
Xiaomei Cai
Keyword(s):  
Dynamical System ◽  
Parameter Estimation ◽  
State Feedback ◽  
Passive Control ◽  
Adaptive Synchronization ◽  
Passive System ◽  
Unknown Parameters ◽  
Chen System ◽  
Smooth State ◽  
Zero Equilibrium

This paper investigates the synchronization and antisynchronization problems of a hyperchaotic complex Chen system with unknown parameters based on the properties of a passive system. The essential conditions are derived under which the synchronization or antisynchronization error dynamical system could be equivalent to a passive system and be globally asymptotically stabilized at a zero equilibrium point via smooth state feedback. Corresponding parameter estimation update laws are obtained to estimate the unknown parameters as well. Numerical simulations verify the effectiveness of the theoretical analysis.

NN-Based Adaptive Output Feedback Stabilization via Passivation of MIMO Uncertain System

2012 ◽  
Vol 588-589 ◽  
pp. 1527-1532
Author(s):  
Yong Hong Zhu ◽  
Jie Yao ◽  
Jian Hong Wang
Keyword(s):  
Output Feedback ◽  
Uncertain System ◽  
Original System ◽  
Feedback Stabilization ◽  
Closed Loop System ◽  
Input Matrix ◽  
Unknown Parameters ◽  
Output Feedback Stabilization ◽  
Nonlinear Input ◽  
Adaptive Laws

An NN-based output feedback stabilization problem is studied via passivation of a class of multi-input multi-output nonlinear systems with unknown nonlinear input matrix and unknown parameters. Neural networks are used to identify unknown nonlinearities, and the update laws of weight parameters are proposed. The design methods of the adaptive passive controllers for this class of systems are discussed in the paper. The corresponding adaptive passive controllers and parametric adaptive laws are designed and presented respectively. It is proved that the closed-loop system composed of the original system and the designed controller is stable by the Lyapunov method, and the controller designed can render the closed system adaptive passive. Finally, a simulation example is given to prove the effectiveness and feasibility of the proposed method.

Proportional Nonlinear Systems: A Liable Class for Global Exponential State-Feedback Stabilization

2013 ◽  
Author(s):  
Francesco Carravetta
Keyword(s):  
Nonlinear Systems ◽  
Algebraic System ◽  
State Feedback ◽  
Original System ◽  
Two Dimensions ◽  
Feedback Stabilization ◽  
Medial Part ◽  
Input Output ◽  
Proportional Systems ◽  
Output Behavior

We introduce, through an analysis overall restricted, for the sake of simplicity, in two-dimensions, the class of proportional systems, a nice subclass of the ΣΠ-algebraic nonlinear systems that we formerly introduced in another paper as a sort of ‘non-linear paradigm’ linking nonlinear to bilinear systems. Also we define a decomposition, which every ΣΠ-algebraic system undergoes, into the cascade of a driver, medial and final bilinear subsystem, having the same input-output behavior as the original. We show that a systematic way for global feedback stabilization can be developed for the class of proportional systems, leading to the global feedback exponential stabilization of the medial part under some ‘natural’ condition of non singularity. We show in an example the capability of the proposed method to achieving global feedback stabilization for the original system as well.

Invariant manifold-based stabilizing controllers for nonholonomic mobile robots

2015 ◽  
Vol 20 (3) ◽  
pp. 276-284
Author(s):  
Yin Yin Aye ◽  
Keigo Watanabe ◽  
Shoichi Maeyama ◽  
Isaku Nagai
Keyword(s):  
Mobile Robots ◽  
Invariant Manifold ◽  
Nonholonomic Mobile Robots ◽  
Stabilizing Controllers

Robust Output-Feedback Formation Control Design for Nonholonomic Mobile Robot (NMRs)

Robotica ◽  
2019 ◽  
Vol 37 (6) ◽  
pp. 1033-1056 ◽  
Author(s):  
Bilal M. Yousuf
Keyword(s):  
Feedback Control ◽  
Mobile Robots ◽  
Output Feedback ◽  
Formation Control ◽  
State Feedback ◽  
Sliding Mode ◽  
Tracking Problem ◽  
Nonholonomic Mobile Robots ◽  
Nonholonomic Mobile Robot ◽  
Control Scheme

SummaryThis paper addresses the systematic approach to design formation control for kinematic model of unicycle-type nonholonomic mobile robots. These robots are difficult to stabilize and control due to their nonintegrable constraints. The difficulty of control increases when there is a requirement to control a cluster of nonholonomic mobile robots in specific formation. In this paper, the design of the control scheme is presented in a three-step process. First, a robust state-feedback point-to-point stabilization control is designed using sliding mode control. In the second step, the controller is modified so as to address the tracking problem for time-varying reference trajectories. The proposed control scheme is shown to provide the desired robustness properties in the presence of the parameter variation, in the region of interest. Finally, in third step, tracking problem of a single nonholonomic mobile robot extends to formation control for a group of mobile robots in the leader–follower scenario using integral terminal- based sliding mode control augmented with stabilizing control. Starting with the transformation of the mathematical model of robots, the proposed controller ensures that the robots maintain a constant distance between each other to avoid collision. The main problem with the proposed controller is that it requires all states specially velocities. Therefore, the state-feedback control scheme is then extended to output feedback by incorporating a highgain observer. With the help of Lyapunov analysis and appropriate simulations, it is shown that the proposed output-feedback control scheme achieves the required control objectives. Furthermore, the closed loop system trajectories reach to desired equilibrium point in finite time while maintaining the special pattern.

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