Design and Stability Analysis of a Fractional Order State Feedback Controller for Trajectory Tracking of a Differential Drive Robot

An efficient approach of inverse optimal control and adaptive control is developed for global asymptotic stabilization of a novel fractional-order four-wing hyperchaotic system with uncertain parameter. Based on the inverse optimal control methodology and fractional-order stability theory, a control Lyapunov function (CLF) is constructed and an adaptive state feedback controller is designed to achieve inverse optimal control of a novel fractional-order hyperchaotic system with four-wing attractor. Then, an electronic oscillation circuit is designed to implement the dynamical behaviors of the fractional-order four-wing hyperchaotic system and verify the satisfactory performance of the controller. Comparing with other fractional-order chaos control methods which may have more than one nonlinear state feedback controller, the inverse optimal controller has the advantages of simple structure, high reliability, and less control effort that is required and can be implemented by electronic oscillation circuit.

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Low-order state-feedback controller design for long-time average cost control of fluid flow systems: A sum-of-squares approach

2015 34th Chinese Control Conference (CCC) ◽

10.1109/chicc.2015.7260020 ◽

2015 ◽

Author(s):

Huang Deqing ◽

Chernyshenko Sergei

Keyword(s):

Fluid Flow ◽

Average Cost ◽

State Feedback ◽

Cost Control ◽

Controller Design ◽

Feedback Controller ◽

State Feedback Controller ◽

Long Time ◽

Time Average ◽

Order State

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Tracking a Chaotic System Using an Observer-Based Nonlinear State-Feedback Controller

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.403-408.4643 ◽

2011 ◽

Vol 403-408 ◽

pp. 4643-4648

Author(s):

Tanushree Roy ◽

Aparajita Sengupta

Keyword(s):

Nonlinear System ◽

Trajectory Tracking ◽

State Feedback ◽

Duffing Oscillator ◽

Feedback Controller ◽

Nonlinear Observer ◽

Single Input Single Output ◽

State Feedback Controller ◽

Single Output ◽

Nonlinear State

This paper attempts to design a Luenberger-like nonlinear observer and a nonlinear state-feedback controller for trajectory tracking of a single-input/single-output nonlinear system exhibiting chaotic dynamics. Using a nonlinear transformation, the nonlinear system is first transformed into a linear system and thereafter a control law is designed for trajectory tracking. The controller, designed on the basis of an input-output linearized model, is applied on both the linearized as well as the nonlinear system. The results are validated through simulation on a Duffing oscillator.

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Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

Advances in Mechanical Engineering ◽

10.1177/1687814020922654 ◽

2020 ◽

Vol 12 (7) ◽

pp. 168781402092265

Author(s):

Xiao Yu ◽

Fucheng Liao

Keyword(s):

Nonlinear Systems ◽

Discrete Time ◽

Trajectory Tracking ◽

Tracking Control ◽

State Feedback ◽

Feedback Controller ◽

Matrix Inequality ◽

State Feedback Controller ◽

Lipschitz Nonlinear Systems ◽

Reference Knowledge

In this article, the observer-based preview tracking control problem is investigated for a class of discrete-time Lipschitz nonlinear systems. To convert the observer-based trajectory tracking problem into a regulation problem, the classical difference technique is used to construct an augmented error system containing tracking error signal and previewable reference knowledge. Then, a state feedback controller with specific structures is taken into consideration. Sufficient design condition is established, based on the Lyapunov function approach, to guarantee the asymptotic stability of the closed-loop system. By means of some special mathematical derivations, the bilinear matrix inequality condition is successfully transformed into a tractable linear matrix inequality. Meanwhile, the gains of both observer and tracking controller can be computed simultaneously only in one step. As for the original system, the developed tracking control law is composed of an integrator, an observer-based state feedback controller, and a preview action term related to the reference signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical method.

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