Control of chaos: Methods and applications in engineering

The problems and methods of control of chaos, which in the last decade was the subject of intensive studies, were reviewed. The three historically earliest and most actively developing directions of research such as the open-loop control based on periodic system excitation, the method of Poincare map linearization (OGY method), and the method of time-delayed feedback (Pyragas method) were discussed in detail. The basic results obtained within the framework of the traditional linear, nonlinear, and adaptive control, as well as the neural network systems and fuzzy systems were presented. The open problems concerned mostly with support of the methods were formulated. The second part of the review will be devoted to the most interesting applications.

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Control of Chaos: Methods and Applications. I. Methods

Variable structure control and active vibration suppression of flexible spacecraft during attitude maneuver

In this paper, a robust adaptive fault-tolerant control approach to attitude tracking of flexible spacecraft is proposed for use in situations when there are reaction wheel/actuator failures, persistent bounded disturbances and unknown inertia parameter uncertainties. The controller is designed based on an adaptive backstepping sliding mode control scheme, and a sufficient condition under which this control law can render the system semi-globally input-to-state stable is also provided such that the closed-loop system is robust with respect to any disturbance within a quantifiable restriction on the amplitude, as well as the set of initial conditions, if the control gains are designed appropriately. Moreover, in the design, the control law does not need a fault detection and isolation mechanism even if the failure time instants, patterns and values on actuator failures are also unknown for the designers, as motivated from a practical spacecraft control application. In addition to detailed derivations of the new controller design and a rigorous sketch of all the associated stability and attitude error convergence proofs, illustrative simulation results of an application to flexible spacecraft show that high precise attitude control and vibration suppression are successfully achieved using various scenarios of controlling effective failures.

Adaptive backstepping fault-tolerant control for flexible spacecraft with unknown bounded disturbances and actuator failures.

Brief paper: Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity

This paper treats the control of chaos in Lorenz systemsin the presence of system parameter uncertainty. An adaptivecontrol law is derived such that in the closed-loop system thestate of the system can be regulated to a specified point inthe state space. Simulation results are presented which showthe suppression of chaotic behavior and the regulation of statevector to the desired terminal point in spite of the uncertaintyin system parameters.

Adaptive control of chaos in Lorenz system

Output Feedback Variable Structure Adaptive Control of a Flexible Spacecraft

Based on the variable structure model reference adaptive control theory, a new control system for the control of an orbiting flexible spacecraft, using output feedback, is designed. The spacecraft consists of a main rigid body to which elastic appendages are attached. For the purpose of control, a moment generating device is located on the rigid hub. For the derivation of control law, it is assumed that the parameters and the structure of the nonlinear functions in the model are unknown. It is shown that in the closed-loop system including the variable structure model reference adaptive control system designed using bounds on uncertain functions, the pitch angle tracks given reference trajectory and the vibration is suppressed. Digital simulation results show that the closed-loop system has good transient behavior and robustness to the uncertainties, unmodeled dynamics, and disturbance inputs.

Output feedback variable structure adaptive control of a flexible spacecraft

This paper presents a new approach to attitude control of spacecraft. It is assumed that the parameters of the spacecraft are not known and disturbance torque is acting on the spacecraft. Rodrigues parameteres and modified Rodrigues parameters are used to describe the orientation of spacecraft. A dynamic decoupling attitude control law is derived for the tracking of reference attitude trajectories. The singular perturbation thoery is used for the stability analysis of the closed-loop system. For the synthesis of the control law, only the attitude error is required. Simulation results are presented to show that in the closed-loop system attitude control is accomplished in spite of the uncertain dynamics of spacecraft.

Yueming Zeng

Papers

Adaptive control of chaos in Lorenz system

Output Feedback Variable Structure Adaptive Control of a Flexible Spacecraft

Output feedback variable structure adaptive control of a flexible spacecraft

Dynamic Feedback Linearizing Attitude Control of Spacecraft with Uncertain Dynamics