Journal•ISSN: 0925-4668
Dynamics and Control
Springer Science+Business Media
About: Dynamics and Control is an academic journal. The journal publishes majorly in the area(s): Nonlinear system & Control theory. It has an ISSN identifier of 0925-4668. Over the lifetime, 222 publications have been published receiving 3391 citations.
Topics: Nonlinear system, Control theory, Adaptive control, Exponential stability, Lyapunov function
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TL;DR: In this paper, two different controllers are designed for the Lorenz system subject to a control input, one based on linear methods and another based on a nonlinear analysis, and the objective of the controller is to drive the system to one of the unstable equilibrium points associated with uncontrolled chaotic motion.
Abstract: The Lorenz equations are well known for their ability to produce chaotic motion. We investigate here the Lorenz system subject to a control input. Two different controllers are designed for this system, one based on linear methods and one based on a nonlinear analysis. The objective of the controller is to drive the system to one of the unstable equilibrium points associated with uncontrolled chaotic motion. Each controller is able to produce stable motion. However, the character of this motion may differ considerably, depending on adjustment of “Gains” used in the controller. In particular, the motion may contain chaotic transients. It is possible to create a system with intermediate-term-sensitive dependence on initial conditions, but with no such long-term dependence.
142 citations
TL;DR: In this paper, an adaptive control law is derived such that in the closed-loop system the state of the system can be regulated to a specified point in the state space, even in the presence of system parameter uncertainty.
Abstract: 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.
140 citations
TL;DR: The control perspective adopted is to implement a two-stage control strategy in which the vibration control problem for fine-motion endpoint positioning is considered separate from the gross-motion, large-angle slew problem.
Abstract: Analysis and experimentation is described for a two-link apparatus in which both members are very flexible. Attention is focused on endpoint position control for point-to-point movements, assuming a fixed reference frame for the base, with two rotary joints. Each link is instrumented with acceleration sensing and is driven by a separate motor equipped with velocity and position sensing. The control perspective adopted is to implement a two-stage control strategy in which the vibration control problem for fine-motion endpoint positioning is considered separate from the gross-motion, large-angle slew problem. In the first stage the control law shapes the actuator inputsfor the large-angle movement in such a way that minimal energy is injected into the flexible modes, while in the second phase an endpoint acceleration feedback scheme is employed in independent joint controlfor vibration suppression at the link endpoints.
91 citations
TL;DR: In this paper, the authors analyzed some dynamical properties of a chaotic Lorenz system driven by a control input, including the input-state and input-output feedback linearizability, the stability of the zero dynamics, and the phase minimality of the system.
Abstract: In this paper we analyze some dynamical properties of a chaotic Lorenz system driven by a control input. These properties are the input-state and the input-output feedback linearizability, the stability of the zero dynamics, and the phase minimality of the system. We show that the controlled Lorenz system is feedback equivalent to a controllable linear system. We also show that the zero dynamics are asymptotically stable when the output is an arbitrary state. These facts allow designing control laws such that the closed-loop system has asymptotically stable equilibrium points with dynamic behavior free from chaotic transients. The controllers are robust in the sense that the closed-loop system is stable and non chaotic around a nominal set of parameter values. The results also show that the proposed controllers give better responses compared to linear algorithms obtained from standard linearization techniques, and exhibit a good performance even when the control input is bounded.
91 citations
TL;DR: In this paper, the authors presented new localized necessary and sufficient conditions for the fixed-time problem that are derived from the original ones, but require information about the primer vector only at a few specific points.
Abstract: Necessary and Sufficient Conditionsare known for the problem of the impulsive minimization of thetotal characteristic velocity of a spacecraft subject to linearequations of motions. These conditions are global in the sensethat the primer vector must be known over the entire flight interval.The purpose of the present paper is to present new localizednecessary and sufficiency conditions for the fixed-time problemthat are derived from the original ones, but require informationabout the primer vector only at a few specific points. Thesenew necessary and sufficiency conditions have both theoreticaland practical value.
84 citations