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Journal ArticleDOI

Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method

TL;DR: In this article, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system, at the same time, the controller is also verified to possess the optimality.
About: This article is published in Journal of Systems Engineering and Electronics.The article was published on 2006-09-01. It has received 4 citations till now. The article focuses on the topics: Adaptive control & Lyapunov redesign.
Citations
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Book ChapterDOI
22 Mar 2011
TL;DR: The chapter presents an approach to control the biped humanoid robot to ambulate through human imitation using tri-axis accelerometers and Lyapunov stability based model reference adaptive controller (MRAC) technique is implemented to address unpredictable variations of the biping system.
Abstract: The chapter presents an approach to control the biped humanoid robot to ambulate through human imitation. For this purpose a human body motion capturing system is developed using tri-axis accelerometers (attached to human legs and torso). The tilt angle patterns information from the human is transformed to control and teach various ambulatory skills for humanoid robot bipedalism. Lyapunov stability based model reference adaptive controller (MRAC) technique is implemented to address unpredictable variations of the biped system.

5 citations

14 Feb 2010
TL;DR: The aim of this paper is to present alternative methods for decision making algorithms that can be introduced for micro-spacecraft, providing robust autonomous control with a modest computational overhead.
Abstract: The drive toward reducing the size and mass of spacecraft has put new constraints on the computational resources available for control and decision making algorithms. The aim of this paper is to present alternative methods for decision making algorithms that can be introduced for micro-spacecraft. The motivation behind this work comes from dynamical systems theory. Systems of differential equations can be built to define behaviors which can be manipulated to define an action selection algorithm. These algorithms can be mathematically validated and shown to be computationally efficient, providing robust autonomous control with a modest computational overhead.

5 citations


Cites background from "Direct adaptive control for nonline..."

  • ...(ėmax/(battmax − battmin)) for ξtra < ξ ≤ (ξ + ξ 1 2 band) (21)...

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  • ...Fig.(21) shows the corresponding values of ξ that lead to the action selection....

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Proceedings ArticleDOI
25 Jul 2012
TL;DR: The model reference adaptive control is used to improve the dynamic response performance of the steering system and the simulation results show that this control method is effective under the condition of a reasonable choice of control parameters.
Abstract: Each axle of the heavy duty vehicle has the independently controlled hydraulic steering mechanism It is of the stronger nonlinearity and load disturbance, therefore using the conventional control method is difficult to get good control effect Based on the kinetic analysis of the steering system, this paper makes use of the model reference adaptive control to improve the dynamic response performance of the steering system The paper studied using the algorithm of model reduction to reduce the complexity of the model and computation The simulation results show that this control method is effective under the condition of a reasonable choice of control parameters

3 citations


Cites methods from "Direct adaptive control for nonline..."

  • ...However, the adaptive control method is more effective [7,8],when there are uncertainties in the system parameters....

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Journal ArticleDOI
TL;DR: In this paper, the authors developed attitude control algorithms for the descent phase onto an asteroid in micro-gravity conditions and drew a comparison between the algorithms considered, and investigated the potential of using direct adaptive control (DAC) as a controller for the surface sampling process.
Abstract: One of the future flagship missions of the European Space Agency is the asteroid sample return mission Marco-Polo. Although there have been a number of past missions to asteroids, a sample has never been successfully returned. The return of asteroid regolith to the Earth's surface introduces new technical challenges. This article develops attitude control algorithms for the descent phase onto an asteroid in micro-gravity conditions and draws a comparison between the algorithms considered. Two studies are also performed regarding the fault detection isolation and recovery of the control laws considered. The potential of using direct adaptive control (DAC) as a controller for the surface sampling process is also investigated. The use of a DAC controller incorporates increased levels of robustness by allowing real-time variation of control gains. This leads to better response to uncertainties encountered during missions.

3 citations

References
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Journal ArticleDOI
TL;DR: In this article, the existence of a smooth control-Lyapunov function implies smooth stabilizability, and the result is extended to real-analytic and rational cases as well.

1,210 citations

Journal ArticleDOI
TL;DR: In this paper, a stabilizing adaptive controller for a nonlinear system depending affinely on some unknown parameters is presented, where the adaptive law is designed using the Lyapunov equation.
Abstract: A stabilizing adaptive controller for a nonlinear system depending affinely on some unknown parameters is presented. It is assumed that this system is feedback stabilizable. A key feature of the method is the use of the Lyapunov equation to design the adaptive law. A result on local stability, two different conditions for global stability, and a local result where the initial conditions of the state of the system only are restricted are given. >

991 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined the possibility of stabilizing one-dimensional systems with a continuous closed loop relaxed control and showed that the family of systems stabilizable with relaxed control is larger than the family stabilisable with ordinary controls, even if each state can be driven asymptotically to the origin.
Abstract: cannot in general be stabilized using a continuous closed loop control U(X), even if each state separately can be driven asymptotically to the origin. (An example is analyzed in Section 2.) In this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control. We find, indeed, that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls. An even larger class is obtained if the continuity of the closed loop at the origin is not required. The latter class includes all one dimensional systems for which states can be driven asymptotically to the origin. This result does not hold in two dimensional systems and we provide a counter-example. It should be pointed that relaxed control-type stabilization is used both in theory and in practice; the method is known as dither. We shall comment on the similarities. Lyapunov functions for the system (1) help us in the construction of the continuous closed loop stabilizers. In fact, we find that the existence of a smooth Lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin; an additional condition on the Lyapunov function implies the continuity at the origin as well. We present these results in Section 4, after a brief introduction of closed loop relaxed controls, notations and terminology in Section 3. Prior to that, in Section 2, we discuss an example illustrating the power of relaxed controls. In the particular case of systems linear in the controls, relaxed controls can be replaced by ordinary controls, this is discussed in Section 5. The role of Lyapunov functions in the stability and stabilization theories is of course well known. Examples of systems with Lyapunov functions are available in the literature. We display some in Section 6, along with general comments on the construction, applications and counterexamples, including one which cannot be continuously stabilized, yet possesses a nonsmooth Lyapunov function. Closed loop stabilization with ordinary controls is analyzed extensively in the literature, see Sontag [8], Sussmann [ll] and references therein. Lyapunov functions techniques in stabil-

964 citations

Journal ArticleDOI
TL;DR: It is shown that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective, and the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws.
Abstract: A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.

683 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a control system is controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls.
Abstract: It is shown that a control system in ${\bf R}^n $ is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls.

565 citations