For finite-dimensional nonlinear control systems we study the relation between asymptotic null-controllability and control lyapunov functions. It is shown that control lyapunov functions (CLFs) may be constructed on t...
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For finite-dimensional nonlinear control systems we study the relation between asymptotic null-controllability and control lyapunov functions. It is shown that control lyapunov functions (CLFs) may be constructed on the domain of asymptotic null-controllability as viscosity solutions of a first order PDE that generalizes Zubov's equation. The solution is also given as the value function of an optimal control problem from which several regularity results may be obtained.
The stabilization of discrete nonlinear systems is studied. Based on control lyapunov functions, a sufficient and necessary condition for a quadratic function to be a controllyapunov function is given. From this cond...
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The stabilization of discrete nonlinear systems is studied. Based on control lyapunov functions, a sufficient and necessary condition for a quadratic function to be a controllyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.
This paper considers the stabilization of nonlinear control affine systems that satisfy Jurdjevic-Quinn conditions. We first obtain a differential one-form associated to the system by taking the interior product of a ...
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This paper considers the stabilization of nonlinear control affine systems that satisfy Jurdjevic-Quinn conditions. We first obtain a differential one-form associated to the system by taking the interior product of a non vanishing two-form with respect to the drift vector field. We then construct a homotopy operator on a star-shaped region centered at a desired equilibrium point that decomposes the system into an exact part and an anti-exact one. Integrating the exact one-form, we obtain a locally-defined dissipative potential that is used to generate the damping feedback controller. Applying the same decomposition approach on the entire control affine system under damping feedback, we compute a controllyapunov function for the closed-loop system. Under Jurdjevic-Quinn conditions, it is shown that the obtained damping feedback is locally stabilizing the system to the desired equilibrium point provided that it is the maximal invariant set for the controlled dynamics. The technique is also applied to construct damping feedback controllers for the stabilization of periodic orbits. Examples are presented to illustrate the proposed method. (C) 2013 Elsevier B.V. All rights reserved.
This paper is concerned with the stabilization of differential inclusions. By using control lyapunov functions, a design method of homogeneous controllers for differential equation systems is first addressed. Then, th...
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This paper is concerned with the stabilization of differential inclusions. By using control lyapunov functions, a design method of homogeneous controllers for differential equation systems is first addressed. Then, the design method is developed to two classes of differential inclusions without uncertainties: homogeneous differential inclusions and nonhomogeneous ones. By means of homogeneous domination theory, a homogeneous controller for differential inclusions with uncertainties is constructed. Comparing to the existing results in the literature, an improved formula of homogeneous controllers is proposed, and the difficulty of the controller design for uncertain differential inclusions is reduced. Finally, two simulation examples are given to verify the preset design. (c) 2013 Elsevier B.V. All rights reserved.
In this paper, the controllyapunov function (CLF) approach is adopted to investigate the finite-time attitude control of rigid spacecraft subject to parameter uncertainty and external disturbance. By using an extende...
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In this paper, the controllyapunov function (CLF) approach is adopted to investigate the finite-time attitude control of rigid spacecraft subject to parameter uncertainty and external disturbance. By using an extended state observer to estimate the parameter uncertainty and external disturbance, a finite-time CLF controller is proposed for attitude stabilization of the spacecraft system. The designed finite-time CLF controller includes two parts. The first part is a classical CLF based attitude controller, which is proposed to ensure the globally asymptotical stability of the nominal spacecraft system. The second one is a sliding mode controller, which is used to ensure the finite-time convergence performance of the spacecraft control system. The advantage of the designed controller is that the states of the system can converge into a small neighourhood of zero in finite time, and simultaneously the given performance index can be minimized. The practical finite-time stability of the resulted closed-loop system is proven via lyapunov stability theory. Finally, simulation results illustrate the effectiveness of the developed finite-time controller.
This study considers the visual stabilization problem of nonholonomic mobile robots and proposes a novel optimization stabilization method for visual servo control of nonholonomic mobile robots with monocular cameras ...
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This study considers the visual stabilization problem of nonholonomic mobile robots and proposes a novel optimization stabilization method for visual servo control of nonholonomic mobile robots with monocular cameras fixed onboard. The main idea of the method is to utilize control lyapunov functions of discrete-time nonlinear systems to design a family of explicit stabilization control laws of the visual servo error system. The parameters of the control laws can indirectly reflect the performance of the visual servo controllers. Then taking account of visibility constraints and actuator limitations, a set of optimal parameters of the control laws is calculated by offline solving a constrained finite horizon optimal control problem. Moreover, the stabilization results on the optimal visual servo controller are established based on the properties of control lyapunov functions. Finally, some simulation experiments are used to illustrate and evaluate the performance of the visual servo control scheme proposed here.
The asymptotic and practical stabilization for the affine in the control nonlinear systems, which extends the results of Artstein, Sontag, and Tsinias is explored. Sufficient conditions for the existence of control Ly...
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The asymptotic and practical stabilization for the affine in the control nonlinear systems, which extends the results of Artstein, Sontag, and Tsinias is explored. Sufficient conditions for the existence of control lyapunov functions are presented guaranteeing stabilization. The corresponding feedback laws are smooth, except possibly at the equilibrium of the system.
In this paper the well-known Vidyasagar's theorem concerning the feedback stabilizability problem for interconnected control systems is generalized. In particular, sufficient conditions are provided for the existe...
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In this paper the well-known Vidyasagar's theorem concerning the feedback stabilizability problem for interconnected control systems is generalized. In particular, sufficient conditions are provided for the existence of control lyapunov functions that, according to the results of Artstein, Sontag, and Tsinias, guarantees asymptotic stabilization by means of a feedback law that is smooth, except possibly at the equilibrium at which it is wished to stabilize the system.
In this paper we study the feedback stabilzation problem for a wide class of nonlinear systems that are affine in the control. We offer sufficient conditions for the existence of 'control lyapunov functions' t...
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In this paper we study the feedback stabilzation problem for a wide class of nonlinear systems that are affine in the control. We offer sufficient conditions for the existence of 'control lyapunov functions' that according to [3,23] and [28-30] guarantee stabilization at a specified equilibrium by means of a feedback law, which is smooth except possibly at the equilibrium. We note that the results of the paper present a local nature.
A method is developed by which control lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the controllyapunov function, a feedback control is obtained to stabilize the clos...
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A method is developed by which control lyapunov functions of a class of nonlinear systems can be constructed systematically. Based on the controllyapunov function, a feedback control is obtained to stabilize the closed-loop system. In addition, this method is applied to stabilize the Benchmark system. A simulation shows the effectiveness of the method.
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