Global stabilization of multiple integrators with bounded controls

Marchand, Nicolas; Hably, Ahmad

doi:10.1016/j.automatica.2005.07.004

Cited by 142 publications

(111 citation statements)

References 14 publications

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“…A discussion on how tuning these parameters can be found in [Johnson and Kannan, 2003] for a very similar control law. For (2), variable saturation levels proposed in [Marchand and Hably, 2005] could be adapted to improve the convergence of the system. With an adequate tuning, the performance of nested saturation control is known to be good.…”

Section: Discussionmentioning

confidence: 99%

“…Once there, x 2 clearly remains in this interval. Moreover, during that time, thanks to Lemma 4 in Marchand and Hably [2005], x 1 can not diverge. Since in this set Q(x 2 ) = q 0 = 0, the control law becomes (whatever the value of β 2 ):…”

Section: The Double Integratormentioning

confidence: 90%

“…This clearly makes V n decrease and hence forces x n to join [− q1 2 , q1 2 ] in finite time and to remain there for all future time. Lemma 4 in Marchand and Hably [2005] proves then that a finite time escape of (x 1 , . .…”

Section: General Chain Of Integratorsmentioning

confidence: 94%

“…The proposed control laws consist in a sum of saturated linear controllers computed with the quantized measurements of the state. It is inspired by Teel [1992], Sussmann et al [1994], Marchand and Hably [2005] where saturated control laws for linear systems are given in a quantization free context. The control strategy proposed in these works relies on a coordinate transformation that puts the system in a feedforward from.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of Lebesgue sampled systems with bounded controls: the chain of integrators case

Marchand

2008

IFAC Proceedings Volumes

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Section: Discussionmentioning

confidence: 99%

Section: The Double Integratormentioning

confidence: 90%

Section: General Chain Of Integratorsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Stabilization of Lebesgue sampled systems with bounded controls: the chain of integrators case

Marchand

2008

IFAC Proceedings Volumes

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“…On the other hand, the aerodynamic forces developed by the flapping flyer's wings are bounded because of the boundedness of the flapping wings' angles. Technically, it is well known that for a system that operates over a wide range of conditions, it may happen that the control law reaches the actuator limits, deteriorating the control performance or even leading to instability [27,28]. As evidenced by the above reviewed literature, very little attention has been dedicated to the attitude stabilization problem using bounded control with different bounds for each axis.…”

mentioning

confidence: 99%

Biomimetic-Based Output Feedback for Attitude Stabilization of Rigid Bodies: Real-Time Experimentation on a Quadrotor

et al. 2015

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The present paper deals with the development of bounded feedback control laws mimicking the strategy adopted by flapping flyers to stabilize the attitude of systems falling within the framework of rigid bodies. Flapping flyers are able to orient their trajectory without any knowledge of their current attitude and without any attitude computation. They rely on the measurements of some sensitive organs: halteres, leg sensilla and magnetic sense, which give information about their angular velocity and the orientation of gravity and magnetic field vectors. Therefore, the proposed feedback laws are computed using direct inertial sensors measurements, that is vector observations with/without angular velocity measurements. Hence, the attitude is not explicitly required. This biomimetic approach is very simple, requires little computational power and is suitable for embedded applications on small control units. The boundedness of the control signal is taken into consideration through the design of the control laws by saturation of the actuators' input. The asymptotic stability Micromachines 2015, 6 994 of the closed loop system is proven by Lyapunov analysis. Real-time experiments are carried out on a quadrotor using MEMS inertial sensors in order to emphasize the efficiency of this biomimetic strategy by showing the convergence of the body's states in hovering mode, as well as the robustness with respect to external disturbances.

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Numerical methods of stabilizer construction via guidance control

Miranda

2012

Math Methods in App Sciences

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This work concerns guidance stabilization of non-autonomous control systems. Global stabilization problem is usually quite complex and difficult to solve. To overcome this difficulty, guidance control is used. A guidance stabilizer uses a trajectory of a globally asymptotically stable auxiliary system as a guide. A local stabilizer keeps the trajectory of the system in a neighborhood of a solution of the auxiliary system. In this way, the trajectory of the system tends to the equilibrium position. The main idea of this method is to solve the global stabilization problem by applying local stabilization methods. The presented procedure also yields additional possibilities for the design of a stabilizer that eliminates the peak effect, that is, the large deviation of the solutions from the equilibrium position at the beginning of the stabilization process. This effect represents a serious obstacle to the design of cascade control systems and to guidance stabilization. The optimal control problem used in this paper eliminates this effect that we have when we apply known construction methods of local stabilizers to obtain a high speed of damping of the control systems trajectories. According to this approach and using -strategies introduced by Pontryagin in the frame of differential games theory, the stabilizing control is constructed as a function of time defined in a small time interval and not as a feedback. An application to a mechanical stabilization problem is provided here.

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Global stabilization of multiple integrators with bounded controls

Cited by 142 publications

References 14 publications

Stabilization of Lebesgue sampled systems with bounded controls: the chain of integrators case

Stabilization of Lebesgue sampled systems with bounded controls: the chain of integrators case

Biomimetic-Based Output Feedback for Attitude Stabilization of Rigid Bodies: Real-Time Experimentation on a Quadrotor

Numerical methods of stabilizer construction via guidance control

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