LaSalle-Yoshizawa Corollaries for Nonsmooth Systems

Fischer, N.; Kamalapurkar, Rushikesh; Dixon, Warren E.

doi:10.1109/tac.2013.2246900

Cited by 189 publications

(112 citation statements)

References 45 publications

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“…From (25), [45,Corollary 1] can be invoked to show that c z (t) 2 → 0 as t → ∞ ∀y (0) ∈ S D . Based on the definition of z in (15), e 1 (t) → 0 as t → ∞ ∀y (0) ∈ S D .…”

Section: Appendix Proof Of Theoremmentioning

confidence: 99%

Nonlinear RISE-Based Control of an Autonomous Underwater Vehicle

et al. 2014

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Abstract-This study focuses on the development of a nonlinear control design for a fully-actuated autonomous underwater vehicle (AUV) using a continuous robust integral of the sign of the error control structure to compensate for system uncertainties and sufficiently smooth bounded exogenous disturbances. A Lyapunov stability analysis is included to prove semiglobal asymptotic tracking. The resulting controller is experimentally validated on an AUV developed at the University of Florida in both controlled and open-water environments.Index Terms-Autonomous underwater vehicles (AUVs), marine robotics, nonlinear control, robust integral of the sign of the error (RISE).

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“…From (25), [45,Corollary 1] can be invoked to show that c z (t) 2 → 0 as t → ∞ ∀y (0) ∈ S D . Based on the definition of z in (15), e 1 (t) → 0 as t → ∞ ∀y (0) ∈ S D .…”

Section: Appendix Proof Of Theoremmentioning

confidence: 99%

Nonlinear RISE-Based Control of an Autonomous Underwater Vehicle

et al. 2014

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“…Owing to discontinuities in some of the functions which will be defined in Section 5, we need to use the following generalised derivative notion in place of the regular derivative: given a dynamic systemẋ = f (x(t), t) and a function V (x(t), t), the generalised derivative of V is defined as [31] V…”

Section: Mathematical Backgroundmentioning

confidence: 99%

“…It is clear that this function is positive definite for the attitude synchronisation equilibrium since tr[R T k R j ] ≤ 3. Next, we compute the generalised time derivative [31] …”

Section: Attitude Synchronisation With Optimal Normmentioning

confidence: 99%

“…Comparing to the results of [9,10], it is clear that we can choose a smaller value of μ for stabilisation. Now, we are in a position to invoke the LaSalle-Yoshizawa theorem for non-smooth systems (Corollary 2 in [31]) and conclude that the equilibrium of the system is asymptotically stable, that is, G k → 0 and r k → 0, k ∈ {1, . .…”

Section: Attitude Synchronisation With Optimal Normmentioning

confidence: 99%

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Robust adaptive attitude synchronisation of rigid body networks onSO(3)

Fadakar¹,

Fi̇dan²,

Huissoon³

2015

IET Control Theory & Applications

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In this study, the authors consider the robust adaptive attitude synchronisation problem for a network of rigid body agents using a modified version of the error function, which is recently introduced for constructing the attitude errors on SO(3). These attitude error vectors are particularly useful for networks with large initial attitude difference. They focus on devising an adaptive geometric approach to cope with situations where the inertia matrices are not available for measurement. The Frobenious norm is used as a measure for the difference between the actual values of moments of inertias and their estimated values, to construct the individual adaptive laws of agents. Compared to the previous methods for synchronisation on SO(3) such as those using quaternions, the authors' approach based on the introduced modified error function enables us to avoid any ambiguity for attitude representation. Finally, they study the robustness of the synchronisation task in the presence of external disturbances and unmodelled dynamics and propose a method to attenuate such effects. Simulation results illustrate the effectiveness of the proposed approach.

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“…The fact that for some implies that in order to obtain a non-trivial region of attraction, the saturation bound has to be large enough so that . From (30), [36,Corollary 1] can be invoked to show that as . Based on the definition of in (19), as .…”

Section: Stability Analysismentioning

confidence: 99%

Saturated RISE Feedback Control for a Class of Second-Order Nonlinear Systems

Fischer

Kan

Kamalapurkar

et al. 2014

IEEE Trans. Automat. Contr.

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Abstract-A saturated controller is developed for a class of uncertain, second-order, nonlinear systems which includes time-varying and nonlinearly parameterized functions with bounded disturbances using a continuous control law with smooth saturation functions. Based on the robust integral of the sign of the error (RISE) control methodology, the developed controller is able to utilize the benefits of high gain control strategies while guaranteeing saturation limits are not surpassed. The bounds on the control are known a priori and can be adjusted by changing the feedback gains. The saturated controller yields asymptotic tracking despite model uncertainty and added disturbances in the dynamics. Experimental results using a two-link robot manipulator demonstrate the performance of the developed controller.

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LaSalle-Yoshizawa Corollaries for Nonsmooth Systems

Cited by 189 publications

References 45 publications

Nonlinear RISE-Based Control of an Autonomous Underwater Vehicle

Nonlinear RISE-Based Control of an Autonomous Underwater Vehicle

Robust adaptive attitude synchronisation of rigid body networks onSO(3)

Saturated RISE Feedback Control for a Class of Second-Order Nonlinear Systems

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