A Sufficiently Smooth Projection Operator

Cai, Zhihua; Queiroz, M.S. de; Dawson, D.M.

doi:10.1109/tac.2005.861704

Cited by 181 publications

(99 citation statements)

References 2 publications

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“…The smoothened projection operator 34 is applied in this article to bound the parameter estimation equation. The projection operator is very helpful for robust adaptive controller that needs multiple derivative of adaptive law.…”

Section: Appendixmentioning

confidence: 99%

Adaptive fuzzy tracking control for non-affine nonlinear yaw channel of unmanned aerial vehicle helicopter

Yan

Huang

2016

International Journal of Advanced Robotic Systems

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The article deals with the problem of the yaw control of the unmanned aerial vehicle helicopter which is non-affine nonlinear by use of a novel projection-based adaptive fuzzy control approach. First, principle model and control design model of the yaw channel of the unmanned aerial vehicle helicopter are described. Then, a dynamic approximation technique is introduced to approach the non-affine model of the unmanned aerial vehicle helicopter into an affine model with variable parameters, which is applied to facilitate the design of nonlinear control scheme. Next, in the proposed controller, fuzzy controller is designed to deal with the unknown uncertainties and disturbances. Meanwhile, the projection-based adaptive law applied in fuzzy controller bounds the parameter estimation function and can also guarantee the robustness of the designed control scheme against uncertain disturbances. Moreover, the convergence and stability of the designed controller are proved by Lyapunov stability theory. Finally, the simulation results of the yaw channel of an unmanned aerial vehicle helicopter are performed to illustrate that the designed controller has good tracking performance, stability, and robustness under the condition of the time-vary uncertain disturbances.

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Section: Appendixmentioning

confidence: 99%

Adaptive fuzzy tracking control for non-affine nonlinear yaw channel of unmanned aerial vehicle helicopter

Yan

Huang

2016

International Journal of Advanced Robotic Systems

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“…The parameter estimate in (25) is generated by the adaptive update law (27) In (27), is a positive constant, and denotes a sufficiently smooth projection algorithm [48] utilized to guarantee that can be bounded as (28) where and denote known constant lower and upper bounds for , respectively. After substituting (25) into (21), the closed-loop error system for can be obtained as (29) In (29), the parameter estimation error is defined as…”

Section: B Closed-loop Error Systemmentioning

confidence: 99%

“…After using (16), (18), (25), and (27), the first time derivative of can be determined as (45) Based on the fact that the projection algorithm for is designed to be sufficiently smooth [48], the expressions in (27) and (45) can be used to determine the second time derivative of as (46) After substituting (18) and (19) into (46) for and , respectively, and substituting (6) and (7) into (46) for , the expression for in the linear parameterization in (31) can be determined without requiring acceleration measurements.…”

Section: Appendix a Expression Ofmentioning

confidence: 99%

“…Proof: Let denote the following nonnegative radially unbounded function (i.e., a Lyapunov function candidate): (47) where (9) and (14) can be utilized to bound as (48) where is defined in (9) and , , and are defined as (49) where denotes the maximum eigenvalue of a matrix and and are the known upper bounds of and , respectively. After using (10), (15), (17), (18), (26), (27), (29), (33), and (35), the time derivative of (47) can be determined as…”

Section: Appendix B Stability Analysis Proofmentioning

confidence: 99%

“…Provided that is selected according to the sufficient condition in (38), then (4), (13), (48), and the fact that (54) for the noncontact case can be used to rewrite (53) as (55) In (55), is a known positive arbitrarily small constant that is defined as Provided that the following sufficient condition is satisfied:…”

Section: Appendix B Stability Analysis Proofmentioning

confidence: 99%

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A force limiting adaptive controller for a robotic system undergoing a non-contact to contact transition

Liang

Bhasin

Dupree

et al. 2007

2007 46th IEEE Conference on Decision and Control

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Abstract-The problem of prescribing, reducing, or controlling the interaction forces between a robot and the environment during a noncontact-to-contact transition is intriguing because large interaction forces can damage both the robot and/or the environment or lead to degraded performance or instabilities. In this paper, we consider a two-link planar robotic arm that transitions from free motion to contact with an unactuated mass-spring system. The objective is to control a robot from a noncontact initial condition to a desired (in-contact) position so that the mass-spring system is regulated to a desired compressed state. The feedback elements for the controller in this paper are contained inside hyperbolic tangent functions as a means to limit the impact forces resulting from large initial conditions as the robot transitions from a noncontact to contact state. The main challenge of this work is that the use of saturated feedback does not allow some coupling terms to be canceled in the stability analysis, resulting in the need to develop state-dependent upper bounds that reduce the stability to a semiglobal result. New control development, closed-loop error systems, and Lyapunov-based stability analysis arguments are used to conclude the result. It is interesting to note that only the position and velocity terms are required for the proposed controller (i.e., the controller does not depend on measuring the impact force and the acceleration terms). Experimental results that successfully demonstrate the control objective are provided.

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Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

Yao

2010

Adaptive Control & Signal

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This paper proposes a novel control method for a special class of nonlinear systems in semi-strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non-uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection-based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection-type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed-loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady-state accuracy in general. The class of system considered here has wide engineering applications, and a practical example-control of mechanical systems with dynamic friction-is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. The deterministic robust controllers are able to guarantee transient performance and final tracking accuracy in the presence of various kinds of uncertainties. However, some problems like switching [1] or infinite-gain [3] feedback will happen, which are undesirable for industrial application. In contrast, the adaptive controllers [4,5] are able to achieve asymptotic tracking in the presence of parametric uncertainties without using discontinuous or infinite-gain feedback. However, this approach may result in unstable closed-loop system in the presence of external disturbances. To remedy, a modification method called robust adaptive control (RAC) [4] has been developed to robust the system. But some trade offs have to be made, since the property of asymptotic tracking may be lost using this technique. In [6,7], an adaptive robust control (ARC) algorithm has been proposed, which incorporates the design methods of DRC and AC effectively. The resulting ARC controllers have the advantages of both DRC and AC while overcoming their practical limitations. The proposed ARC algorithm has been successfully applied to various systems such as electro-mechanical systems [8,9] and electro-hydraulic systems [10].Besides parametric uncertainties and uncertain nonlinearities, some systems may be further subjected to dynamic uncertainties. This kind of system has exogenous dynamic systems whose states cannot be measured. The control of this kind of system has received more and more attention in the recent years not only because there are few previous results available,...

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A Sufficiently Smooth Projection Operator

Cited by 181 publications

References 2 publications

Adaptive fuzzy tracking control for non-affine nonlinear yaw channel of unmanned aerial vehicle helicopter

Adaptive fuzzy tracking control for non-affine nonlinear yaw channel of unmanned aerial vehicle helicopter

A force limiting adaptive controller for a robotic system undergoing a non-contact to contact transition

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

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