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## Nonlinear Systems With Unknown Dead Zones and Control Directions

### Citations

219 | Gaussian networks for direct adaptive control. IEEE transactions on neural networks / a publication of the
- Sanner, Slotine
- 1992
(Show Context)
Citation Context ...trol. I. INTRODUCTION I N recent years, adaptive control system design using ei-ther neural networks (NNs) or fuzzy logic systems to parametrize the unknown nonlinearities has received much attention =-=[1]-=-–[5]. Direct adaptive tracking control was proposed for a class of continuous-time nonlinear systems using radial basis function NNs in [1]. By utilizing modulation function and fuzzy systems, adaptiv... |

81 |
Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis
- Su, Stepanenko, et al.
- 2000
(Show Context)
Citation Context ...ol was proposed for a class of continuous-time nonlinear systems using radial basis function NNs in [1]. By utilizing modulation function and fuzzy systems, adaptive fuzzy control was investigated in =-=[2]-=-. Multilayer-neural-network-based indirect adaptive control was developed for feedback linearization of a class of nonlinear systems in [3]. Using a families of novel integral Lyapunov functions for a... |

49 |
Apphed Nonlinear Control," Englewood Cliffs, New Jersy 07632
- Slotine, Li
(Show Context)
Citation Context ...now that , , , , and , . Furthermore, it is easy to obtain , , and . This means that is uniformly continuous in the interval . According to Barbalat’s lemma, we conclude that . From the discussion in =-=[31]-=-, we have . Let be the upper bound of in , , then . Similarly, we obtain , , and . The following theorem shows the stability and control performance of the closed-loop adaptive system. Theorem 3: Cons... |

41 |
Some remarks on a conjecture in parameter adaptive control
- Nussbaum
- 1983
(Show Context)
Citation Context ...tion control gains in [9] and [10]. When there is no a priori knowledge about the signs of control gains, adaptive control of such systems becomes much more difficult. The first solution was given in =-=[11]-=- for a class of firstorder linear systems, where the Nussbaum-type gain was originally proposed. When the high-frequency control gains and their signs are unknown, gains of Nussbaum-type [11] have bee... |

34 |
Stable Adaptive Neural Network Control
- Ge, Hang, et al.
- 2002
(Show Context)
Citation Context .... I. INTRODUCTION I N recent years, adaptive control system design using ei-ther neural networks (NNs) or fuzzy logic systems to parametrize the unknown nonlinearities has received much attention [1]–=-=[5]-=-. Direct adaptive tracking control was proposed for a class of continuous-time nonlinear systems using radial basis function NNs in [1]. By utilizing modulation function and fuzzy systems, adaptive fu... |

28 |
Feedback linearization using neural networks
- Yesidirek, Lewis
- 1995
(Show Context)
Citation Context ...nd fuzzy systems, adaptive fuzzy control was investigated in [2]. Multilayer-neural-network-based indirect adaptive control was developed for feedback linearization of a class of nonlinear systems in =-=[3]-=-. Using a families of novel integral Lyapunov functions for avoiding the possible controller singularity problem without using projection, adaptive neural controls were presented for a class of nonlin... |

17 | Deadzone compensation in motion control systems using augmented multilayer neural networks
- Selmic, Lewis
- 2001
(Show Context)
Citation Context ...e was achieved analytically under the condition that the output of a dead zone was measurable in [16]. A compensation scheme was presented for general nonlinear actuator dead zone of unknown width in =-=[18]-=-. In [19], by a given matching condition to the reference model, adaptive control with adaptive dead-zone inverse has been introduced. By using a new description of a dead zone with equal slopes, robu... |

15 |
Discrete-Time Adaptive Control of Systems with Unknown Dead-Zones
- Tao, Kokotovic
- 1995
(Show Context)
Citation Context ...y has been drawing much interest in the control community for a long time [14]–[20]. To handle the systems with unknown dead zones, adaptive dead-zone inverses were proposed in [14]–[16]. In [14] and =-=[15]-=-, adaptive dead-zone inverses were built for linear systems with unmeasurable dead-zone outputs. Asymptotical adaptive cancellation of an unknown dead zone was achieved analytically under the conditio... |

14 |
1991] “A universal adaptive stabilizer for a class of nonlinear systems
- Ryan
(Show Context)
Citation Context ...m gain technique is employed in this paper. A function is called a Nussbaum-type function if it has the following properties: 1) 2) Commonly used Nussbaum functions include: , , and [11], [13], [22], =-=[26]-=-. For clarity, the even Nussbaum function is used throughout this paper. Lemma 1 [12]: Let and be smooth functions defined on with , , and be an even smooth Nussbaum-type function. If the following in... |

12 | Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients
- Ge, Hong, et al.
- 2004
(Show Context)
Citation Context ... high-frequency control gains and their signs are unknown, gains of Nussbaum-type [11] have been effectively used in controller design in solving the difficulty of unknown control directions [12] and =-=[13]-=-. Nonsmooth nonlinear characteristics such as dead zone, backlash, and hysteresis are common in actuator and sensors such as mechanical connections, hydraulic actuators, and electric servomotors. Dead... |

12 | Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis
- Zhou, Wen, et al.
- 2004
(Show Context)
Citation Context ... if (11) if if if (12) (13) if if (14) if if (15) if if if . (16) Remark 1: For the case of linear dead zone outside the deadband, control system design has been extensively studied [14], [15], [20], =-=[25]-=-. To the best of our knowledge, (9) is to capture the most realistic situation, and as such it is different from the existing idealized description [14], [16], [17], [19], [20], [23]. As shown in [24]... |

11 |
Adaptive nonlinear design without a priori knowledge of control directions
- Ye, Jiang
- 1998
(Show Context)
Citation Context ... When the high-frequency control gains and their signs are unknown, gains of Nussbaum-type [11] have been effectively used in controller design in solving the difficulty of unknown control directions =-=[12]-=- and [13]. Nonsmooth nonlinear characteristics such as dead zone, backlash, and hysteresis are common in actuator and sensors such as mechanical connections, hydraulic actuators, and electric servomot... |

11 |
A nonlinear universal servomechanism
- Ryan
- 1994
(Show Context)
Citation Context ...ncertain large scale linear systems with state time-delay and dead-zone input. However, the parameters of the dead zones [21] need to be known, and the disturbances satisfy the matching condition. In =-=[22]-=-, a servomechanism problem of controlling a scalar output variable to -track was addressed for a class of special SISO linear system with nonlinear actuator characteristics. Adaptive output feedback c... |

11 |
Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs
- Zhang, Ge
(Show Context)
Citation Context ...lled circular argument as commonly understood in the classical-model-based control. To help understand the above proof, the defined three compact sets in Theorem 1 are shown in Fig. 2 as discussed in =-=[29]-=-. Remark 2: Because the output of an unknown dead zone is not available, controller design based on the inverse of a dead zone usually needs to estimate some unknown parameters related to the dead zon... |

10 |
Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function
- Zhang, Ge, et al.
- 2000
(Show Context)
Citation Context ...gral Lyapunov functions for avoiding the possible controller singularity problem without using projection, adaptive neural controls were presented for a class of nonlinear systems in a Brunovsky form =-=[4]-=-, and for a class of multiple-input–multiple-output (MIMO) nonlinear systems with a triangular structure in the control inputs in [5] and Manuscript received June 26, 2007; revised April 07, 2008 and ... |

10 |
An adaptive dead-zone inverse controller for systems with sandwiched dead-zones
- Taware, Tao
(Show Context)
Citation Context ...tensively studied [14], [15], [20], [25]. To the best of our knowledge, (9) is to capture the most realistic situation, and as such it is different from the existing idealized description [14], [16], =-=[17]-=-, [19], [20], [23]. As shown in [24], we know that . The control objective is to design an adaptive controller for system (1) such that the output follows the specified desired trajectory , . Define a... |

10 |
Adaptive output control of nonlinear systems with unknown deadzone
- Zhou, Wen, et al.
(Show Context)
Citation Context ...EE Xplore.sRestrictions apply. 484 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 3, MARCH 2009 function of the dead zone was proposed for a class of SISO nonlinear systems with unknown dead zone =-=[23]-=-. In this paper, we consider a class of uncertain MIMO nonlinear systems with both unknown dead zones and unknown gain signs. By employing analytic extension for the functions outside the dead band an... |

10 |
Design and performance analysis of a direct adaptive controller for nonlinear systems
- Zhang, Ge, et al.
- 1999
(Show Context)
Citation Context ...e of their good capabilities of nonlinear function approximation, learning, and fault tolerance. In this paper, three-layer NNs will be used to approximate a continuous function as described by [27], =-=[28]-=- (20) Authorized licensed use limited to: National University of Singapore. Downloaded on March 25, 2009 at 08:48 from IEEE Xplore.sRestrictions apply. 486 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 2... |

5 |
Convergence results for an adaptive dead zone inverse
- Cho, Bai
- 1998
(Show Context)
Citation Context ...ance; and its study has been drawing much interest in the control community for a long time [14]–[20]. To handle the systems with unknown dead zones, adaptive dead-zone inverses were proposed in [14]–=-=[16]-=-. In [14] and [15], adaptive dead-zone inverses were built for linear systems with unmeasurable dead-zone outputs. Asymptotical adaptive cancellation of an unknown dead zone was achieved analytically ... |

4 |
Stable adaptive control for nonlinear multivariable systems with a triangular control structure
- Ge, Hang, et al.
- 2000
(Show Context)
Citation Context ...Singapore (e-mail: samge@nus.edu.sg). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNN.2008.2010349 =-=[6]-=-. Furthermore, two design schemes of adaptive controller for single-input–single-output (SISO)/MIMO uncertain nonlinear systems were proposed in [7] and [8], and ensured tracking error converging to z... |

4 |
Design of large-scale time-delayed systems with dead-zone input via variable structure control
- Shyu, Liua, et al.
- 2005
(Show Context)
Citation Context ...uced. By using a new description of a dead zone with equal slopes, robust adaptive control was developed for a class of nonlinear systems in [20] without constructing the inverse of the dead zone. In =-=[21]-=-, decentralized variable structure control was proposed for a class of uncertain large scale linear systems with state time-delay and dead-zone input. However, the parameters of the dead zones [21] ne... |

2 |
Stable adaptive fuzzy sliding mode control of interconnected systems
- Zhang
- 2001
(Show Context)
Citation Context ...uzzy systems, decentralized indirect and direct adaptive fuzzy control schemes were proposed for a class of nonlinear systems with unknown constant control gains and unknown function control gains in =-=[9]-=- and [10]. When there is no a priori knowledge about the signs of control gains, adaptive control of such systems becomes much more difficult. The first solution was given in [11] for a class of first... |

2 |
Stable Direct Adaptive Fuzzy Control for a Class of MIMO Non-Linear Systems
- Zhang
(Show Context)
Citation Context ...tems, decentralized indirect and direct adaptive fuzzy control schemes were proposed for a class of nonlinear systems with unknown constant control gains and unknown function control gains in [9] and =-=[10]-=-. When there is no a priori knowledge about the signs of control gains, adaptive control of such systems becomes much more difficult. The first solution was given in [11] for a class of firstorder lin... |

2 |
Adaptive sliding control of plants with unknown dead-zone
- Tao, Kokotovic
- 1994
(Show Context)
Citation Context ...ost important nonsmooth nonlinearities in many industrial processes, which can severely limit system performance; and its study has been drawing much interest in the control community for a long time =-=[14]-=-–[20]. To handle the systems with unknown dead zones, adaptive dead-zone inverses were proposed in [14]–[16]. In [14] and [15], adaptive dead-zone inverses were built for linear systems with unmeasura... |

2 |
Robust adaptive neural control of SISO nonlinear systems with unknown nonlinear dead-zone and gain sign
- Zhang, Ge
- 2006
(Show Context)
Citation Context ... a very general class of . As , , , and are all unknown, control system design becomes difficult. To facilitate control system design, we need to make the following assumptions that first appeared in =-=[24]-=-. Assumption 1: The dead-zone outputs are not available. Assumption 2: The dead-zone parameters and are unknown bounded constants, but their signs are known, i.e., and , . Assumption 3: The functions ... |

1 |
Direct adaptive neural network control based on integral Lyapunov function
- Zhang
- 2003
(Show Context)
Citation Context ... Digital Object Identifier 10.1109/TNN.2008.2010349 [6]. Furthermore, two design schemes of adaptive controller for single-input–single-output (SISO)/MIMO uncertain nonlinear systems were proposed in =-=[7]-=- and [8], and ensured tracking error converging to zero. Based on the principle of sliding mode control and the approximation capability of fuzzy systems, decentralized indirect and direct adaptive fu... |

1 |
Adaptive fuzzy sliding mode control based on a modified Lyapunov function
- Zhang
- 2002
(Show Context)
Citation Context ... Object Identifier 10.1109/TNN.2008.2010349 [6]. Furthermore, two design schemes of adaptive controller for single-input–single-output (SISO)/MIMO uncertain nonlinear systems were proposed in [7] and =-=[8]-=-, and ensured tracking error converging to zero. Based on the principle of sliding mode control and the approximation capability of fuzzy systems, decentralized indirect and direct adaptive fuzzy cont... |

1 |
Model reference adaptive control of continuous time systems with an unknown dead-zone
- Wang, Hong, et al.
- 2003
(Show Context)
Citation Context ...ieved analytically under the condition that the output of a dead zone was measurable in [16]. A compensation scheme was presented for general nonlinear actuator dead zone of unknown width in [18]. In =-=[19]-=-, by a given matching condition to the reference model, adaptive control with adaptive dead-zone inverse has been introduced. By using a new description of a dead zone with equal slopes, robust adapti... |

1 |
Multilayer neural network robot controller with guaranteed tracking performance
- Lewis, Yesildirek, et al.
- 1996
(Show Context)
Citation Context ...because of their good capabilities of nonlinear function approximation, learning, and fault tolerance. In this paper, three-layer NNs will be used to approximate a continuous function as described by =-=[27]-=-, [28] (20) Authorized licensed use limited to: National University of Singapore. Downloaded on March 25, 2009 at 08:48 from IEEE Xplore.sRestrictions apply. 486 IEEE TRANSACTIONS ON NEURAL NETWORKS, ... |

1 |
Adaptive output control of nonlinear time-delayed systems with uncertain dead-zone input
- Zhou, Er, et al.
(Show Context)
Citation Context ...the output of an unknown dead zone is not available, controller design based on the inverse of a dead zone usually needs to estimate some unknown parameters related to the dead zone [14], [19], [23], =-=[30]-=-. However, for controller design based on (9), there is no need to estimate the parameters related to dead zones, and can avoid the need for parameter bounds of dead zones (for example, the parameters... |