Adaptive control of non‐linear systems with unknown virtual control coefficients

Disturbance attenuation by output feedback for a class of nonlinear systems

“…Here, the control directions are that of the signs of high-frequency gains in linear systems; in nonlinear systems, they usually represent the signs of the unknown multiplicative parameters or disturbances. The work related to the unknown control directions can be found in Nussbaum (1983), Ye (1999Ye ( , 2001, Ding (2000), Ge and Wang (2002), Wei et al (2006Wei et al ( , 2007Wei et al ( , 2008, etc.…”

“…Another scheme is the so-called Nussbaumtype gain technique, which was originally proposed by Nussbaum (1983), and initially has been adopted in the adaptive control of first-order nonlinear systems and nonlinearly perturbed high-order linear systems (see Martensson, 1990;Ryan, 1991, etc.). Later on, the Nussbaum-type gain method was adopted to deal with the control problem for classes of systems, such as a class of strict feedback nonlinear systems with unknown constant parameters and without disturbances by Ding (2000), and nonlinear systems with unknown control coefficients, uncertain parameters and disturbances by Ge and Wang (2002). Recently, Ye (1999Ye ( , 2001) incorporated the Nussbaum-type gain into the backstepping design and proposed a robust asymptotic regulating control scheme for a class of time-varying uncertain nonlinear systems.…”

Disturbance attenuation by output feedback for a class of nonlinear systems

“…Here, the control directions are that of the signs of high-frequency gains in linear systems; in nonlinear systems, they usually represent the signs of the unknown multiplicative parameters or disturbances. The work related to the unknown control directions can be found in Nussbaum (1983), Ye (1999Ye ( , 2001, Ding (2000), Ge and Wang (2002), Wei et al (2006Wei et al ( , 2007Wei et al ( , 2008, etc.…”

“…Another scheme is the so-called Nussbaumtype gain technique, which was originally proposed by Nussbaum (1983), and initially has been adopted in the adaptive control of first-order nonlinear systems and nonlinearly perturbed high-order linear systems (see Martensson, 1990;Ryan, 1991, etc.). Later on, the Nussbaum-type gain method was adopted to deal with the control problem for classes of systems, such as a class of strict feedback nonlinear systems with unknown constant parameters and without disturbances by Ding (2000), and nonlinear systems with unknown control coefficients, uncertain parameters and disturbances by Ge and Wang (2002). Recently, Ye (1999Ye ( , 2001) incorporated the Nussbaum-type gain into the backstepping design and proposed a robust asymptotic regulating control scheme for a class of time-varying uncertain nonlinear systems.…”

Adaptive leaderless consensus control of uncertain multiagent systems with unknown control directions

“…Based on a novel Nussbaum function, an adaptive control law for first‐order and second‐order multiagent systems is proposed in Reference 23. The Nussbaum gain methods are also used to high‐order nonlinear system with unknown control directions in References 24 and 26‐29. In Reference 30, the consensus of high‐order nonlinear multiagent systems with unknown backlash‐like hysteresis and unknown control directions is solved by combining Nussbaum function with backstepping technique 33 …”

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

“…Typical examples may be found in the area of uncalibrated visual servoing control and robotic systems . As for single nonlinear systems with unknown control directions, the Nussbaum‐type function, which was independently presented in the work of Nussbaum, has been extensively adopted to design control methods . Nevertheless, for a multiagent system, where each agent possesses an unknown control direction, developing distributed controllers constitutes a quite challenging issue.…”

Disturbance attenuation by output feedback for a class of nonlinear systems

“…Here, the control directions are that of the signs of high-frequency gains in linear systems; in nonlinear systems, they usually represent the signs of the unknown multiplicative parameters or disturbances. The work related to the unknown control directions can be found in Nussbaum (1983), Ye (1999Ye ( , 2001, Ding (2000), Ge and Wang (2002), Wei et al (2006Wei et al ( , 2007Wei et al ( , 2008, etc.…”

“…Another scheme is the so-called Nussbaumtype gain technique, which was originally proposed by Nussbaum (1983), and initially has been adopted in the adaptive control of first-order nonlinear systems and nonlinearly perturbed high-order linear systems (see Martensson, 1990;Ryan, 1991, etc.). Later on, the Nussbaum-type gain method was adopted to deal with the control problem for classes of systems, such as a class of strict feedback nonlinear systems with unknown constant parameters and without disturbances by Ding (2000), and nonlinear systems with unknown control coefficients, uncertain parameters and disturbances by Ge and Wang (2002). Recently, Ye (1999Ye ( , 2001) incorporated the Nussbaum-type gain into the backstepping design and proposed a robust asymptotic regulating control scheme for a class of time-varying uncertain nonlinear systems.…”

Adaptive leaderless consensus control of uncertain multiagent systems with unknown control directions

“…Based on a novel Nussbaum function, an adaptive control law for first‐order and second‐order multiagent systems is proposed in Reference 23. The Nussbaum gain methods are also used to high‐order nonlinear system with unknown control directions in References 24 and 26‐29. In Reference 30, the consensus of high‐order nonlinear multiagent systems with unknown backlash‐like hysteresis and unknown control directions is solved by combining Nussbaum function with backstepping technique 33 …”

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

“…Typical examples may be found in the area of uncalibrated visual servoing control and robotic systems . As for single nonlinear systems with unknown control directions, the Nussbaum‐type function, which was independently presented in the work of Nussbaum, has been extensively adopted to design control methods . Nevertheless, for a multiagent system, where each agent possesses an unknown control direction, developing distributed controllers constitutes a quite challenging issue.…”

Disturbance attenuation by output feedback for a class of nonlinear systems

“…Here, the control directions are that of the signs of high-frequency gains in linear systems; in nonlinear systems, they usually represent the signs of the unknown multiplicative parameters or disturbances. The work related to the unknown control directions can be found in Nussbaum (1983), Ye (1999Ye ( , 2001, Ding (2000), Ge and Wang (2002), Wei et al (2006Wei et al ( , 2007Wei et al ( , 2008, etc.…”

“…Another scheme is the so-called Nussbaumtype gain technique, which was originally proposed by Nussbaum (1983), and initially has been adopted in the adaptive control of first-order nonlinear systems and nonlinearly perturbed high-order linear systems (see Martensson, 1990;Ryan, 1991, etc.). Later on, the Nussbaum-type gain method was adopted to deal with the control problem for classes of systems, such as a class of strict feedback nonlinear systems with unknown constant parameters and without disturbances by Ding (2000), and nonlinear systems with unknown control coefficients, uncertain parameters and disturbances by Ge and Wang (2002). Recently, Ye (1999Ye ( , 2001) incorporated the Nussbaum-type gain into the backstepping design and proposed a robust asymptotic regulating control scheme for a class of time-varying uncertain nonlinear systems.…”

Adaptive leaderless consensus control of uncertain multiagent systems with unknown control directions

“…Based on a novel Nussbaum function, an adaptive control law for first‐order and second‐order multiagent systems is proposed in Reference 23. The Nussbaum gain methods are also used to high‐order nonlinear system with unknown control directions in References 24 and 26‐29. In Reference 30, the consensus of high‐order nonlinear multiagent systems with unknown backlash‐like hysteresis and unknown control directions is solved by combining Nussbaum function with backstepping technique 33 …”

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

“…Typical examples may be found in the area of uncalibrated visual servoing control and robotic systems . As for single nonlinear systems with unknown control directions, the Nussbaum‐type function, which was independently presented in the work of Nussbaum, has been extensively adopted to design control methods . Nevertheless, for a multiagent system, where each agent possesses an unknown control direction, developing distributed controllers constitutes a quite challenging issue.…”