Fault‐tolerant leader‐follower formation control of marine surface vessels with unknown dynamics and actuator faults

2018

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Summary This paper focuses on the output‐feedback tracking control problem for a class of nonlinear systems with both unknown nonlinearities and unknown control directions. An adaptive prescribed performance controller combined with a Nussbaum gain and a dividing line is proposed to solve the problem. Compared with the existing results, (i) both the convergence rate and the ultimate bound of the tracking error can be prescribed; (ii) no approximating structures such as neuro/fuzzy systems are used, regardless of unknown nonlinear functions; and (iii) the computational burden is alleviated in the sense that the iterative calculation of command derivatives is avoided and the number of online learning parameters is largely reduced. Simulation results are given to further illustrate the established theoretical findings.

“…By , and , it follows that

x_{2} = sans-serif g s_{2} = sans-serif g e_{2} + sans-serif g ŝ_{2} = sans-serif g e_{2} + sans-serif g z_{2} + sans-serif g α_{1} .

Differentiating by using and leads to

{\overset{z}{true}}_{1} = f_{1} false(η, y false) + d_{1} false(x, t false) - \overset{r}{true} false(t false) + sans-serif g e_{2} + sans-serif g z_{2} + sans-serif g α_{1} .

Differentiating by using , and yields

{\overset{z}{true}}_{i} = - l_{i} ŝ_{1} - {\overset{α}{true}}_{i - 1} + z_{i + 1} + α_{i} = - {\overset{α}{true}}_{i - 1} + z_{i + 1} - γ_{i} ϕ_{i} false(t false), i = 2, …, n

with z n + 1 = 0. By seeking a contradiction as in the works of Zhang and Yang, it is to be established that

false| z_{i} false(t false) false| < k_{i} false(t false), i = 1, …, n, t \geq 0 .

Suppos...…”

Section: Stability Analysismentioning

confidence: 99%

z_{1}^{'}

and p , respectively. Therefore, the obstacle of how to utilize symmetric barrier Lyapunov functions to tackle the asymmetric constraint problem is conquered.…”

Section: Further Extensionmentioning

confidence: 99%

Adaptive prescribed performance control of nonlinear output‐feedback systems with unknown control direction

2018

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“…The control objective is to globally stabilize the aforementioned system with the following performance specifications:

| x_{i} | < b_{i} = \frac{1}{t} + 0.1, i = 1, 2 .

A comparative study is carried out based on system to show the efficacy of the adaptive gain technique proposed in intuitively. In the absence of the designed adaptive scheme

\overset{r}{true}

, the control law in becomes u = − γ η ϕ , as used in the work of Zhang and Yang . Setting γ = 1, the obtained simulation result is displayed in Figure .…”

Section: Simulation Studymentioning

confidence: 99%

Adaptive asymptotic stabilization of a class of unknown nonlinear systems with specified convergence rate

2018

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Summary This paper focuses on the asymptotic stabilization problem for a class of multivariable nonlinear systems with relative degree one, practical examples of which incorporate the liquid level control of water tanks, and the speed control of interconnected carts. The presence of the unknown (other than uncertain) additive and multiplicative nonlinearities renders asymptotic stability difficult to be achieved by the existing robust control methods. To conquer this obstacle, a novel adaptive control strategy is proposed. In the control design, the state constraint technique is newly introduced to the adaptive design to generate a proper control gain to compensate for unknown nonlinearities, instead of the use of extra approximating structures. By this means, both the prescribed transient performance regarding the convergence rate and the expected asymptotic stability are preserved. Finally, simulation results are given to illustrate the established theoretical findings.

“…Therefore, substantial research efforts have been devoted to robust control designs for uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems during the past decades. Up to now, a series of successful stories have been reported . By introducing an auxiliary design system, a way to achieve output tracking under input constraints was provided in the works of Chen et al By making use of command filters, the explosion of complexity issue was also evaded in the backstepping procedure.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the finite‐time convergence of tracking errors was guaranteed by Jin . A systematic method to predefine the transient and steady‐state performance regarding the overshoot, convergence rate, and steady‐state error was formulated in other works . The potential robustness of the method was further exploited in the works of Theodorakopoulos et al and Zhang and Yang .…”

Section: Introductionmentioning

confidence: 99%

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

2019

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Summary This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.