Tangent barrier Lyapunov function‐based constrained control of flexible manipulator system with actuator failure

In this paper, the problem of state constraints control is investigated for a class of output constrained flexible manipulator system with varying payload. The dynamic behavior of the flexible manipulator is represented by partial differential equations. To prevent states of the flexible manipulator system from violating the constraints, a barrier Lyapunov function which grows to infinity whenever its arguments approach to some limits is employed. Then, based on the barrier Lyapunov function, boundary control laws are given. To solve the problem of varying payload, an adaptive boundary controller is developed. Furthermore, based on the theory of barrier Lyapunov function and the adaptive algorithm, state constraints and output control under vibration condition can be achieved. The stability of the closed-loop system is carried out by the Lyapunov stability theory. Numerical simulations are given to illustrate the performance of the closed-loop system.

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Inverse Optimal Control with Set-Theoretic Barrier Lyapunov Function for Handling State Constraints

2020 American Control Conference (ACC) ◽

10.23919/acc45564.2020.9147707 ◽

2020 ◽

Author(s):

Meryem Deniz ◽

P.L Devi ◽

S. N. Balakrishnan

Keyword(s):

Optimal Control ◽

Lyapunov Function ◽

State Constraints ◽

Inverse Optimal Control ◽

Barrier Lyapunov Function

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Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220985637 ◽

2021 ◽

pp. 014233122098563

Author(s):

Fei Shen ◽

Xinjun Wang ◽

Xinghui Yin

Keyword(s):

Adaptive Control ◽

Nonlinear Systems ◽

Lyapunov Function ◽

Dead Zone ◽

Small Neighborhood ◽

Unmodeled Dynamics ◽

Stochastic Nonlinear Systems ◽

Dynamic Surface ◽

Barrier Lyapunov Function ◽

Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

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