Adaptive constraint control for flexible manipulator systems modeled by partial differential equations with dead‐zone input

Abstract

Summary In this article, based on partial differential equations (PDEs), the flexible manipulator system with both dead‐zone input and state constraints is studied. The dynamic model of the flexible manipulator system is described by PDEs. The parameters of the dead‐zone input are unknown, and the state constraint problem is also considered. An adaptive approach is proposed to offset the effects caused by dead‐zone input. Thus, to guarantee that all states remain within their respective constraint regions, the boundary control law based on the barrier Lyapunov function is given, and an adaptive controller is designed. According to the Lyapunov analysis method, the control method is given to ensure that all signals of the closed‐loop system are bounded and all states satisfy the constraint conditions. Finally, simulation results show the effectiveness of the proposed control method in this article.

Finite‐time parameter estimation based boundary control for a class of 2×2 hyperbolic partial differential equation systems with uncertain transport speeds

“…In the parametric models (6), all the functions p i , q i , r i , i = 1, 2 can be obtained using the available measurements u(x, t) and v(x, t). Therefore, the unknown parameters b i , c i , i = 1, 2 can be identified from the parametric models (6). In this work, the least-squares method is utilized to estimate the unknown parameters in finite time.…”

“…being an arbitrary time interval. With the parametric model (6), it is obvious that bi = b i , ĉi = c i , i = 1, 2 can minimize the cost functions J 1 and J 2 .…”

“…During the past few decades, much attentions have been paid to the control problem of systems described by partial differential equation (PDE) in References 1‐6. It is well recognized that PDE can be categorized into three groups: the parabolic PDE, the hyperbolic PDE, and the elliptic PDE.…”

Event‐triggered adaptive fault‐tolerant vibration control for a flexible robotic manipulator based on the partial differential equation model

“…Boundary control is an effective and practical method for managing vibration in flexible systems. [4][5][6][7] In order to realize motion control and vibration suppression, many researchers have combined boundary control with some traditional algorithms. [8][9][10][11][12][13] All of this research is, however, carried out under the condition that the actuator is fault-free.…”

“…In essence, the flexible manipulator is a distributed parameter system (DPS), which is usually expressed by partial differential equations (PDEs). Boundary control is an effective and practical method for managing vibration in flexible systems 4–7 . In order to realize motion control and vibration suppression, many researchers have combined boundary control with some traditional algorithms 8–13 .…”