Lyapunov‐based finite‐time control of robot manipulators

Abstract

The objective of this work is to propose new families of finite‐time controllers providing bounded and unbounded control signals. We show that this new family of controllers can be applied to solve the regulation problem for robot manipulators in finite‐time with unbounded and bounded torques. The key idea to accomplish this objective is to propose a novel family of Lyapunov functions, which is more suitable for designing finite‐time regulators for robot manipulators. The efficacy of these controllers, compared with other schemes, is illustrated by a simulation example, which shows that the proposed controllers are a good alternative to solve the finite‐time regulation problem for robot manipulators.

Adaptive finite‐time stabilization with prescribed output convergence via an integrated scheme

“…where x = [x 1 , … , x n ] T ∈ R n is the system state with the initial condition x(0) = x 0 and x [i] = [x 1 , … , x i ] T ; u ∈ R and y ∈ R are the control input and system output, respectively; f i 's are continuous functions satisfying f i (t, 0) ≡ 0, termed the system nonlinearities. Remarkably, system (1) covers numerous practical models, such as tunnel-diode circuit, 1 ship steering model 2 and robotic manipulator, 3 and hence has been constantly studied during the past few decades (see e.g., References 4 and 5).…”

“…Nonlinear control has been arguably the most ubiquitous in the control community, whether in theory or in practice. [1][2][3][4][5] In 1970's and 1980's, its basic issues, such as controllability, observability, stabilizability, and robustness, have attracted extensive attention, but rarely underlining system performance. The research focus later turned to the construction/realization of various nonlinear controls to achieve stabilization, tracking, noise rejection and adaptive regulation, yet lacking the systemic treatment on system performance.…”

Robust backstepping non‐smooth practical tracking for nonlinear systems with mismatched uncertainties

“…It was proved that finite-time stable systems enjoy faster convergence, better robustness, and disturbance rejection property. 1,2 Since Lyapunov and converse Lyapunov results were introduced for finite-time stability in References 2,3, in which the relations between the regularity property of the settling time function and those of Lyapunov function were investigated, (practical) finite-time stability have been widely applied to controller design for spacecraft attitude control, 4,5 robot manipulator control, 6 automobile electronic throttle control, 7 quadrotor position, and attitude control, 8 especially the stabilization and tracking problems of high-order nonlinear systems. 9,10 In actual application scenarios, multiple physical systems, especially the mechanical ones, are of high-order dynamics with uncertainties and disturbances.…”

Full-Order Sliding Mode Bounded Control for Euler-Lagrange Systems with External Disturbances

“…Since the convergence rate for EL systems is an important indicator of the control performance, some scholars have proposed finite-time control methods that have the advantage of faster convergence than asymptotic convergence methods [25] and exponential convergence methods [26]. In a general way, the finite-time controllers are usually designed by using the homogeneous method [27], adding a power integrator method [28], terminal sliding mode (TSM) control method [29], and so on. The finite-time controller that is designed by homogeneous method is suitable for EL systems without external disturbances.…”