Integrator Backstepping using Barrier Functions for Systems with Multiple State Constraints

Abstract

Abstract-The problem of stabilization for a class of feedback linearizable systems with multiple state constraints is addressed. The design procedure is constructive, and yields a continuous final control law which guarantees that all specified states remain within certain bounds for all time. The achieved bounds on the states are independent of the initial conditions. The procedure entails shaping the control Lyapunov function, and propagating hard-bounds imposed on the pertinent stabilising functions and associated error signals through the steps of the backstepping control design framework.

Backstepping dynamic surface control for an anti-skid braking system

“…The barrier Lyapunov function (BLF) and its variants have been widely applied to state constraint and output constraint problems (Niu & Zhao, 2013;Ren et al, 2010;Tee et al, 2009Tee et al, , 2011 for nonlinear systems in Brunovsky form (Ngo, Mahony, & Jiang, 2005) using the backstepping technique (Krstic, Kanellakopoulos, & Kokotovic, 1995). With these approaches, good tracking performance without violation of any constraints has been achieved.…”

Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints

“…Recently, the control design approaches based on Barrier Lyapunov Function (BLF) have been actively presented to deal with constraints in Brunovsky-type systems [13] and nonlinear strict-feedback systems [14][15][16][17]. In [18], a backstepping control design approach was derived for nonlinear systems with a time-varying output constraint.…”

Chaos RBF dynamics surface control of brushless DC motor with time delay based on tangent barrier Lyapunov function

“…Recently, a barrier Lyapunov function (BLF) which is proposed for constraint handling in Brunovaky-type system and nonlinear systems in strict feedback form are introduced for the special property of approaching infinity whenever its arguments approach some limits [14,15]. In addition, backstepping design method is an effective tool, which is often applied in nonlinear systems control with non-matching conditions, as well as systems with uncertain functions [16,17].…”