Design and stability analysis of a variable structure adaptive backstepping controller

Abstract

This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS-ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS-ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments.

Robust Stabilization of Ship Course Via Convex Optimization

“…Here R[x] denotes the set of all multivariate polynomials in x with real coefficients. In this respect, the sum of squares approach has been widely used in control theory for constructing Lyapunov functions; see, for example, backstepping [6,15]. Up to date, the sum of squares technique has been applied in different fields.…”

Overcoming Limitations of Uncalibrated Robotics Visual Servoing by means of Sliding Mode Control and Switching Monitoring Scheme

“…Consider the plant (9) with UVC law (20) and monitoring function (21)- (22). If the modulation function (25) is applied, then the control direction switching stops, assuring that all signals in the closed loop system remain uniformly bounded and the tracking error e(t) is globally exponentially convergent to zero. Moreover, if δ > 0 in (25), then the ideal sliding mode on the manifold e = 0 is reached in finite time.…”

“…The proof is carried out in three parts. (14), (16) and (25); (iii) −KpSq is Hurwitz. In this case, from (i), φm(t) > ζ(t), ∀t ∈ [tκ, tκ+1), with ζ in (19).…”

Nonlinear controller synthesis for ship course with actuator using sum-of-squares optimization

“…The SOS approach has been extensively used in control theory for constructing Lyapunov functions; see, for example, backstepping [2,14]. Up to date, the SOS technique has been applied in different fields.…”