New developments in dynamical adaptive backstepping control

Abstract

We consider a number of dynamical adaptive backstepping control algorithms for the class of observable non-minimum phase nonlinear continuous uncertain systems (triangular and non-triangular), as well as systems with disturbances which can be converted to the parametric semi-strict feedback form. Nonlinear, sliding and second-order sliding control laws are developed. Adaptive backstepping algorithms with tuning functions, and modular parameter identification approaches are presented. BACK, a Maple symbolic algebra package, has been developed as a tool for the design of dynamical adaptive nonlinear controllers for regulation and tracking tasks. IntroductionThe control of nonlinear systems is very important because there are many practical applications in which it is inappropriate t'or the nonlinear equations to be assumed approximately linear. In particular, if there are some unknown parameters, uncertain dynamics, and external and internal disturbances, classical methods do not provide suitable control.Adaptive control is usually employed for the regulation of uncertain systems, when no information is available about the bounds of the unknown parameters. In the 1990s a new family of adaptive control algorithms, using the backstepping approach, was developed [11,16]. This control scheme allows the systematic design of adaptive controllers for triangular nonlinear systems containing unmatched parametric uncertainty. The various backstepping control design algorithms [10,11,16] compiled in [17], provide a systematic framework for the design of tracking and regulation strategies suitable for large classes of nonlinear systems. These static adaptive backstepping (SAB) algorithms enlarged the class of nonlinear systems controlled via a Lyapunov-based control law to uncertain systems transformable into the parametric strict feedback (PSF) form and the parametric pure feedback (PPF) form. In general, local stability is achieved for systems in the PPF form, whilst global stability is guaranteed for systems in the

Dynamical Adaptive Integral Sliding Backstepping Control of Nonlinear Nontriangular Uncertain Systems

“…The claim is substantiated by a practical example by applying the proposed algorithm on a chemical plant. For that, a highly nonlinear model of continuous stirred tank reactor (CSTR) [23,24] is selected. The computer simulation results are presented to support the claims of proposed method.…”

“…The triangular systems such as parametric strict form and parametric pure feedback form can also be controlled with DAB. The problem can be defined by considering uncertain nonlinear systems described as [24] = 0 ( ) + ( ) + ( 0 ( ) + ( ) ) ,…”

“…where 1 is a positive scalar design constant. By using (25) in (20) and (24) one getṡ (ĥ (1) )̇+ (ĥ (1) )̇+ (ĥ (1) )…”

“…Thus the system (74) can be rewritten aṡ . DAB-SMC controller [24] is applied on system (76) to reproduce results for comparison, which resulted in coordinate transformation as…”

“…The following is the control law reported in [24], formulated in the last step of DAB-SMC procedure:…”