Ali J. Koshkouei

Adaptive backstepping control of nonlinear systems with unmatched uncertainty

Considers control design using an adaptive backstepping algorithm for a class of nonlinear continuous uncertain processes with disturbances which can be converted to a parametric semi-strict feedback form. Sliding mode control using a combined adaptive backstepping sliding mode control algorithm is also studied. The algorithm follows a systematic procedure for the design of adaptive control laws for the output of observable minimum phase nonlinear systems with matched and unmatched uncertainty. An existing sufficient condition for sliding is not needed by the new algorithm.

Discrete-Time Sliding Mode Control Design

Abstract The concept of the discrete-time sliding mode is clarified and a new sufficient condition for its existence is presented. A new method of control design using discrete sliding mode properties is proposed and the robust stability of the sliding mode dynamics is presented. Furthermore, the problem of the stabilization of discrete-time systems is studied.

Sliding mode observers for a class of nonlinear systems

The stability of a nonlinear observer for systems with uncertainties usually requires some sufficient conditions. In this paper we consider a class of systems with two uncertain parts: one which satisfies the Lipschitz condition, whilst the other does not satisfy the Lipschitz condition but is a bounded uncertainty. Sliding mode theory is applied to yield feedforward compensation control to stabilize the error estimation system with and without Lipschitz uncertainty. New sufficient conditions for stability of the Thau observer are proposed. These conditions ensure the stability of the nonlinear observer by selecting a suitable observer gain matrix.

Adaptive Output Tracking Backstepping Sliding Mode Control of Nonlinear Systems

Abstract This paper considers the design of sliding mode control using a combined adaptive backstepping sliding mode control (SMC) algorithm for a class of nonlinear continuous uncertain processes which can be converted to a semi-parametric strict feedback form. The algorithm follows a systematic procedure for the design of dynamical adaptive SMC laws for the output of observable minimum phase nonlinear systems with matched and unmatched uncertainty. An existing sufficient condition for sliding is not needed by the new algorithm.

Sliding lattice design for discrete-time linear multivariable systems

Sliding mode control of discrete-time systems has not been developed as much as its continuous counterpart. The sliding mode control of multivariable discrete-time systems is studied in this paper. The concept of the discrete-time sliding mode is clarified and new sufficient conditions for the existence of the sliding mode are presented. A new method of control design using discrete sliding mode properties is proposed and the robust stability of the sliding mode dynamics is presented. The problem of stabilization of discrete-time systems is studied.

Adaptive Backstepping Control

Adaptive backstepping algorithms for a class of nonlinear continuous uncertain processes with disturbances are considered. Sliding mode control using a combined adaptive backstepping sliding mode control algorithm is also studied. The algorithms follow a systematic procedure for the design of adaptive control laws for the output of observable minimum phase nonlinear systems. This class of systems may include unmatched uncertainty including disturbances and unmodelled dynamics. The design methods are based upon (i) the backstepping approach, and (ii) a combination of sliding and backstepping.

Sliding mode state observers for linear multivariable systems

In this paper we discuss necessary conditions in sliding mode observer design for multivariable systems, a method for the design of asymptotically stable sliding observers and the stability of reconstruction error systems via the method of Lyapunov. Furthermore, some techniques for finding the feedforward injection map and the external feedforward compensation signal are presented.

Sliding mode controller-observer systems with unmatched uncertainty

Abstract This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics and a method for the design of asymptotically stable sliding observers for linear multivariable systems are studied. The sliding observer design ensures that, in the presence of unmatched uncertainty, the estimated state nearly approaches the actual state. Certain sufficient conditions should be satisfied for the asymptotic stability of the error system.

Backstepping algorithms for a class of disturbed nonlinear nontriangular systems

This paper presents a method for the design of dynamical adaptive nonlinear controllers for regulation and tracking of a class of observable minimum phase uncertain nonlinear systems. This method also allows one to design non-adaptive controllers for systems without uncertainty, and dynamical adaptive sliding mode controllers (ASMC).

Adaptive feedback passivity of nonlinear systems with sliding mode

Passivity of a class of nonlinear systems with unknown parameters is studied in this paper. There is a close connection between passivity and Lyapunov stability. This relationship can be shown by employing a storage function as a Lyapunov function. Passivity is the property stating that any storage energy in a system is not larger than the energy supplied to it from external sources. An appropriate update law is designed so that the new transformed system is passive. Sliding mode control is designed to maintain trajectories of a passive system on the sliding hyperplane and eventually to an equilibrium point on this surface.