Alessandro Jacoud Peixoto

Sliding Mode Control of Uncertain Multivariable Nonlinear Systems With Unknown Control Direction via Switching and Monitoring Function

A novel output-feedback tracking sliding mode control strategy is proposed for a class of uncertain multi-input-multi-output (MIMO) systems with strong nonlinearities and unknown high-frequency gain (HFG) matrix, that is, the control direction is assumed unknown. A switching scheme based on a monitoring function is designed to handle the control direction uncertainty. The proposed method provides global stability properties and exact output tracking. Simulation results about a robotics visual servoing system using a fixed but uncalibrated camera illustrate the robustness and practical viability of the proposed scheme.

Output-feedback global tracking for unknown control direction plants with application to extremum-seeking control

This paper addresses the design of a sliding mode tracking controller for single-input-single-output (SISO) uncertain plants with relative degree one and unknown control direction, i.e., with unknown sign of the high frequency gain (HFG). We demonstrate that, for a class of linear plants with nonlinear output function, it is possible to achieve global exact tracking using only output-feedback by combining a recently introduced periodic switching function with a well-known control parameterization of Model Reference Control (MRC). Simulation results are presented to illustrate the good tracking performance. One significant advantage of the new scheme is its robustness to time-varying control direction which is here theoretically justified for jump variations of the HFG and successfully tested by simulation in more general conditions. This property makes it adequate for solving extremum-seeking problems. Theoretical justification is presented for a class of systems with nonlinear output function using only output-feedback. An application to the wheel slip control in Antilock Braking Systems (ABSs) illustrates the practical viability of the proposed control scheme.

Global real-time optimization by output-feedback extremum-seeking control with sliding modes☆

Abstract This paper addresses the design of a sliding mode based extremum-seeking controller for a class of single-input–single-output (SISO) uncertain nonlinear systems with unmatched and state-dependent strong nonlinearities. We demonstrate that it is possible to achieve an arbitrarily small neighborhood of the desired optimal point using only output-feedback. The key idea is the combination of a periodic switching function with a norm state observer. As an important advantage, we show that the proposed scheme achieves extremum-seeking for all initial conditions, i.e., the real-time optimization algorithm has global convergence properties. An application to a simple nonderivative optimizer illustrates the viability of the proposed approach.

Sliding mode control of uncertain multivariable nonlinear systems applied to uncalibrated robotics visual servoing

An output-feedback sliding mode controller using monitoring functions was recently introduced for linear uncertain single-input-single-output (SISO) systems with unknown control direction. Here, a generalization is developed for multivariable systems with strong nonlinearities. The monitoring scheme is extended to handle the uncertainty of the plant high frequency gain matrix Kp. Our strategy provides global stability properties and exact output tracking. Experimental results with a robotics visual servoing system, using a fixed but uncalibrated camera, illustrate the robustness and practical viability of the proposed scheme.

Sliding Mode Control of Uncertain Nonlinear Systems with Arbitrary Relative Degree and Unknown Control Direction

This paper considers the model reference tracking control for a class of uncertain nonlinear systems, based on sliding mode and output-feedback. No particular growth condition is imposed on the nonlinearity. Moreover, the design does not assume the prior knowledge of the control direction. For plants of arbitrary relative degree, global or semi-global asymptotic stability with respect to a compact set is guaranteed. Ultimate finite-time or exponential convergence of the tracking error to zero is achieved by using a hybrid lead filter based on 2-sliding mode exact differentiators. A monitoring function is used to determine the unknown control direction

Global exact tracking for uncertain MIMO linear systems by output feedback sliding mode control

Abstract This paper presents a solution to the problem of global exact output tracking for uncertain MIMO (multiple-input–multiple-output) linear plants with non-uniform arbitrary relative degree using output feedback sliding mode control. The key idea to overcome the relative degree obstacle is to generalize our previous hybrid estimation scheme to a multivariable version by combining, through switching, a standard linear lead filter with a non-linear one based on robust exact differentiators, achieving uniform global exponential practical stability and exact tracking.

Dwell-time and monitoring schemes for peaking avoidance in high-gain observer based output-feedback control

A peaking free tracking sliding mode controller based on high-gain observers and dwell-time control activation is introduced for a rather general class of uncertain strongly nonlinear systems. Global or semi-global practical exponential stability is proved using a novel lemma for output-feedback. Larger stability domains and significantly improved transient behavior are obtained. A new monitoring scheme is also given to deal with peaking induced by output disturbances.

Peaking free output-feedback control of uncertain nonlinear systems

Output-feedback sliding mode controllers are designed for single-input-single-output (SISO) uncertain nonlinear plants with state dependent nonlinearities. The sliding surface is generated using the states of a high gain observer (HGO) and the control law is peaking free. The control signal amplitude is either obtained from a simple norm observer or from the HGO states in conjunction with a dwell-time strategy, depending on the nonlinearity growth condition. Global or semi-global exponential stability with respect to a small residual set is proved without requiring the control to be a priori globally bounded. The advantages are better transient behavior and improved domain of stability.

Global tracking sliding mode control for uncertain nonlinear systems based on variable high gain observer

An output-feedback sliding mode controller is proposed for a class of single-input-single-output (SISO) uncertain nonlinear systems. The sliding surface is generated using the state of a high gain observer (HGO) while the control signal amplitude is generated from a norm observer free of peaking. The proposed scheme achieves global tracking with respect to a small residual set by means of a time varying observer gain (HGO) synthesized from measurable signals.

Sliding Mode Control of Uncertain Systems with Arbitrary Relative Degree and Unknown Control Direction: Theory and Experiments

This paper addresses the design of output feedback sliding mode tracking control for single-input-single-output (SISO) uncertain linear plants with arbitrary relative degree. A monitoring function is used to cope with the lack of knowledge of the control direction, i.e., the high frequency gain sign. The proposed scheme guarantees global asymptotic stability with respect to a compact set. Moreover, asymptotically exact output tracking is obtained. To this end, a key element is a hybrid nonlinear filter which performs exact signal differentiation based on higher order sliding modes. The proposed controller is evaluated with a DC motor control experiment