Tiago Roux Oliveira

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.

Global and exact HOSM differentiator with dynamic gains for output-feedback sliding mode control

In this paper we introduce a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains to solve the problem of trajectory tracking via output-feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Uniform global stability and robust exact tracking are guaranteed employing the proposed HOSM based exact differentiator. The obtained results are not restricted to first-order sliding mode control feedback, but applies for second order sliding mode algorithms (twisting, super-twisting and variable gain super-twisting) as well as quasi-continuous HOSM finite-time controllers. Simulations with an aircraft pitch-control application illustrate the claimed properties, even in the presence of measurement noise.

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 differentiator based on higher-order sliding modes and dynamic gains for globally stable output-feedback control

In this paper, we propose a global exact differentiator with dynamic gains based on higher-order sliding modes to solve the problem of global trajectory tracking via output-feedback for a class of uncertain nonlinear plants with disturbances. Norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state-dependent and time-varying. Differently from some previous works in the literature, no hybrid switching scheme is necessary to state global stability using only input-output information. For the first time, uniform global exponential stability and ultimate exact tracking are guaranteed exclusively employing higher-order sliding modes based exact differentiators. Numerical simulations are presented to validate the analysis and show the effectiveness of the proposed method.

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.

Extremum Seeking for Static Maps With Delays

In this paper, we address the design and analysis of multi-variable extremum seeking for static maps subject to arbitrarily long time delays. Both Gradient and Newton-based methods are considered. Multi-input systems with different time delays in each individual input channel as well as output delays are dealt with. The phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation-based (averaging-based) estimate of the Hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the time delay. In particular, a new backstepping-like transformation is introduced to design the predictor for the Gradient-based extremum seeking scheme with multiple and distinct input delays. The proposed Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in the literature free of delays. A source seeking example illustrates the performance of the proposed delay-compensated extremum seeking schemes.

Predictor-feedback for multi-input LTI systems with distinct delays

In this paper, we propose a predictor-based state feedback controller for multi-input linear time-invariant systems with different time delays in each individual input channel. The controller is designed based on the backstepping method. Since the conventional backstepping transformation is not applicable to the systems due to the differences among delays, a modified transformation is introduced. This transformation enables us to design an exponentially stabilizing controller under which the plant behaves as if the delay were absent after a finite time interval. In addition, an explicit Lyapunov functional is constructed. The performance of the controller is demonstrated by a numerical simulation.