Predictor‐based adaptive dynamic surface control for consensus of uncertain nonlinear systems in strict‐feedback form

Abstract

This paper investigates the leader-follower consensus problem of uncertain nonlinear systems in strictfeedback form. By parameterizations of unknown nonlinear dynamics of the agents, an adaptive dynamic surface control with the aid of predictors, tracking differentiators is proposed to realize output consensus of the multi-agent systems. Unlike the existing adaptive consensus methods, the predictor errors are used to learn the unknown parameters, which can achieve fast learning without high-frequency signals in control inputs. As a fast precise signal filter, the tracking differentiator is used in the control design instead of first-order filters, which can further improve the control performance. Based on graph theory and Lyapunov stability theory, it is shown that the outputs of all followers ultimately synchronize to that of the leader with bounded tracking errors. Simulation results are provided to validate the effectiveness and advantage of the proposed consensus algorithm.

Dynamic output feedback control for desired motion tracking on synchronous motors

“…In Section 4, first-order Taylor polynomial expansions were considered to suppress uncertainty signals, yielding a satisfactory closed-loop planned motion trajectory tracking. Moreover, control parameters can be algebraically computed and adjusted online using (27) to improve the approximation of uncertainty signals, as may be required by some highly uncertain motion control application.…”

“…A sliding‐mode adaptive control strategy based on modelled mechanical load disturbance estimation for a surface‐mounted permanent‐magnet synchronous motor has been proposed in Cao et al A disturbance observer‐based model predictive control scheme of an interior permanent‐magnet synchronous motor has been introduced in Mwasilu et al In this predictive control technique, an online accurate constant load torque estimation is required to avoid a significant speed regulation error. A predictor‐based neural dynamic surface control approach for a class of nonlinear dynamic systems in strict‐feedback form, with efficient rejection capability of model uncertainty and bounded unknown external disturbances, has been proposed in Peng et al Here, predictors are properly designed to identify system uncertainties without sacrificing control robustness (see also the literature and references therein). Under a different control design perspective, the present paper deals with the closed‐loop efficient tracking problem of planned motion reference trajectories for interior‐ and surface‐permanent‐magnet nonlinear synchronous motors, by processing measurable output signals only.…”

Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

“…More recently, instead of using the linear filters, several DSC methods have been addressed to improve the control performance. () In the works of Farrell et al( ) and Dong et al,() a command filtered backstepping consisting of a second‐order filter for derivative generation was proposed, and the rigorous proof of the closed‐loop stability was studied via Tikhonov's theorem. By incorporating the sliding mode–based integral filters and command filtered backstepping, an input‐to‐state stability–modular approach was proposed in the work of Zong et al To increase the error convergence rate, adaptive dynamic surface based nonsingular fast terminal sliding mode control was presented for semistrict‐feedback systems in the work of Li et al In the works of Sun et al( ) and Wang et al,() the tracking differentiators were incorporated to improve the transient tracking‐error performance in the DSC design.…”

Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

“…In , a modified DSC approach was developed for multi‐motor servomechanism with backlash, friction, and other disturbances, where a continuous hybrid differentiator was employed to replace the first‐order linear filter. With the tracking differentiators, a predictor‐based DSC scheme was presented for consensus of uncertain nonlinear strict‐feedback systems . To extend the DSC technique to nonaffine pure‐feedback systems, several adaptive control schemes were proposed via the mean value theorem, which was used to translate the nonaffine systems into strict‐feedback case .…”