Adaptive practical tracking control by output feedback for a class of nonlinear systems

Abstract

This paper investigates the problem of adaptive practical tracking control by output feedback for a class of nonlinear systems in which the nonlinearities are restricted to be upper bounded by a constant plus a polynomial function of the output multiplied by unmeasured states. To solve the problem, an observer with a dynamic high-gain is first introduced, and then an adaptive output feedback tracking controller is successfully designed using the universal control methodology. It is shown that all the states of the closed-loop system are bounded, and the tracking error can be made arbitrarily small by an appropriate choice of the design parameters after some large enough time. A simulation example is also provided to illustrate the correctness of the theoretical results.

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

“…Over the years, the problem of output feedback control has received much attention for nonlinear systems with unmeasured states dependent growth 1–9. It has been pointed out in the remarkable paper 1 that if the power of the nonlinearity growth with respect to unmeasured states is greater than 2, there are counterexamples for which no output feedback controls exist.…”

Global Practical Tracking for Nonlinear Systems With More Unknowns via Adaptive Output‐Feedback

“…Over the past decades, practical tracking control has been intensively investigated (see e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). Different from asymptotic tracking, practical tracking requires the tracking error to reach a prescribed accuracy after a finite period of time, rather than to converge to zero as time tends to infinity.…”

“…Up to now, quite a few practical tracking strategies via output-feedback have been proposed for various uncertain nonlinear systems with unmeasured states dependent growth (see e.g. [7,9,10,[12][13][14][15][16][17]). However, most of the related literature impose somewhat serious restrictions on the unknowns of the systems and the reference signals.…”

“…However, most of the related literature impose somewhat serious restrictions on the unknowns of the systems and the reference signals. Specifically, [7,9,14] need known control coefficients (equal to 1) and a known rate for the growth of the system nonlinearities, and require the reference signal therein to belong to a known interval. Subsequently, [10,13] consider the cases with unknown Manuscript received September 13, 2015; revised January 21, 2017; accepted April 8, 2017.…”

“…We would like to illustrate the difference between the tracking problem in this paper and those in the existing related works [7,9,10,12,[14][15][16][17]. Assumption 1 shows that the control coefficients of system (1) are unknown functions of time, which belong to a known bounded interval excluding zero and have bounded derivatives with known bound.…”