Global Practical Tracking for High-Order Uncertain Nonlinear Systems with Unknown Control Directions

Yan, Xuehua; Liu, Yungang

doi:10.1137/090769727

Cited by 98 publications

(71 citation statements)

References 19 publications

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“…Suppose for contradiction that L is unbound on [0, +∞), i.e., lim t→+∞ L(t) = +∞. Then, it is easy to see that (13) still holds on [t s , +∞). This shows that Z is bounded on [t s , +∞), and on [0, +∞) as well.…”

Section: Part II Boundedness Of All Closed-loop Signals On [0 +∞)mentioning

confidence: 99%

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Global output-feedback tracking for nonlinear cascade systems with unknown growth rate and control coefficients

2014

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This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth. The systems investigated are substantially different from the closely related works, and have zero-dynamics, unknown growth rate, and unknown time-varying control coefficients. This makes the problem much more difficult to solve. Motivated by the authors' recent works, this paper proposes a new adaptive control scheme to achieve the global practical tracking. It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. This is achieved by combining the methods of universal control and dead zone with backstepping technique, and using the framework of performance analysis in the closely related works. A numerical example demonstrates the effectiveness of the theoretical results.

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Section: Part II Boundedness Of All Closed-loop Signals On [0 +∞)mentioning

confidence: 99%

“…Practical tracking control has received much attention over the last two decades for nonlinear systems, see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13]. Particularly, [1][2][3][4][5] studied various nonlinear systems with unmeasured states dependent growth and proposed effective output-feedback tracking control design schemes.…”

Section: Introductionmentioning

confidence: 99%

Global output-feedback tracking for nonlinear cascade systems with unknown growth rate and control coefficients

2014

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“…For many control applications, asymptotical tracking, due to the extra restrictions on the system and the reference signal (such as good models and the smooth reference signal), is impossible to accomplish. Accordingly, as a degenerated case, practical tracking (ie, -tracking), which only requires that the tracking error converges to a prescribed sufficiently small range, has attracted lots of attention from many scholars during the last decades (see, eg, other works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the references therein). In particular, the universal controllers achieving -tracking are developed in the works of Ryan and Ilchmann 1,2 for nonlinearly perturbed systems with relative degree one.…”

Section: Introductionmentioning

confidence: 99%

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

Yan

Zheng

Liu

2019

Intl J Robust & Nonlinear

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Summary This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate the effectiveness of the theoretical results.

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“…5 Moreover, actuation sign errors have been observed in attitude control of microsatellites. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] On the other hand, the nonlinear PI method provides an effective alternative strategy to the unknown control direction problem (see section 6 in the work of Ortega et al 1 ). 7 This approach has received increased popularity over the years as it provides a design tool for general classes of systems and can be combined successfully with parameter adaptation algorithms.…”

Section: Introductionmentioning

confidence: 99%

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

Psillakis

Lagos

2017

Adaptive Control & Signal

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In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict-feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict-feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.

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Global Practical Tracking for High-Order Uncertain Nonlinear Systems with Unknown Control Directions

Cited by 98 publications

References 19 publications

Global output-feedback tracking for nonlinear cascade systems with unknown growth rate and control coefficients

Global output-feedback tracking for nonlinear cascade systems with unknown growth rate and control coefficients

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

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