Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

Abstract

a b s t r a c tThis paper investigates the problem of adaptive stabilization control design for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts, including unmodeled dynamics, and dynamics modeled with unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterized system into a linear-like parameterized system. Then, by the use of input-state scaling technique and adding a power integrator backstepping approach, an adaptive state feedback controller is obtained. The adaptive control based switching strategy is proposed to eliminate the phenomenon of uncontrollability. Global asymptotic regulation of the closed-loop system states and the boundedness of other signals are guaranteed. Simulation examples demonstrate the effectiveness of the proposed scheme.

Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback

“…By (16), (24), e i ¼ ðz i Àẑ i Þ 1=r i and the definition of the homogeneous norm, one gets Proof of Proposition 3.5. From e i ¼ ðz i Àẑ i Þ 1=r i , (16) and Lemma 2.3, there is a positive constant k i5 such that jẑ i j ¼ j z i À e r i i j r j z i j þ j e i j r i r k i5 ðj ξ i À 1 j r i þ j ξ i j r i þ j e i j r i Þ ð A:4Þ …”

“…To overcome this difficulty, with the effort of many researchers a number of intelligent approaches have been proposed, which can mainly be classified into discontinuous time-invariant stabilization [2,3], smooth timevarying stabilization [4][5][6] and hybrid stabilization [7,8], see the survey paper [9] and references therein for more details. Mainly thanks to these valid approaches, the robust issue of nonholonomic systems has been well-studied and a number of interesting results have been established over the last years, for example, one can see [10][11][12][13][14][15][16][17][18][19][20] and the references therein.…”

Adaptive finite-time stabilization for a class of uncertain high order nonholonomic systems

“…It is worth pointing out that Assumption 2.1 is less restrictive than those in the closely related papers [21,22,[31][32][33], where the control coefficients are exactly known or bounded by known constants. This means that the system studied in this paper allows for a much broader class of systems.…”

“…Using these valid approaches, the robustness issue of nonholonomic systems with drift uncertainties has been extensively studied [12][13][14][15][16][17][18][19][20]. In particular, as the extension of the classical nonholonomic systems, the high order nonholonomic systems in power chained form have recently achieved investigation [21][22][23]. However, it should be mentioned that most of the existing works only consider the feedback stabilizer that makes the trajectories of the systems converge to the equilibrium as the time goes to infinity.…”

State-feedback stabilization for stochastic high-order nonholonomic systems with Markovian switching

“…The design procedure proposed in [16] is also based on a combined application of a state scaling technique, the σ -process, and the adding a power integrator backstepping method. In [17], Gao studied the problem of adaptive stabilization control design for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts. All the above references considered the high-order nonholonomic systems in the deterministic case.…”