Exponential Stabilization of High-Order Chained Systems

Laiou, Maria-Christina; Astolfi, Alessandro

doi:10.1016/s1474-6670(17)40406-x

Cited by 12 publications

(9 citation statements)

References 13 publications

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“…For system (33 0 ), the control law can be derived similarly as for (33). So the singularity problem can be solved by switching between the two controllers designed for systems (33) Figure 2 shows the time plots of state variables ðx; y; y; ' x x; ' y y; ' y yÞ; the estimated parameters ð # d d 11 ; # d d 21 ; # p p 21 Þ; and the control inputs ðF ; T Þ in the adaptive control case.…”

Section: Remarkmentioning

confidence: 99%

“…So the singularity problem can be solved by switching between the two controllers designed for systems (33) Figure 2 shows the time plots of state variables ðx; y; y; ' x x; ' y y; ' y yÞ; the estimated parameters ð # d d 11 ; # d d 21 ; # p p 21 Þ; and the control inputs ðF ; T Þ in the adaptive control case. Figure 3 shows the time plots of state variables ðx; y; y; ' x x; ' y y; ' y yÞ and control inputs ðF ; T Þ in the robust control case.…”

Section: Remarkmentioning

confidence: 99%

“…Recently, a discontinuous stabilization scheme has been proposed for the high-order chained form [33] and generalized high-order chained form [34]; however, the original physical models do not generally appear in such a chained form, but can be so represented via coordinate and input feedback transformations. A problem may arise when some unknown parameters, unmodelled dynamics or external disturbances are included in the model.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed adaptive and robust control schemes guarantee that all the states are bounded and tend to zero asymptotically in spite of the presence of uncertain terms. Compared with the discontinuous stabilization scheme proposed in References [33,34], the proposed stabilization schemes are robust for certain input uncertainties.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive/robust time‐varying stabilization of second‐order non‐holonomic chained form with input uncertainties

Tso

Wang

2002

Intl J Robust & Nonlinear

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SUMMARYAdaptive and robust time-varying control schemes are constructed to stabilize second-order nonholonomic chained form in the presence of input uncertainties. The proposed control schemes guarantee that all the state variables converge to zero asymptotically in spite of input uncertainties, and are applied to the stabilization of a planar rigid body driven by active force and torque with unknown inertia and geometric parameters. The basic idea of the proposed stabilization schemes is to first convert the nonholonomic system into a linear time-varying form by time-varying co-ordinate transformation, and then design control laws to stabilize the converted linear time-varying system.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive/robust time‐varying stabilization of second‐order non‐holonomic chained form with input uncertainties

Tso

Wang

2002

Intl J Robust & Nonlinear

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“…In [5] and [6], recursive techniques based on backstepping are proposed. See also [8], [9], [11], [17], [18], and [22]. In all of these works, the objective is to achieve either exponential or asymptotic stabilization/tracking.…”

Section: Introductionmentioning

confidence: 99%

An Exponentially$epsilon$-Convergent Control Algorithm for Chained Systems and Its Application to Automatic Parking Systems

Liu

Dao

Inoue

2006

IEEE Trans. Contr. Syst. Technol.

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In this brief, a simple control approach is proposed for the multichain systems based on a switching algorithm of two sets of steering laws. Global exponential convergence to any prescribed norm bound ( -convergence) is guaranteed and the convergence rate is explicitly given. This approach has a distinctive feature that one of the inputs (driving input) is free. This feature plays a key role in achieving realistic parking tasks. For the design of steering laws, a method based on backstepping is proposed and analyzed in detail. Further, this control algorithm is applied to the automatic parking systems. The corresponding system package is developed which is composed of control laws for the steering angle and the driving velocity, algorithms for various kinds of parking tasks under steering angle and parking space limitations. A prototype system is built to validate this package, and the system works well in experiments subject to various parking situations.Index Terms-Automatic parking, chained system, constraint of parking space, exponential -convergence, parking algorithm, piecewise smooth algorithm, steering angle limitation, switching control.

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Cooperative Control of Dynamical Systems

2009

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Exponential Stabilization of High-Order Chained Systems

Cited by 12 publications

References 13 publications

Adaptive/robust time‐varying stabilization of second‐order non‐holonomic chained form with input uncertainties

Adaptive/robust time‐varying stabilization of second‐order non‐holonomic chained form with input uncertainties

An Exponentially$epsilon$-Convergent Control Algorithm for Chained Systems and Its Application to Automatic Parking Systems

Cooperative Control of Dynamical Systems

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