Global<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" display="inline" overflow="scroll"><mml:mi>κ</mml:mi></mml:math>-exponential way-point maneuvering of ships: Theory and experiments

Fredriksen, E.; Pettersen, Kristin Y.

doi:10.1016/j.automatica.2005.12.020

Cited by 153 publications

(124 citation statements)

References 22 publications

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“…It is shown by Fredriksen and Pettersen (2006) that the interconnection term g (t, x, ξ) in (51) has linear growth in x. Furthermore, the perturbing system (52) is time-invariant, linear and GES.…”

Section: Proof See Appendix Bmentioning

confidence: 99%

“…Remark 1 In addition to the convergence properties proven here being slightly stronger than the global κ-exponential stability proven in Fredriksen and Pettersen (2006), USGES is important from a robustness perspective. In particular, it is seen from Lemmas 9.2-3 in Khalil (2002) that ULAS and ULES both provide robustness to small uniformly bounded (UB) disturbances.…”

Section: Theorem 1 (Proportional Los Guidance Law)mentioning

confidence: 99%

“…UGAS/ULES is also referred to as global κ-exponential stability as defined by Sørdalen and Egeland (1995). The result of Pettersen and Lefeber (2001) was further extended to include a more complete vehicle model by Børhaug and Pettersen (2005), and Fredriksen and Pettersen (2006).…”

Section: +4773594599mentioning

confidence: 99%

“…2 LOS proportional guidance law Equation (13) is similar to the formulae used by Healey and Lienard (1993), Pettersen and Lefeber (2001), Børhaug and Pettersen (2005), Breivik and Fossen (2005), Fredriksen and Pettersen (2006), and Breivik and Fossen (2009). The proportional LOS guidance law for (15) is chosen as:…”

Section: Kinematic Equationsmentioning

confidence: 99%

See 3 more Smart Citations

On uniform semiglobal exponential stability (USGES) of proportional line-of-sight guidance laws

Fossen¹,

Pettersen²

2014

Automatica

207

101

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This paper presents a uniform semiglobal exponential stability (USGES) proof for a class of proportional line-of-sight (LOS) guidance laws used for vehicle path-following control. The LOS guidance law under consideration is a lookahead-based guidance law for marine craft. The USGES proof extends previous results that only guarantee global κ-exponential stability. Typical applications are marine craft and aircraft motion control systems for path following where the total system is a cascade of the motion controller and guidance law error dynamics.

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Section: Proof See Appendix Bmentioning

confidence: 99%

Section: Theorem 1 (Proportional Los Guidance Law)mentioning

confidence: 99%

Section: +4773594599mentioning

confidence: 99%

Section: Kinematic Equationsmentioning

confidence: 99%

See 2 more Smart Citations

On uniform semiglobal exponential stability (USGES) of proportional line-of-sight guidance laws

Fossen¹,

Pettersen²

2014

Automatica

207

101

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“…This is possible as long as the center of mass is located along the centreline of the vessel. Coordinate transformations for this translation can be found in [14].…”

Section: Assumptionmentioning

confidence: 99%

Leader–Follower Synchronisation for a Class of Underactuated Systems

Belleter

Pettersen

2016

Nonlinear Systems

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In this work leader-follower synchronization is considered for underactuated followers in an inhomogeneous multi-agent system. The goal is to synchronise the motion of a leader and an underactuated follower. Measurements of the leader's position, velocity, acceleration, and jerk are available, while the dynamics of the leader is unknown. The leader velocities are used as input for a constant bearing guidance algorithm to assure that the follower synchronises its motion to the leader. It is also shown that the proposed leader-follower scheme can be applied to multi-agent systems that are subjected to unknown environmental disturbances. Furthermore, the trajectory of the leader does not need to be known. The closed-loop dynamics are analysed and it is shown that under certain conditions all solutions remain bounded and the synchronisation error kinematics are shown to be integral input-to-state stable with respect to changes in the unactuated sway velocity. For straight-line motions, i.e. where the desired yaw rate and sway velocity go to zero, synchronisation is achieved. Simulation results are presented to validate the proposed control strategy.

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References

2021

Handbook of Marine Craft Hydrodynamics and Motion Control

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Globalκ-exponential way-point maneuvering of ships: Theory and experiments

Cited by 153 publications

References 22 publications

On uniform semiglobal exponential stability (USGES) of proportional line-of-sight guidance laws

On uniform semiglobal exponential stability (USGES) of proportional line-of-sight guidance laws

Leader–Follower Synchronisation for a Class of Underactuated Systems

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