Extremum seeking control for an acceleration controlled unicycle

Suttner, Raik

doi:10.1016/j.ifacol.2019.12.040

Cited by 19 publications

(16 citation statements)

References 13 publications

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“…This implies that the set P × Θ is globally uniformly asymptotically stable for the cascade of ( 25) and (26). In other words, the set K in Theorem 2 is globally asymptotically stable for the averaged system of (22) in the variables (23). Therefore the claim follows from Corollary 1.…”

Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 71%

“…We can see in the plot on the right of Figure 1 that the second component t → p 2 (t) of the position t → p(t) first increases from p 2 (0) = 1 to values ≈ 2 and then converges into a neighborhood of the origin. This behavior can be explained by the change of variables (23). If we apply (23b)-(23e) to the initial velocity components w 1 = 0 and w 2 = 0 at time t = 0, then we get w1 = 0 and w2 = 2κ/mα(ψ(p 0 ) − η 0 ).…”

Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 91%

“…In this section, we apply the theory from Section 4 to two particular extremum seeking problems. Further applications can be found in [23,25].…”

Section: Examplesmentioning

confidence: 99%

“…is semi-globally practically uniformly asymptotically stable for the system with coordinate representation (22) in the variables (23).…”

Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 99%

“…Here, we use approximations of symmetric products to obtain information about descent directions of the objective function. Applications of this strategy to double-integrator points and unicycles can be found in [23,24,25]. In this paper, we investigate this new symmetric product approach to extremum seeking control for a more general class of mechanical systems and indicate further applications.…”

Section: Introductionmentioning

confidence: 99%

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Extremum Seeking Control for a Class of Nonholonomic Systems

Suttner¹

2020

SIAM J. Control Optim.

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We present a novel extremum seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis reveals that the solutions of the closed-loop system converge locally uniformly to the solutions of an averaged system in the large-amplitude high-frequency limit. This in turn leads to the effect that stability properties of the averaged system carry over to the approximating closed-loop system. Descent directions of the objective function are given by symmetric products of vector fields in the averaged system. Under suitable assumptions, we prove that minimum points of the objective function are asymptotically stable for the averaged system and therefore practically asymptotically stable for the closed-loop system. We illustrate our results by examples and numerical simulations.

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Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 71%

Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 91%

“…In this section, we apply the theory from Section 4 to two particular extremum seeking problems. Further applications can be found in [23,25].…”

Section: Examplesmentioning

confidence: 99%

“…is semi-globally practically uniformly asymptotically stable for the system with coordinate representation (22) in the variables (23).…”

Section: Planar Rigid Body With Two Thrustersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extremum Seeking Control for a Class of Nonholonomic Systems

Suttner¹

2020

SIAM J. Control Optim.

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Path planning for fast swarm source seeking in unknown environments

Chen,

Yuan,

Zhu

et al. 2023

Adaptive Control & Signal

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SummaryThis article proposes a novel path planning method for source seeking by UAV swarm using extremum seeking control mechanism and combined artificial potential functions, without the knowledge of position information. In particular, the swarm source seeking problem is reformulated as a minimum seeking of a combined artificial potential function that considers the potentials of obstacles, source, and collision avoidance between UAVs. The explicit form of the combined artificial potential function is unknown and its value can be measured by the sensors mounted on UAVs. The fast extremum seeking mechanism based on the normalized extremum seeking method is exploited to find the gradient of the combined artificial potential function and the target is located without using its position information. Finally, extensive simulations of source seeking for single UAV and swarm are presented to illustrate the effectiveness of the proposed path planning method.

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Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

Suttner,

Krstić

2023

Intl J Robust & Nonlinear

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SummaryIn this paper, we investigate the stabilizing effect of an extremum seeking control law on a class of underactuated Lagrangian control systems with symmetry. Our study is motivated by the problem of attitude optimization for satellites with reaction wheels. The goal is to minimize the value of an analytically unknown configuration‐dependent objective function without being reliant on measurements of the current configuration and velocity. This work extends our previous work on extremum seeking control for fully actuated mechanical systems on Lie groups in the absence of dissipation. We show that the earlier method for fully actuated systems can also be successfully applied to a certain class of underactuated systems, which are controlled by internal momentum exchange devices (reaction wheels) so that the total momentum is conserved. Conservation of momentum allows us to reduce the control system to a system on a smaller state manifold. The reduced control system is not of Lagrangian form but fully actuated. For the reduced control system we prove that the extremum seeking method leads to practical uniform asymptotic stability. We illustrate our findings by the example of a rigid body with internal rotors.

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Extremum seeking control for an acceleration controlled unicycle

Cited by 19 publications

References 13 publications

Extremum Seeking Control for a Class of Nonholonomic Systems

Extremum Seeking Control for a Class of Nonholonomic Systems

Path planning for fast swarm source seeking in unknown environments

Attitude optimization by extremum seeking for rigid bodies actuated by internal rotors only

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