Hybrid Dynamical Systems

Abstract-The paper presents a hybrid systems strategy for consensus (or formation realization) for a fleet of non-holonomic agents. In the proposed model, each agent has a smooth continuous-time dynamics and a piecewise constant impulsive reference. The jumps on the reference trajectory take place at some updating instants that are decided independently by each agent. The jumps computation is based on the relative distance with respect to some time-varying neighbors at the update instants. Between the updates of its reference each robot will track its own constant reference trajectory. Our results provide consensus (formation realization) as far as a minimum dwell-time condition between consecutive updates is satisfied. A numerical example illustrates the theoretical results.

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“…. , n} we end up with the following hybrid dynamics (see [22] for an exhaustive presentation of hybrid dynamics):…”

Section: Resultsmentioning

confidence: 99%

“…We now express (22) only for the x component (for the y component the argument will be equivalent) and thus introduce…”

Section: B Analysis Of the Jump Mapmentioning

confidence: 99%

Hybrid Framework for Consensus in Directed and Asynchronous Network of Non-Holonomic Agents

Borzone

Morărescu

Jungers

et al. 2018

IEEE Control Syst. Lett.

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“…A hybrid signal is a function defined on a hybrid time domain. For more details on properties of solutions to hybrid system (1), we refer the reader to [3], [8].…”

Section: Preliminariesmentioning

confidence: 99%

“…In this section, we explain how to formulate the closedloop system as a hybrid dynamical model [8]. We define the sampling-induced error as e s :=ŷ q −q µ (y), which is reset to zero at each transmission instant t k , k ∈ N. We also define the quantization error as e q := q µ (y) − y.…”

Section: Hybrid Modelmentioning

confidence: 99%

Input-to-state stabilizing event-triggered control for linear systems with output quantization

Abdelrahim

Dolk

Heemels

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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To cite this version:M. Abdelrahim, V.S. Dolk Abstract-In this paper, we are interested in the stabilization of a linear plant based on output measurements that are subject to dynamic quantization. Moreover, to save communication resources, these measurements are transmitted to the controller using an output-based event-triggering condition. The proposed event-triggering mechanism and the dynamic quantization strategy ensure an input-to-state stability (ISS) property of a set around the origin with respect to the external disturbances. The existence of a strictly positive lower bound is ensured on both the inter-transmission times and the inter-zoom times in order to prevent the occurrence of Zeno behaviour. The chattering between zoom-in and zoom-out actions is avoided, and the zoom variable of the dynamic quantizer is guaranteed to be bounded. We characterize the inherent tradeoff between transmissions and quantization in terms of design parameters that can be tuned by the user. The effectiveness of the approach is illustrated on a numerical example.

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“…The issue of hybrid control in dynamic ship positioning, discussed by Nguyen et al, (2007), was also examined by Brodtkorb et al, (2014), who used the structure of the hybrid control system described by Goedel et al (2012). Their hybrid controller consisted of four component controllers, and switching between them took place when the state of the sea changed from calm to extreme.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Switching Controller Design for the Maneuvering and Transit of a Training Ship

Tomera

2017

International Journal of Applied Mathematics and Computer Science

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The paper presents the design of a hybrid controller used to control the movement of a ship in different operating modes, thereby improving the performance of basic maneuvers. This task requires integrating several operating modes, such as maneuvering the ship at low speeds, steering the ship at different speeds in the course or along the trajectory, and stopping the ship on the route. These modes are executed by five component controllers switched on and off by the supervisor depending on the type of operation performed. The desired route, containing the coordinates of waypoints and tasks performed along consecutive segments of the reference trajectory, is obtained by the supervisory system from the system operator. The former supports switching between component controllers and provides them with new set-points after each change in the reference trajectory segment, thereby ensuring stable operation of the entire hybrid switching controller. The study also presents designs of all controller components, which are done using a complex mathematical model of the selected ship, after its simplification depending on the type of controller. The developed control system was tested on the training ship Blue Lady and used to train captains at the Ship Handling Research and Training Center near Iława in Poland. The conducted research involved an automatic movement of the ship from one port to another. The performed transit route required the ship to leave the port, pass the water area, and berth at the port of destination. The study revealed good quality of the designed hybrid controller.

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Hybrid Dynamical Systems

Cited by 469 publications

References 0 publications

Hybrid Framework for Consensus in Directed and Asynchronous Network of Non-Holonomic Agents

Hybrid Framework for Consensus in Directed and Asynchronous Network of Non-Holonomic Agents

Input-to-state stabilizing event-triggered control for linear systems with output quantization

Hybrid Switching Controller Design for the Maneuvering and Transit of a Training Ship

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