Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)

Chai, Jun; Sanfelice, Ricardo G.

doi:10.1109/tac.2018.2882158

Cited by 42 publications

(107 citation statements)

References 30 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…The mild regularity conditions satisfied by the hybrid system (18), as in the next lemma, guarantee the applicability of many results in the proof of our main result. Lemma 5: The hybrid system with data (F, F, J , J) satisfies the hybrid basic conditions in [15, Ass.…”

Section: Resultssupporting

confidence: 57%

“…3.3], and solutions are complete. Finally, we anticipate here a straightforward corollary of completeness and Lemma 7 below: since the number of jumps is finite by Lemma 7, all maximal solutions to (18) are actually complete in the ordinary time direction. Now, we will prove item ii) in two steps.…”

Section: A Proof Of Theoremmentioning

confidence: 91%

“…Therefore, all maximal solutions do not have finite escape times. By [18,Thm. 4.3] again, the set K is actually forward invariant [18,Def.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

“…By [18,Thm. 4.3] again, the set K is actually forward invariant [18,Def. 3.3], and solutions are complete.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

“…First, we prove in the following Lemma 6 that the set A is globally asymptotically stable for the system without jumps. To this end, the jumpless system has data H 0 = (F, F, ∅, ∅) with flow map F and flow set F defined in (18). We emphasize that H 0 is obtained in accordance to [19,Eqq. (38)-(39)] by identifying all jumps with events.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

See 4 more Smart Citations

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

Berkane

Bisoffi

Dimarogonas

2019

2019 18th European Control Conference (ECC)

View full text Add to dashboard Cite

For a vehicle moving in an n-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.

show abstract

Section: Resultssupporting

confidence: 57%

Section: A Proof Of Theoremmentioning

confidence: 91%

“…Therefore, all maximal solutions do not have finite escape times. By [18,Thm. 4.3] again, the set K is actually forward invariant [18,Def.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

“…By [18,Thm. 4.3] again, the set K is actually forward invariant [18,Def. 3.3], and solutions are complete.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

Section: A Proof Of Theoremmentioning

confidence: 99%

See 3 more Smart Citations

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

Berkane

Bisoffi

Dimarogonas

2019

2019 18th European Control Conference (ECC)

View full text Add to dashboard Cite

show abstract

Set‐invariance‐based interpretations for the L₁ performance of nonlinear systems with non‐unique solutions

Choi

Kim

2022

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article is concerned with tackling the L1$$ {L}_1 $$ performance analysis problem of continuous and piecewise continuous nonlinear systems with non‐unique solutions by using the involved arguments of set‐invariance principles. More precisely, this article derives a sufficient condition for the L1$$ {L}_1 $$ performance of continuous nonlinear systems in terms of the invariant set. With respect to the case such that solving a nonlinear differential equation is difficult and thus an employment of the invariant set‐based sufficient condition is a non‐trivial task, we also derive another sufficient condition through the extended invariance domain approach. Because this extended approach characterizes set‐invariance properties in terms of the corresponding vector field and an extended version of contingent cones, the L1$$ {L}_1 $$ performance analysis problem could be solved without considering both the explicit solutions for the differential equation and the relevant solution uniqueness. These arguments associated with the L1$$ {L}_1 $$ performance of continuous systems are further extended to the involved case of piecewise continuous nonlinear systems, and we establish parallel results relevant to the set‐invariance principles obtained for the continuous nonlinear systems. Finally, numerical examples are provided to demonstrate the effectiveness as well as the applicability of the overall results derived in this article.

show abstract

A hybrid observer for linear systems under delayed sporadic measurements

Guarro,

Ferrante,

Sanfelice

2024

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

SummaryThis paper proposes a hybrid observer for state estimation over a network. The network provides delayed measurements of the output of the plant at time instants that are not necessarily periodic and are accompanied by timestamps provided by a clock that synchronizes with the clock of the observer in finite time. The proposed observer, along with the plant and communication network, are modeled by a hybrid dynamical system that has two timers, a logic variable, and two memory states to capture the mechanisms involved in the events associated with sampling and arrival of information, as well as the logic in the estimation algorithm. The hybrid model also includes a generic clock synchronization scheme to cope with a mismatch between the clocks at the plant and the observer. Convergence properties of the estimation error of the system are shown analytically and supported by numerical examples.

show abstract

Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)

Cited by 42 publications

References 30 publications

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

Set‐invariance‐based interpretations for the L₁ performance of nonlinear systems with non‐unique solutions

A hybrid observer for linear systems under delayed sporadic measurements

Contact Info

Product

Resources

About

Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)

Cited by 42 publications

References 30 publications

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

A Hybrid Controller for Obstacle Avoidance in an $n$-dimensional Euclidean Space

Set‐invariance‐based interpretations for the L1 performance of nonlinear systems with non‐unique solutions

A hybrid observer for linear systems under delayed sporadic measurements

Contact Info

Product

Resources

About

Set‐invariance‐based interpretations for the L₁ performance of nonlinear systems with non‐unique solutions