Monotone trajectories of differential inclusions and functional differential inclusions with memory

Haddad, Georges

doi:10.1007/bf02762855

Cited by 164 publications

(65 citation statements)

References 11 publications

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“…Consequently, Theorem II-1 of Haddad [6] applies and yields a solution for (15), hence for (12) also.…”

Section: Inclusions With Time-varying Constraintsmentioning

confidence: 87%

“…Since ip -> intTfc(y/(0)) has an open graph (see, for example, Aubin-Cellina [2]), lemma ß of Flytzanis-Papageorgiou [5] implies that y/ -> Gn(t, ip) n intrx(^(0)) is 1.S.C, therefore \p -► GEnß(t, y/) n int 7^(0)) = GE"ß(t, y/) n 7>(^(0)) is l.s.c. Hence according to Lemma 2, we can find g""e : TxJf ^R" a function measurable in t, continuous in ip such that (6) gx<e(t,ip)£Gf(t,y/)nTK(y,(0)) forall(t,ip)£TxX.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Delay Differential Inclusions with Constraints

Hu¹,

Papageorgiou²

1995

Proceedings of the American Mathematical Society

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Abstract. In this paper we examine functional differential inclusions with memory and state constraints. For the case of time-independent state constraints, we show that the solution set is R¿ under Carathéodory conditions on the orientor field. For the case of time-dependent state constraints we prove two existence theorems. For this second case, the question of whether the solution set is R¿ remains open.

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“…Consequently, Theorem II-1 of Haddad [6] applies and yields a solution for (15), hence for (12) also.…”

Section: Inclusions With Time-varying Constraintsmentioning

confidence: 87%

Section: Preliminariesmentioning

confidence: 99%

Delay Differential Inclusions with Constraints

Hu¹,

Papageorgiou²

1995

Proceedings of the American Mathematical Society

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“…(ii) The total number of vehicles for t ≥ 0 is invariant and is equal to V = i v i (0). Proof: To prove (i), it can be checked that all assumptions of Theorem II-1 in [10] for the existence of Filippov solutions to time-delayed differential equations with discontinuous righthand side are satisfied, and the claim follows.…”

Section: A Well-posedness Of Modelmentioning

confidence: 99%

Load Balancing for Mobility-on-Demand Systems

Pavone

Smith

Rus

2011

Robotics: Science and Systems VII

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Abstract-In this paper we develop methods for maximizing the throughput of a mobility-on-demand urban transportation system. We consider a finite group of shared vehicles, located at a set of stations. Users arrive at the stations, pick-up vehicles, and drive (or are driven) to their destination station where they drop-off the vehicle. When some origins and destinations are more popular than others, the system will inevitably become out of balance: Vehicles will build up at some stations, and become depleted at others. We propose a robotic solution to this rebalancing problem that involves empty robotic vehicles autonomously driving between stations.We develop a rebalancing policy that minimizes the number of vehicles performing rebalancing trips. To do this, we utilize a fluid model for the customers and vehicles in the system. The model takes the form of a set of nonlinear time-delay differential equations. We then show that the optimal rebalancing policy can be found as the solution to a linear program. By analyzing the dynamical system model, we show that every station reaches an equilibrium in which there are excess vehicles and no waiting customers. We use this solution to develop a real-time rebalancing policy which can operate in highly variable environments. We verify policy performance in a simulated mobility-on-demand environment with stochastic features found in real-world urban transportation networks.

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“…3 The first theorem in the framework of differential inclusion was defined by Bebernes and Schuur (1970) and Haddad (1981).…”

Section: Some Glimpses Of the Viability Theorymentioning

confidence: 99%