Balancing the size of vehicle fleet and the quality of transportation service is important yet challenging for urban transportation systems. This paper studies the optimal fleet selection problem in dial-a-ride regime. To achieve this, a two-stage mixed-integer programming formulation is presented. It is demonstrated that there exists an optimal vehicle set provided that the considered dial-a-ride problem is weakly solvable. The strong solvability problem is also discussed by introducing a discount factor to strike a trade-off between the fleet size and routing cost associated. When the probability measure of the vehicle set is unavailable, the Wasserstein measure, anchored by an empirical distribution derived from training data, is used for approximation. It is revealed that a nontrivial duality gap exists, leading to an infeasibility of the Lagrangian argument employed in the distributionally robust framework that transforms an infinite stochastic program into a finite alternative. By employing a robust primal decomposition method, it is shown that the relaxed version of the considered program is equivalent to a finite-dimensional quadratic conic program. Subsequently, a set of disjunctions is constructed to extract the optimizer with a finite number of iterations. Furthermore, the “distance” between the empirical and true vehicle sets is discussed as well. Finally, the benchmark data is carried out to illustrate the theoretical justification and significance of the proposed method.

In this paper, we study the package delivery problem where the transportation tasks, including arriving at the delivery locations and returning to the depots, are required to be completed within a time window. To this end, a time-homogeneous preset-time algorithm is presented to coordinate multiple vehicles within an identical time window, where arrival time delays are used to characterize the arrival time of the vehicles. Consequently, the considered package delivery problem is formulated by two phases: “Active phase” and “Sleeping phase”, over which vehicles use the neighboring information to achieve coordination. For the proposed algorithm, we use Lyapunov based method to derive condition guaranteeing the coordination of vehicles, under a very mild communication topology condition. As an extension, a time-heterogeneous preset-time algorithm is designed. We demonstrate that coordination among vehicles is determined by the maximal preset-time. Built upon this observation, we further show that there is an equivalence between the proposed formulation and the dynamical equation of the interacting vehicles. Finally, a numerical example for a package delivery problem, comprised of two coordination phases, is carried out to illustrate the proposed preset-time coordination formulation, and the time-heterogeneous case is further discussed as well.

This article addresses the differential privacy problem for second-order multiagent systems (MASs) over signed digraph. To this end, both position and velocity states are disturbed by Laplacian noise. As for structurally balanced case, necessary and sufficient conditions for almost sure bipartite consensus are presented, upon which an$\epsilon$-differential privacy algorithm is designed. Along with the devised setup, the tradeoff between system performance and degree of privacy protection is discussed, and the optimal noise is elaborated as well. The proposed privacy preserving scheme is further extended to the case with structurally unbalanced graph, and criteria for almost sure stability or interval bipartite consensus are induced. Finally, numerical simulations and the application to power systems show the effectiveness of the theoretical findings as well as the developed privacy scheme.

Of particular interest in this paper is to study the active synchronization (act-synchronization) problem for double-integrator network systems without velocity information. To this end, scaling parameters are suggested to quantify the degree of act-synchronization for different agents. And weighted gains are employed to assure that there is a simple zero eigenvalue with the other ones sharing positive real parts. An auxiliary variable is introduced to mitigate the unavailability on velocity information. Thus only the directed spanning tree requirement in the content of algebraic graph theory is required. This exhibits a clear distinction from signed-graph or scaled consensus as non-unitary signs for scaling parameter and weighted gain are allowed. It is shown that the condition for act-synchronization is related to weighted gain, scaling parameter, the real and imaginary parts of the involved eigenvalues. With the constraint on identical weighted gain and scaling parameter for position and auxiliary variables, it is proven that act-synchronization can be exponentially guaranteed using the Lyapunov-based technique. Finally, the multiple unmanned ground vehicles system and the 10-generator in IEEE 39-bus system are given to facilitate the proposed configuration and the theoretical findings.

In this article, we study the consensus problem in the framework of networked multiagent systems with constraint where there exists antagonistic information. A major difficulty is how to characterize the communication among the interacting agents in the presence of antagonistic information without resorting to the signed graph theory, which plays a central role in the Altafini model. It is shown that the proposed control protocol enables us to solve the consensus problem in a node-based viewpoint where both cooperative and antagonistic interactions coexist. Moreover, the proposed setup is further extended to the case of input saturation, leading to the semiglobal consensus. In addition, the consensus region associated with antagonistic information among participating individuals is also elaborated. Finally, the deduced theoretical results are applied to the task distribution problem via unmanned ground vehicles.

This article studies the consensus problem of multiagent systems (MASs) subject to Denial-of-Service (DoS) attacks from the perspective of control. The considered DoS attacks blocking the information exchange in the group of agents pose limitations on the frequency and the duration of them. A distributed observer-based controller is proposed to reconstruct the states of the agents. We prove that MASs under DoS attacks can still achieve consensus by the proposed controller. The scenario where DoS attacks simultaneously jam both the communication networks associated with the controller and the observer is also addressed, and a sufficient condition is obtained to maintain the consensus performance of MASs. Finally, numerical simulations are provided to illustrate the theoretical results.

This article is dedicated to the consensus problem for interacting agents of the double-integrator dynamics subject to antagonistic reciprocity, described by negative scalar parameters. To this end, we first show the existence of the weighted gains which play an essential role for solving the consensus problem. Then, we establish the relationship between the weighted gains and scalar parameters to guarantee that the underlying "Laplacian" matrix contains a simple zero eigenvalue and the remaining eigenvalues enjoy positive real parts. Based on the above analysis, we further proceed to solve the considered problem. A major difficulty is that the Laplacian matrices, associated with the position and velocity information, are entirely distinct from each other, leading to the failure of the conventional consensus method for the second-order dynamics. We derive some criteria involving the weighted gains, the scaling parameters, and the real/image parts of the Laplacian matrix of the interaction graph. Moreover, some special frameworks, which have been extensively studied in the literature, are also elaborated on. Compared with the Altafini's model, we do not need to redefine a new Laplacian matrix, and more important, the restriction on the digon sign-symmetry property is removed. It is worth mentioning that the proposed consensus algorithm cannot be deduced by the Altafini's model or its variants. Finally, a wheeled multirobot system is formulated to validate the efficiency of the theoretical results.