Data-driven fleet load balancing strategies for shared Mobility-on-Demand systems

Mobility on Demand (MoD) systems utilize shared vehicles to supplement or replace mass transit and private vehicles. Such systems include traditional taxis as well as Transportation Network Companies (TNCs) that offer bike and ride sharing. MoD systems face myriad operational challenges, but this dissertation focuses on the data-driven load balancing problem of redistributing vehicles among service regions. This is a difficult resource reallocation problem because customer demands follow a stochastic process subject to dynamic temporal-spatial patterns. The first half of this dissertation considers the load balancing problem for a bike sharing system in which bikes are redistributed among stations via trucks. The objective is to avoid situations in which a user wishes to rent (return) a bike to a station but cannot because the station is empty (full). First, a station and interval-specific inventory level is defined as a function of station capacity and interval demand rates as observed from analyzed data. Second, using a graph network framework, a receding horizon controller is proposed to determine the optimal paths -- over a short period of time -- for the fleet of trucks to take. When calculating the optimal paths the controller considers the current and projected inventory subject to the dynamically changing rent and return rates for every station in the network. The second half of this dissertation tackles the redistribution of an autonomous taxi fleet in which the vehicles themselves are capable of performing load balancing operations across service regions. The objective is to minimize the fraction of customers whose demands are dropped due to vehicle unavailability as well as the fraction of time the vehicles spend on load balancing operations (i.e driving empty). The system is represented by a queuing model and, as such, dynamic programming can find the optimal solution; however, the state-space of the model grows quickly rendering all but a minuscule system impossible to solve. To this end a parametric control is proposed that uses thresholds to dictate redistribution actions and well performing parameters are found via concurrent estimation methods of simulation

Optimal control approaches for persistent monitoring problems.

Thesis (Ph. D.)--Boston UniversityPersistent monitoring tasks arise when agents must monitor a dynamically changing environment which cannot be fully covered by a stationary team of available agents. It differs from traditional coverage tasks due to the perpetual need to cover a changing environment, i.e., all areas of the mission space must be visited infinitely often. This dissertation presents an optimal control framework for persistent monitoring problems where the objective is to control the movement of multiple cooperating agents to minimize an uncertainty metric in a given mission space. In an one-dimensional mission space, it is shown that the optimal solution is for each agent to move at maximal speed from one switching point to the next, possibly waiting some time at each point before reversing its direction. Thus, the solution is reduced to a simpler parametric optimization problem: determining a sequence of switching locations and associated waiting times at these switching points for each agent. This amounts to a hybrid system which is analyzed using Infinitesimal Perturbation Analysis (IPA) , to obtain a complete on-line solution through a gradient-based algorithm. IPA is a method used to provide unbiased gradient estimates of performance metrics with respect to various controllable parameters in Discrete Event Systems (DES) as well as in Hybrid Systems (HS). It is also shown that the solution is robust with respect to the uncertainty model used, i.e., IPA provides an unbiased estimate of the gradient without any detailed knowledge of how uncertainty affects the mission space. In a two-dimensional mission space, such simple solutions can no longer be derived. An alternative is to optimally assign each agent a linear trajectory, motivated by the one dimensional analysis. It is proved, however, that elliptical trajectories outperform linear ones. With this motivation, the dissertation formulates a parametric optimization problem to determine such trajectories. It is again shown that the problem can be solved using IPA to obtain performance gradients on line and obtain a complete and scalable solution. Since the solutions obtained are generally locally optimal, a stochastic comparison algorithm is incorporated for deriving globally optimal elliptical trajectories. The dissertation also approaches the problem by representing an agent trajectory in terms of general function families characterized by a set of parameters to be optimized. The approach is applied to the family of Lissajous functions as well as a Fourier series representation of an agent trajectory. Numerical examples indicate that this scalable approach provides solutions that are near optimal relative to those obtained through a computationally intensive two point boundary value problem (TPBVP) solver. In the end, the problem is tackled using centralized and decentralized Receding Horizon Control (RHC) algorithms, which dynamically determine the control for agents by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon

An event-driven approach to control and optimization of multi-agent systems

This dissertation studies the application of several event-driven control schemes in multi-agent systems. First, a new cooperative receding horizon (CRH) controller is designed and applied to a class of maximum reward collection problems. Target rewards are time-variant with finite deadlines and the environment contains uncertainties. The new methodology adapts an event-driven approach by optimizing the control for a planning horizon and updating it for a shorter action horizon. The proposed CRH controller addresses several issues including potential instabilities and oscillations. It also improves the estimated reward-to-go which enhances the overall performance of the controller. The other major contribution is that the originally infinite-dimensional feasible control set is reduced to a finite set at each time step which improves the computational cost of the controller. Second, a new event-driven methodology is studied for trajectory planning in multi-agent systems. A rigorous optimal control solution is employed using numerical solutions which turn out to be computationally infeasible in real time applications. The problem is then parameterized using several families of parametric trajectories. The solution to the parametric optimization relies on an unbiased estimate of the objective function's gradient obtained by the "Infinitesimal Perturbation Analysis" method. The premise of event-driven methods is that the events involved are observable so as to "excite" the underlying event-driven controller. However, it is not always obvious that these events actually take place under every feasible control in which case the controller may be useless. This issue of event excitation, which arises specially in multi-agent systems with a finite number of targets, is studied and addressed by introducing a novel performance measure which generates a potential field over the mission space. The effect of the new performance metric is demonstrated through simulation and analytical results

An event-driven approach to control and optimization of multi-agent systems

This dissertation studies the application of several event-driven control schemes in multi-agent systems. First, a new cooperative receding horizon (CRH) controller is designed and applied to a class of maximum reward collection problems. Target rewards are time-variant with finite deadlines and the environment contains uncertainties. The new methodology adapts an event-driven approach by optimizing the control for a planning horizon and updating it for a shorter action horizon. The proposed CRH controller addresses several issues including potential instabilities and oscillations. It also improves the estimated reward-to-go which enhances the overall performance of the controller. The other major contribution is that the originally infinite-dimensional feasible control set is reduced to a finite set at each time step which improves the computational cost of the controller. Second, a new event-driven methodology is studied for trajectory planning in multi-agent systems. A rigorous optimal control solution is employed using numerical solutions which turn out to be computationally infeasible in real time applications. The problem is then parameterized using several families of parametric trajectories. The solution to the parametric optimization relies on an unbiased estimate of the objective function's gradient obtained by the "Infinitesimal Perturbation Analysis" method. The premise of event-driven methods is that the events involved are observable so as to "excite" the underlying event-driven controller. However, it is not always obvious that these events actually take place under every feasible control in which case the controller may be useless. This issue of event excitation, which arises specially in multi-agent systems with a finite number of targets, is studied and addressed by introducing a novel performance measure which generates a potential field over the mission space. The effect of the new performance metric is demonstrated through simulation and analytical results

Receding Horizon based Cooperative Vehicle Control with Optimal Task Allocation

The problem of cooperative multi-target interception in an uncertain environment is investigated in this thesis. The targets arrive in the mission space sequentially at a priori unknown time instants and a priori unknown locations, and then move on a priori unknown trajectories. A group of vehicles with known dynamics are employed to visit the targets as quickly and efficiently as possible. To this end, a time-discounting reward is defined for each target which can be collected only if one of the vehicles visits that target. A cooperative receding horizon scheme is designed, which predicts the future positions of the targets and maximizes the estimate of the expected total collectible rewards, accordingly. The problem is initially investigated for the case when there are a finite number of targets arriving in the mission space sequentially. It is shown that the number of targets that are not visited by any vehicle in the mission space will be sufficiently small if the targets arrive sufficiently infrequently. The problem is then generalized to the case of infinite number of targets and a finite-time convergence analysis is also presented. A more practical case where the vehicles have limited sensing and communication ranges is also investigated using a game-theoretic approach. The problem is then solved for the case when a cluster of vehicles is required to visit each target. Simulations confirm the efficacy of the proposed strategies