Distributed Approaches For Finite-horizon Resource Allocation And Their Applications

Finite-horizon resource allocation investigates how to allocate available resources to system nodes(e.g.,agents,sensors and computing cells)on multiple continuous time units,so as to meet the resource demand of the node and minimize the costs of the system within the resource allocation period.Compared with the traditional resource allocation problem,it focuses on the resource allocation process in a finite time horizon,in which the coupling constraints of the node state variables among the time units are considered and the real-time allocation of multiple resources in parallel can be realized.It is of both theoretical significance and practical value for application scenarios where the resource allocation process changes over time.Taking into account the heterogeneity of large-scale network nodes and the complexity of communication links,it is a significant challenge to solve the finite-horizon resource allocation problem in a fully distributed manner.Firstly,with the heterogeneity of the nodes resulting a directed and unbalanced communication topology considered,this paper explores the finite-horizon resource allocation problem under directed time-invariant topology,and proposes a fully distributed algorithm to solve it.The cost function of the node takes the quadratic form and the objective is to minimize the total cost of all nodes within the finite time horizon,while enforcing a total amount of resources per time unit and per node.The main difficulty of this problem lies in the coupled equality constraints across the nodes and time units,which should be satisfied simultaneously in the end.This paper develops a distributed surplus-based method to solve the problem in which the multipliers are iterated in an alternating way.By taking the techniques of matrix perturbation and system eigenvalues analysis,we show that the convergence and optimality of the proposed method can be ensured provided that the digraph within the time horizon is strongly connected.Secondly,with the disturbance of communication link leading to the decrease of channel transmission efficiency or node failure taken into account,a novel distributed algorithm is proposed to solve the finite-horizon resource allocation problem with a time-varying switching topology.Compared with the finite-horizon resource allocation problem under directed time-invariant topology,the network constraint condition of this problem is more complex,and the objective function of the node is a convex function,which is more general than the quadratic form.The major difficulty of this problem is the local asymmetric and time-varing structure imposed by the switching topology within the time horizon should be taken into account when solving the problem.This paper proposes a distributed non-negative surplus-based method to solve the problem,in which the penalty term is added to the objective function to decouple the equality constraints across the nodes and time units.The concept of virtual node is introduced to facilitate the design of the distributed algorithm,and the convergence of the algorithm is analyzed by functional monotonicity analysis.We show that the optimality of the proposed method can be ensured when the time-varying digraph within the time horizon is joint strongly connected.Finally,this paper applies the distributed finite-horizon resource allocation algorithm to multi-period coordinated energy dispatch for a number of electric vehicles(EVs).The optimal energy scheduling of EVs investigates how to optimally distribute the power to a number of EVs from the grid,or how to feed the stored power back to the grid from the EVs.In this paper,the multi-period coordinated dispatching process of EVs is described through a multi-objective optimization model,and the idea of moving horizon optimization is introduced to solve the random access and departure cases of EV owners.To simultaneously optimize the power load response curve and reduce the costs of the owner,this paper develops a hierarchical optimal algorithm achieving a win-win for the supply and demand side of the power grid.The effectiveness of the proposed algorithms are verified by numerical simulations in each chapter...