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In this paper, we study the relationship between general maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems, where the control domain is not necessarily convex. The original problem is…
This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve…
This paper examines the question of finding feasible points to discrete-time optimal control problems. The optimization problem of finding a feasible trajectory is transcribed to an unconstrained optimal control problem. An efficient…
With the growing global emphasis on sustainability and the implementation of contemporary environmental policies, photovoltaic (PV) generation is playing an increasingly important role in modern power systems, while its intrinsic…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
Minimizing the peak power consumption and matching demand to supply, under fixed threshold polices, are two key requirements for the success of the future electricity market. In this work, we consider dynamic pricing methods to minimize the…
Demand response (DR) is a cost-effective and environmentally friendly approach for mitigating the uncertainties in renewable energy integration by taking advantage of the flexibility of customers' demands. However, existing DR programs…
For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman's principle of optimality. A wide range of…
The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. Dynamic programming is ubiquitous in control theory, and is also the foundation of reinforcement learning. In this paper,…
This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm,…
Multi stage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management.…
We consider a microgrid where different prosumers exchange energy altogether by the edges of a given network. Each prosumer is located to a node of the network and encompasses energy consumption, energy production and storage capacities…
We prove the dynamic programming principle (DPP) in a class of problems where an agent controls a $d$-dimensional diffusive dynamics via both classical and singular controls and, moreover, is able to terminate the optimisation at a time of…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
Demand response (DR) has been demonstrated to be an effective method for reducing peak load and mitigating uncertainties on both the supply and demand sides of the electricity market. One critical question for DR research is how to…
The growing integration of distributed energy resources (DERs) into the power grid necessitates an effective coordination strategy to maximize their benefits. Acting as an aggregator of DERs, a virtual power plant (VPP) facilitates this…