Fixed Horizon Control Research Articles

Dispatch-aware planning for feasible power system operation

Maintaining stable energy production with increasing penetration of variable renewable energy requires sufficient flexible generation resources and dispatch algorithms that accommodate renewables’ uncertainty. In this work, we study the feasibility properties of real-time economic dispatch (RTED) algorithms and establish fundamental limits on their performance. We propose a joint methodology for resource procurement and online economic dispatch with guaranteed feasibility. Our algorithm, Feasible Fixed Horizon Control (FFHC) is a regularized form of Receding Horizon Control (RHC) that balances exploitation of good near-term demand predictions with feasibility requirements. Empirical evaluation of FFHC in comparison to the standard RHC on realistic load profiles highlights that FFHC achieves near-optimal performance while ensuring feasibility in high-ramp scenarios where RHC becomes infeasible. • Increasing variability of net demand requires dispatch-aware power system planning. • Offline planning is insufficient to ensure online dispatch feasibility. • Feasible planning algorithm uses affine feedback policies to approximate dispatch. • Online economic dispatch algorithm adapts standard receding horizon control. • Joint algorithm achieves guaranteed feasibility with near-optimal dispatch efficiency.

Online Optimization with Predictions and Non-convex Losses

We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be nonconvex, while incurring a movement cost when changing actions between rounds. We ask: under what general conditions is it possible for an online learner to leverage predictions of future cost functions in order to achieve near-optimal costs? Prior work has provided nearoptimal online algorithms for specific combinations of assumptions about hitting and switching costs, but no general results are known. In this work, we give two general sufficient conditions that specify a relationship between the hitting and movement costs which guarantees that a new algorithm, Synchronized Fixed Horizon Control (SFHC), achieves a 1 + O(1/w) competitive ratio, where w is the number of predictions available to the learner. Our conditions do not require the cost functions to be convex, and we also derive competitive ratio results for non-convex hitting and movement costs. Our results provide the first constant, dimension-free competitive ratio for online non-convex optimization with movement costs. We also give an example of a natural problem, Convex Body Chasing (CBC), where the sufficient conditions are not satisfied and prove that no online algorithm can have a competitive ratio that converges to 1.

Online Optimization with Predictions and Non-convex Losses

We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be non-convex, while incurring a movement cost when changing actions between rounds. We ask:under what general conditions is it possible for an online learner to leverage predictions of future cost functions in order to achieve near-optimal costs? Prior work has provided near-optimal online algorithms for specific combinations of assumptions about hitting and switching costs, but no general results are known. In this work, we give two general sufficient conditions that specify a relationship between the hitting and movement costs which guarantees that a new algorithm, Synchronized Fixed Horizon Control (SFHC), achieves a 1+O(1/w) competitive ratio, where w is the number of predictions available to the learner. Our conditions do not require the cost functions to be convex, and we also derive competitive ratio results for non-convex hitting and movement costs. Our results provide the first constant, dimension-free competitive ratio for online non-convex optimization with movement costs. We also give an example of a natural problem, Convex Body Chasing (CBC), where the sufficient conditions are not satisfied and prove that no online algorithm can have a competitive ratio that converges to 1.

Distributed Online Energy Management in Interconnected Microgrids

In this article, a hierarchical online distributed algorithm (HODA) is developed to achieve optimal energy management in interconnected microgrids (IMG). The energy management objectives include maximizing users' utility, optimizing the output power of controllable generators, and keeping the system operating in an economic manner. We formulate the problem as an online least absolute shrinkage and selection operator (LASSO) problem, considering both reactive power and system operation characteristics. We then employ averaging fixed horizon control (AFHC) to solve the formulated problem under some mild assumptions on the uncertainties in renewable power generation and load demand. The alternating direction method of multipliers (ADMM) is adopted to decouple the coupled constraints. The proposed online algorithm is asymptotically optimal, since its solution converges to the offline optimal solution. The performance of the proposed algorithm is validated using data traces obtained from a real-world IMG system.

Cost-Minimizing Online Algorithms for Geo-Distributed Data Analytics

Modern enterprises often manage geographically distributed datacenters around the globe. In such environment, datasets are naturally collected and stored in different data centers and were later queried for complex analytics. In this paper, we study the Wide-Area Data Analytics problem, which aims to efficiently control data movements and achieve low latency for overall queries processing, both constrained by limited and expensive network resources across datacenters. Previous papers focus on offline settings of single analytical queries and do not consider time in optimizing system performance, and therefore ignores the dynamics of data and task placement in terms of inter-DC bandwidth utilization. In this paper, we consider the online setting and formulate a cost-minimizing optimization problem over time for arbitrary Directed Acyclic Graph query processing. Considering dynamics of network resource usage, we developed two online algorithms, Online Switch Resist (OSR) and Most Fixed Horizon Control (MFHC) with good competitive ratios. We performed extensive simulations and comparative studies using the TPC-CH benchmark and verified the efficacy of proposed algorithms. The algorithm we proposed is better than the existing algorithm, and its performance approximates the theoretical optimal value.

Optimizing Stored Video Delivery for Wireless Networks: The Value of Knowing the Future

This paper considers the design of cross-layer opportunistic transport protocols for stored video over wireless networks with a slow varying (average) capacity. We focus on two key principles: 1) scheduling data transmissions when capacity is high; and 2) exploiting knowledge of future capacity variations. The latter is possible when users’ mobility is known or predictable, for example, users riding on public transportation or using navigation systems. We consider the design of cross-layer transmission schedules, which minimize system utilization (and, thus, possibly transmit/receive energy) while avoiding, if at all possible, rebuffering/delays in several scenarios. For the single-user anticipative case where all future capacity variations are known beforehand, we establish the optimal transmission schedule in a generalized piecewise constant thresholding (GPCT) scheme. For the single-user partially anticipative case where only a finite window of future capacity variations is known, we propose an online greedy fixed horizon control (GFHC). An upper bound on the competitive ratio of GFHC and GPCT is established showing how performance loss depends on the window size, receiver playback buffer, and capacity variability. We also consider the multiuser case where one can exploit both future temporal and multiuser diversity. Finally, we investigate the impact of uncertainty in knowledge of future capacity variations, and propose an offline approach as well as an online algorithm to deal with such uncertainty. Our simulations and evaluation based on a measured wireless capacity trace exhibit robust potential gains for our proposed transmission schemes.

An Efficient Online Algorithm for Dynamic SDN Controller Assignment in Data Center Networks

Software defined networking is increasingly prevalent in data center networks for it enables centralized network configuration and management. However, since switches are statically assigned to controllers and controllers are statically provisioned, traffic dynamics may cause long response time and incur high maintenance cost. To address these issues, we formulate the dynamic controller assignment problem (DCAP) as an online optimization to minimize the total cost caused by response time and maintenance on the cluster of controllers. By applying the randomized fixed horizon control framework, we decompose DCAP into a series of stable matching problems with transfers, guaranteeing a small loss in competitive ratio. Since the matching problem is NP-hard, we propose a hierarchical two-phase algorithm that integrates key concepts from both matching theory and coalitional games to solve it efficiently. Theoretical analysis proves that our algorithm converges to a near-optimal Nash stable solution within tens of iterations. Extensive simulations show that our online approach reduces total cost by about 46%, and achieves better load balancing among controllers compared with static assignment.

Using Predictions in Online Optimization

We consider online convex optimization (OCO) problems with switching costs and noisy predictions. While the design of online algorithms for OCO problems has received considerable attention, the design of algorithms in the context of noisy predictions is largely open. To this point, two promising algorithms have been proposed: Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC). The comparison of these policies is largely open. AFHC has been shown to provide better worst-case performance, while RHC outperforms AFHC in many realistic settings. In this paper, we introduce a new class of policies, Committed Horizon Control (CHC), that generalizes both RHC and AFHC. We provide average-case analysis and concentration results for CHC policies, yielding the first analysis of RHC for OCO problems with noisy predictions. Further, we provide explicit results characterizing the optimal CHC policy as a function of properties of the prediction noise, e.g., variance and correlation structure. Our results provide a characterization of when AFHC outperforms RHC and vice versa, as well as when other CHC policies outperform both RHC and AFHC.

Online Convex Optimization Using Predictions

Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. We prove that achieving sublinear regret and constant competitive ratio for online algorithms requires the use of an unbounded prediction window in adversarial settings, but that under more realistic stochastic prediction error models it is possible to use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant-sized prediction window. Furthermore, we show that the performance of AFHC is tightly concentrated around its mean.

Moving Big Data to The Cloud: An Online Cost-Minimizing Approach

Cloud computing, rapidly emerging as a new computation paradigm, provides agile and scalable resource access in a utility-like fashion, especially for the processing of big data. An important open issue here is to efficiently move the data, from different geographical locations over time, into a cloud for effective processing. The de facto approach of hard drive shipping is not flexible or secure. This work studies timely, cost-minimizing upload of massive, dynamically-generated, geo-dispersed data into the cloud, for processing using a MapReduce-like framework. Targeting at a cloud encompassing disparate data centers, we model a cost-minimizing data migration problem, and propose two online algorithms: an online lazy migration (OLM) algorithm and a randomized fixed horizon control (RFHC) algorithm , for optimizing at any given time the choice of the data center for data aggregation and processing, as well as the routes for transmitting data there. Careful comparisons among these online and offline algorithms in realistic settings are conducted through extensive experiments, which demonstrate close-to-offline-optimum performance of the online algorithms.