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We develop a new algorithm for scheduling the charging process of a large number of electric vehicles (EVs) over a finite horizon. We assume that EVs arrive at the charging stations with different charge levels and different flexibility windows. The arrival process is assumed to have a known distribution and that the charging process of EVs can be preemptive. We pose the scheduling problem as a dynamic program with constraints. We show that the resulting formulation leads to a monotone dynamic program with Lipschitz continuous value functions that are robust against perturbation of system parameters. We propose a simulation based fitted value iteration algorithm to determine the value function approximately, and derive the sample complexity for computing the approximately optimal solution., Comment: 21 pages, submitted to SEGAN

A wide variety of real life complex networks are prohibitively large for modeling, analysis and control. Understanding the structure and dynamics of such networks entails creating a smaller representative network that preserves its relevant topological and dynamical properties. While modern machine learning methods have enabled identification of governing laws for complex dynamical systems, their inability to produce white-box models with sufficient physical interpretation renders such methods undesirable to domain experts. In this paper, we introduce a hybrid black-box, white-box approach for the sparse identification of the governing laws for complex, highly coupled dynamical systems with particular emphasis on finding the influential reactions in chemical reaction networks for combustion applications, using a data-driven sparse-learning technique. The proposed approach identifies a set of influential reactions using species concentrations and reaction rates,with minimal computational cost without requiring additional data or simulations. The new approach is applied to analyze the combustion chemistry of H2 and C3H8 in a constant-volume homogeneous reactor. The influential reactions determined by the sparse-learning method are consistent with the current kinetics knowledge of chemical mechanisms. Additionally, we show that a reduced version of the parent mechanism can be generated as a combination of the significantly reduced influential reactions identified at different times and conditions and that for both H2 and C3H8 fuel, the reduced mechanisms perform closely to the parent mechanisms as a function of the ignition delay time over a wide range of conditions. Our results demonstrate the potential of the sparse-learning approach as an effective and efficient tool for dynamical system analysis and reduction. The uniqueness of this approach as applied to combustion systems lies in the ability to identify influential reactions in specified conditions and times during the evolution of the combustion process. This ability is of great interest to understand chemical reaction systems.

Chemical kinetic mechanisms can be represented by sets of elementary reactions that are easily translated into mathematical terms using physicochemical relationships. The schematic representation of reactions captures the interactions between reacting species and products. Determining the minimal chemical interactions underlying the dynamic behavior of systems is a major task. In this paper, we introduce a novel approach for the identification of the influential reactions in chemical reaction networks for combustion applications, using a data-driven sparse-learning technique. The proposed approach identifies a set of influential reactions using species concentrations and reaction rates, with minimal computational cost without requiring additional data or simulations. The new approach is applied to analyze the combustion chemistry of H2 and C3H8 in a constant-volume homogeneous reactor. The influential reactions identified by the sparse-learning method are consistent with the current kinetics knowledge of chemical mechanisms. Additionally, we show that a reduced version of the parent mechanism can be generated as a combination of the influential reactions identified at different times and conditions and that for both H2 and C3H8 this reduced mechanism performs closely to the parent mechanism as a function of ignition delay over a wide range of conditions. Our results demonstrate the potential of the sparse-learning approach as an effective and efficient tool for mechanism analysis and mechanism reduction.

In this paper, we propose an optimization-based sparse learning approach to identify the set of most influential reactions in a chemical reaction network. This reduced set of reactions is then employed to construct a reduced chemical reaction mechanism, which is relevant to chemical interaction network modeling. The problem of identifying influential reactions is first formulated as a mixed-integer quadratic program, and then a relaxation method is leveraged to reduce the computational complexity of our approach. Qualitative and quantitative validation of the sparse encoding approach demonstrates that the model captures important network structural properties with moderate computational load., Comment: The paper is presented at NIPS workshop on Advances in Modeling and Learning Interactions from Complex Data

This paper presents an anomaly detection method using a hybrid observer -- which consists of a discrete state observer and a continuous state observer. We focus our attention on anomalies caused by intelligent attacks, which may bypass existing anomaly detection methods because neither the event sequence nor the observed residuals appear to be anomalous. Based on the relation between the continuous and discrete variables, we define three conflict types and give the conditions under which the detection of the anomalies is guaranteed. We call this method conflict-driven anomaly detection. The effectiveness of this method is demonstrated mathematically and illustrated on a Train-Gate (TG) system.

This paper considers the problem of fault detection and isolation (FDI) for switched affine models. We first study the model invalidation problem and its application to guaranteed fault detection. Novel and intuitive optimization-based formulations are proposed for model invalidation and T-distinguishability problems, which we demonstrate to be computationally more efficient than an earlier formulation that required a complicated change of variables. Moreover, we introduce a distinguishability index as a measure of separation between the system and fault models, which offers a practical method for finding the smallest receding time horizon that is required for fault detection, and for finding potential design recommendations for ensuring T-distinguishability. Then, we extend our fault detection guarantees to the problem of fault isolation with multiple fault models, i.e., the identification of the type and location of faults, by introducing the concept of I-isolability. An efficient way to implement the FDI scheme is also proposed, whose run-time does not grow with the number of fault models that are considered. Moreover, we derive bounds on detection and isolation delays and present an adaptive scheme for reducing isolation delays. Finally, the effectiveness of the proposed method is illustrated using several examples, including an HVAC system model with multiple faults., Comment: This material is copyrighted by IEEE and will appear in IEEE Conference on Decision and Control, 2017

This paper considers the optimal design of input signals for the purpose of discriminating among a finite number of affine models with uncontrolled inputs and noise. Each affine model represents a different system operating mode, corresponding to unobserved intents of other drivers or robots, or to fault types or attack strategies, etc. The input design problem aims to find optimal separating/discriminating (controlled) inputs such that the output trajectories of all the affine models are guaranteed to be distinguishable from each other, despite uncertainty in the initial condition and uncontrolled inputs as well as the presence of process and measurement noise. We propose a novel formulation to solve this problem, with an emphasis on guarantees for model discrimination and optimality, in contrast to a previously proposed conservative formulation using robust optimization. This new formulation can be recast as a bilevel optimization problem and further reformulated as a mixed-integer linear program (MILP). Moreover, our fairly general problem setting allows the incorporation of objectives and/or responsibilities among rational agents. For instance, each driver has to obey traffic rules, while simultaneously optimizing for safety, comfort and energy efficiency. Finally, we demonstrate the effectiveness of our approach for identifying the intention of other vehicles in several driving scenarios.

The participation of renewable energy sources in energy markets is challenging, mainly because of the uncertainty associated with the renewables. Aggregation of renewable energy suppliers is shown to be very effective in decreasing this uncertainty. In the present paper, we propose a cost sharing mechanism that entices the suppliers of wind, solar and other renewable resources to form or join an aggregate. In particular, we consider the effect of a bonus for surplus in supply, which is neglected in previous work. We introduce a specific proportional cost sharing mechanism, which satisfies the desired properties of such mechanisms that are introduced in the literature, e.g., budget balancedness, ex-post individual rationality and fairness. In addition, we show that the proposed mechanism results in a stable market outcome. Finally, the results of the paper are illustrated by numerical examples.

This paper presents a sound and complete fault detection approach for cyber-physical systems represented by hidden-mode switched affine models with time varying parametric uncertainty. The fault detection approach builds upon techniques from model invalidation. In particular, a set-membership approach is taken where the noisy input-output data is compared to the set of behaviors of a nominal model. As we show, this set-membership check can be reduced to the feasibility of a mixed-integer linear programming (MILP) problem, which can be solved efficiently by leveraging the state-of-the-art MILP solvers. In the second part of the paper, given a system model and a fault model, the concept of T-detectability is introduced. If a pair of system and fault models satisfies T-detectability property for a finite T, this allows the model invalidation algorithm to be implemented in a receding horizon manner, without compromising detection guarantees. In addition, the concept of weak-detectability is introduced which extends the proposed approach to a more expressive class of fault models that capture language constraints on the mode sequences. Finally, the efficiency of the approach is illustrated with numerical examples motivated by smart building radiant systems., Comment: This paper will appear in IFAC Automatica, Elsevier