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With the increasing prevalence of variable-supply electricity production, dynamic market structures, including time-varying prices and/or peak demand charges are becoming more common for electricity consumers. This framework requires consumers to consider both the time-varying amount of electricity (i.e., energy) consumed throughout the day as well as the maximum rate of electricity purchase (i.e., power) over a given period, typically a month. Because of this complexity, online optimization techniques such as economic model predictive control (MPC) are a natural tool for consumers to use to minimize cost. However, while closed-loop optimization of these pricing structures is already being proposed for various applications, little has been established about stability or performance properties of the closed-loop system. Due in particular to the peak penalty (which violates the principle of optimality if naively included in the objective function), this theoretical gap leaves the potential for pathological closed-loop behavior despite high-quality open-loop solutions. In this paper, we derive asymptotic performance and stability results for general time-varying economic MPC. We then present a novel extended-state formulation to convert peak demand charges into a time-varying stage cost that can be optimized using economic MPC. In addition, we give a terminal cost and constraint for the augmented system that avoids reducing the feasible set in the original space. Finally, we demonstrate these structures and the closed-loop properties that they satisfy via two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper investigates distributed control and incentive mechanisms to coordinate distributed energy resources (DERs) with both continuous and discrete decision variables as well as device dynamics in distribution grids. We formulate a multiperiod social welfare maximization problem, and based on its convex relaxation propose a distributed stochastic dual gradient algorithm for managing DERs. We further extend it to an online real-time setting with time-varying operating conditions, asynchronous updates by devices, and feedback being leveraged to account for nonlinear power flows as well as reduce communication overhead. The resulting algorithm provides a general online stochastic optimization algorithm for coordinating networked DERs with discrete power setpoints and dynamics to meet operational and economic objectives and constraints. We characterize the convergence of the algorithm analytically and evaluate its performance numerically. [ABSTRACT FROM AUTHOR]

In recent years, data have played an increasingly important role in the economy as a good in its own right. In many settings, data aggregators cannot directly verify the quality of the data they purchase, nor the effort exerted by data sources when creating the data. Recent work has explored mechanisms to ensure that the data sources share high-quality data with a single data aggregator, addressing the issue of moral hazard. Oftentimes, there is a unique, socially efficient solution. In this paper, we consider data markets where there is more than one data aggregator. Since data can be cheaply reproduced and transmitted once created, data sources may share the same data with more than one aggregator, leading to free-riding between data aggregators. This coupling can lead to nonuniqueness of equilibria and social inefficiency. We examine a particular class of mechanisms that have received study recently in the literature, and we characterize all the generalized Nash (GN) equilibria of the resulting data market. We show that, in contrast to the single-aggregator case, there is either infinitely many GN equilibria or none. We also provide necessary and sufficient conditions for all equilibria to be socially inefficient. In our analysis, we identify the components of these mechanisms that give rise to these undesirable outcomes, showing the need for research into mechanisms for competitive settings with multiple data purchasers and sellers. [ABSTRACT FROM AUTHOR]

Reinforcement learning (RL) is a powerful tool to perform data-driven optimal control without relying on a model of the system. However, RL struggles to provide hard guarantees on the behavior of the resulting control scheme. In contrast, nonlinear model predictive control (NMPC) and economic NMPC (ENMPC) are standard tools for the closed-loop optimal control of complex systems with constraints and limitations, and benefit from a rich theory to assess their closed-loop behavior. Unfortunately, the performance of (E)NMPC hinges on the quality of the model underlying the control scheme. In this paper, we show that an (E)NMPC scheme can be tuned to deliver the optimal policy of the real system even when using a wrong model. This result also holds for real systems having stochastic dynamics. This entails that ENMPC can be used as a new type of function approximator within RL. Furthermore, we investigate our results in the context of ENMPC and formally connect them to the concept of dissipativity, which is central for the ENMPC stability. Finally, we detail how these results can be used to deploy classic RL tools for tuning (E)NMPC schemes. We apply these tools on both, a classical linear MPC setting and a standard nonlinear example, from the ENMPC literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new framework for model-predictive control (MPC) with generalized zone tracking. The proposed zone MPC tracks a generalized target set of system state and input which is not necessarily control-invariant. In this context, the classical MPC theory no longer applies because the target zone may not be stable in the sense of Lyapunov. We extend LaSalle's invariance principle and develop new theories for stability analysis of zone MPC. It is proved that under the zone MPC design, the system converges to the maximal control invariant set in the target zone. Sufficient conditions for asymptotic stability of the maximal control-invariant set are also discussed. By tracking the generalized target zone, the proposed zone MPC is able to: (i) yield smaller zone tracking errors than all existing methods which essentially track some steady-state subset of the target zone, and (ii) allow more admissible operations and release more degrees of freedom to achieve other economic objectives. Further discussions are made on extending the prediction horizon of the zone MPC based on an auxiliary control law as well as handling a secondary economic objective via a second-step economic optimization. [ABSTRACT FROM AUTHOR]

Controlling complex systems to desired states is of primary importance in science and engineering. In the classical control framework, the plants to be controlled usually do not have their own payoff or objective functions; however, this is not the case in many practical situations in, for examples, social, economic, and “intelligent” engineering systems. This motivates our introduction of the game-based control system (GBCS), which has a hierarchical decision-making structure: one regulator and multiple agents. The regulator is regarded as the global controller that makes decision first, and then, the agents try to optimize their respective objective functions to reach a possible Nash equilibrium as a result of noncooperative dynamic game. A fundamental issue in the GBCS is: Is it possible for the regulator to change the macrostates by regulating the Nash equilibrium formed by the agents at the lower level? This leads to the investigation of controllability of the Nash equilibrium of the GBCS. In this paper, we will first formulate this new problem in a general nonlinear framework and then focus on linear systems. Some explicit necessary and sufficient algebraic conditions on the controllability of the Nash equilibrium are given for a linear GBCS, by solving the controllability problem of the associated forward and backward dynamic equations, which is a key technical issue and has rarely been explored in the literature. [ABSTRACT FROM AUTHOR]

This paper presents a dual-objective nonlinear model predictive control (NMPC) algorithm for stabilizing a target neighborhood of a state-space manifold of a nonlinear dynamical system and for concurrently optimizing an economic objective in this neighborhood. The control design is based on the transverse normal form description of the system dynamics. The NMPC scheme solves two optimal control problems (OCPs) in sequence, the first (transversal) OCP provides conditions for the convergence to the target neighborhood. The second (tangential) OCP optimizes the economic objective without compromising the convergence. The stability and performance properties of the resulting control scheme are discussed and its efficacy is illustrated in a tutorial example. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of placing energy storage resources in a power network when all storage devices are optimally controlled to minimize system-wide costs. We propose a discrete optimization framework to accurately model heterogeneous storage capital and installation costs as these fixed costs account for the largest cost component in most grid-scale storage projects. Identifying an optimal placement strategy is challenging due to the combinatorial nature of such placement problems, and the spatial and temporal transfers of energy via transmission lines and distributed storage devices. To develop a scalable near-optimal placement strategy with a performance guarantee, we characterize a tight condition under which the placement value function is submodular by exploiting our duality-based analytical characterization of the optimal cost and prices. The proposed polyhedral analysis of a parametric economic dispatch problem with optimal storage control also leads to a simple but rigorous verification method for submodularity, and the novel insight that the spatiotemporal congestion pattern of a power network is critical to submodularity. A modified greedy algorithm provides a $(1-1/e)$ -optimal placement solution and can be extended to obtain risk-aware placement strategies when submodularity is verified. [ABSTRACT FROM AUTHOR]

This paper is concerned with the first passage discounted payoff criterion for continuous-time $N$ -person nonzero-sum stochastic games in countable states and Borel action spaces, where the discount factor is nonconstant. For the game with unbounded reward functions and transition rates, the optimality is over the set of all randomized history-dependent policies. After showing the uniqueness of the solution to the Shapley equation, we give some suitable conditions imposed on the primitive data for the existence of Nash equilibria. Then, a financial system is introduced to illustrate the applications of the main result here. [ABSTRACT FROM AUTHOR]

In this paper, we study the system theoretic properties of a reference tracking model predictive control (MPC) scheme for general reference trajectories and nonlinear discrete-time systems subject to input and state constraints. Contrary to other existing theoretical results for reference tracking MPC, we do not modify the optimization problem with artificial references or terminal ingredients. Instead, we consider a simple, intuitive implementation and derive theoretical guarantees under a stabilizability condition on the system and suitable conditions on the reference trajectory. We provide sufficient conditions for exponential reference tracking for reachable reference trajectories. In addition, we study unreachable reference trajectories and derive sufficient conditions to ensure practical stability of the unknown optimal reachable reference trajectory. For both cases, we characterize the region of attraction. The results build on the notion of incremental stabilizability, strict dissipativity, and results in (economic) MPC without terminal constraints. [ABSTRACT FROM AUTHOR]

Motivated by recent advances in the study of linear time-invariant (LTI) positive systems, we explore analysis techniques of general, not necessarily positive, LTI systems using positive system theory. Even though a positive system is characterized by its peculiar property that its impulse response is nonnegative, we often deal with nonnegative impulse responses even in general LTI system analysis. A typical example is the computation of the $H_2$ norm, where we focus on squared impulse responses. To deal with such products of impulse responses in a systematic fashion, in this paper, we first establish a construction technique of an LTI system whose impulse response is given by the product of impulse responses of two different LTI systems. Then, as the main result, we reduce the $H_2$ norm computation problem of a general LTI system into the $L_\infty$ -induced norm computation problem (or $L_1$ problem in short) of a positive system, by which we can derive various formulas for the $H_2$ norm computation. [ABSTRACT FROM AUTHOR]

This paper considers the dynamic economic dispatch problem for a group of distributed energy resources (DERs) with storage that communicate over a weight-balanced strongly connected digraph. The objective is to collectively meet a certain load profile over a finite time horizon while minimizing the aggregate cost. At each time slot, each DER decides on the amount of generated power, the amount sent to/drawn from the storage unit, and the amount injected into the grid to satisfy the load. Additional constraints include bounds on the amount of generated power, ramp constraints on the difference in generation across successive time slots, and bounds on the amount of power in storage. We synthesize a provably correct distributed algorithm that solves the resulting finite-horizon optimization problem starting from any initial condition. Our design consists of two interconnected systems, one estimating the mismatch between the injection and the total load at each time slot, and another using this estimate to reduce the mismatch and optimize the total cost of generation while meeting the constraints. [ABSTRACT FROM PUBLISHER]

This paper presents a model predictive control (MPC) scheme where a combination of a stabilizing stage cost and an economic stage cost is employed to allow the minimization of an economic performance index while still guaranteeing convergence toward a desired steady state. Input-to-state-stability with respect to the economic stage cost is provided. More precisely, for the case of an economic stage cost converging to zero, the economic optimization only affects the transient behavior of the closed-loop trajectories preserving the convergence to the desired steady state. Alternatively, if the economic stage cost is merely bounded, or convergent to a bound, the closed-loop state trajectory is ultimately bounded around the desired steady state with the size of the bound being monotonically increasing with the magnitude of the economic stage cost. The loosening of the closed-loop guarantees, i.e., moving from convergence to ultimate boundedness, gives space to the increase of economic performance. Numerical results illustrate the effectiveness of the proposed method on an energy efficient trajectory-tracking control problem of a marine robotic vehicle navigating in the presence of water currents. [ABSTRACT FROM PUBLISHER]

In this paper, we study a dissipativity property which was recently used in several results on economic model predictive control to ensure optimal operation of a system at steady-state as well as stability. In particular, we first investigate whether this dissipativity property is not only sufficient, but also necessary for optimal steady-state operation. In the most general case, this is not true; nevertheless, under an additional controllability assumption, we show that dissipativity is in fact necessary. Second, we provide a robustness analysis of the dissipativity property with respect to changes in the constraint set, which can result in a change in the considered supply rate. [ABSTRACT FROM AUTHOR]

Economic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant, as well as to ensure stability of the economic setpoint. However, throughout the operation of the plant, economic criteria are usually subject to frequent changes, due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. A different economic criterion determines a change of the optimal operation point and this may cause a loss of feasibility and/or stability. In this paper a stabilizing economic MPC for changing economic criterion for linear prediction models is presented. The proposed controller always ensures feasibility for any given economic criterion, thanks to the particular choice of the terminal ingredients. Asymptotic stability is also proved, providing a Lyapunov function. [ABSTRACT FROM PUBLISHER]