On a discounted notion of strict dissipativity

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions using model predictive control schemes, and strict dissipativity. An important feature of these results is that strict dissipativity provides a checkable condition for the other two properties. These results relate to optimal control problems with undiscounted stage cost. Motivated by applications in economics, we consider optimal control problems with discounted stage cost and define a notion of discounted strict dissipativity. As in the undiscounted case, we show that discounted strict dissipativity provides a checkable condition for various properties of the solutions of the optimal control problem associated with the appropriately defined discounted available storage function

The Impact of Perspective in Identifying and Responding to Potential Sexual Misconduct: A Study of University Students

Recent events have demonstrated a divergent understanding of sexual harassment and other forms of sexual misconduct. Although sociocultural standards regarding sexual misconduct have changed over time, including improved social and workplace standards and protections, it is clear that not everyone views these events through the same lens. The lens is even less clear when potential misconduct is viewed from the distinct perspectives of a “victim” and a “perpetrator.” We surveyed 424 undergraduate and graduate students at Indiana University Kokomo to identify the impact of perspective and various sociodemographic characteristics that may influence perceptions of what is, and is not, sexual misconduct. In addition, we examined if these factors also influence opinions on the severity of response toward this misconduct. Students completed a gender-neutral survey that presented eight potential sexualmisconduct scenarios in a first-person narrative. In each scenario, the fact pattern was identical, but some surveys were in the perspective of the “victim” and some were in the perspective of the “perpetrator.” We find that perspective matters, as do reported preconceived attitudes toward sexual misconduct. We also find preliminary evidence that the impact of perspective and the severity of the response may depend on whether the misconduct occurs in an organizational setting, in a date setting, or without a distinct victim

Strict dissipativity for discrete time discounted optimal control problems

The paradigm of discounting future costs is a common feature of economic applications of optimal control. In this paper, we provide several results for such discounted optimal control aimed at replicating the now wellknown results in the standard, undiscounted, setting whereby (strict) dissipa-tivity, turnpike properties, and near-optimality of closed-loop systems using model predictive control are essentially equivalent. To that end, we introduce a notion of discounted strict dissipativity and show that this implies various properties including the existence of available storage functions, required sup-ply functions, and robustness of optimal equilibria. Additionally, for discount factors sufficiently close to one we demonstrate that strict dissipativity implies discounted strict dissipativity and that optimally controlled systems, derived from a discounted cost function, yield practically asymptotically stable equi-libria. Several examples are provided throughout

A real-time pricing scheme for residential energy systems using a market maker

Voltage rise is an undesirable side-effect of solar photovoltaic (PV) generation, arising from the flow of surplus electrical power back into the grid when PV generation exceeds local demand. Customers deploying residential-scale battery storage are likely to further exacerbate voltage rise problems for electrical utilities unless the charge/discharge schedules of batteries are appropriately coordinated. In this paper, we present a real-time pricing mechanism for use in a network of distributed residential energy systems (RESs), each employing solar PV generation and battery storage. The pricing mechanism proposed in this paper is based on a Market Maker algorithm in which predicted power profiles and real-time pricing information is iteratively exchanged between a central entity and each of the RESs. The Market Maker formulation presented in this paper is shown via simulation studies to converge to a fixed price vector, thereby reducing the price volatility observed in an earlier formulation, while achieving the same reduction in power usage variability as a centralised model predictive control (MPC) scheme presented previously

Predictive control of a smart grid: a distributed optimization algorithm with centralized performance properties

The authors recently proposed several model predictive control (MPC) approaches to manage residential level energy generation and storage, including centralized, distributed, and decentralized schemes. As expected, the distributed and decentralized schemes result in a loss of performance but are scalable and more flexible with regards to network topology. In this paper we present a distributed optimization approach which asymptotically recovers the performance of the centralized optimization problem performed in MPC at each time step. Simulations using data from an Australian electricity distribution company, Ausgrid, are provided showing the benefit of a variable step size in the algorithm and the impact of an increasing number of participating residential energy systems. Furthermore, when used in a receding horizon scheme, simulations indicate that terminating the iterative distributed optimization algorithm before convergence does not result in a significant loss of performance