A smooth finite-time distributed control architecture is introduced and analyzed for the cooperative engagement problem. Using a time transformation method as well as Lyapunov stability theory, it is shown that the proposed architecture guarantees finite-time cooperative engagement in that the difference between the positions of each agent and a time-varying target, where this difference represents a dynamic equilibrium point, vanishes in a-priori given, user-defined finite-time. In addition, this finite-time convergence is achieved without dependence on the initial conditions of agents and in the presence of unknown but bounded velocity of the target. Specifically, we first time transformed the proposed smooth finite-time distributed control architecture into an infinite-time (that is, stretched) interval. This time transformation method is then allowed to utilize tools from standard Lyapunov stability theory in that we analyze convergence properties of this architecture and boundedness of local control signals of each agent in this infinite-time interval. While this note focuses on a particular problem in the context of multiagent systems, the proposed time transformation method and the analysis procedure can be used for many other problems, where a-priori given, user-defined finite-time convergence is necessary with smooth control laws.

Finite-time consensus has attracted significant research interest due to its wide applications in multiagent systems. Various results have been developed to enable multiagent systems to complete desired tasks in finite-time. However, most existing results in the literature can only ensure finite-time consensus without considering temporal constraints, where the time used to achieve consensus cannot be preset arbitrarily and is generally determined by the system initial conditions, prohibiting its application in time-sensitive tasks. Motivated to achieve consensus within a desired time frame, user-specified finite-time consensus is developed in the present work for a multiagent system to ensure consensus at a prespecified time instant. The interaction among agents (e.g., communication and information exchange) is modeled as a time-varying graph, where each edge is associated with a time-varying weight representing the time-varying interaction between neighboring agents. Consensus over such time-varying graph is then proven based on a time transformation and is guaranteed to be completed within a prespecified time frame. To demonstrate the developed framework, finite-time rendezvous of a multiagent system is considered as an example application, where agents with limited communication capabilities are desired to meet at a common location at a preset time instant with constraints on preserving global network connectivity. A numerical simulation is provided to demonstrate the efficiency of the developed result.

Predicting future energy demand will allow for better planning and operation of electricity providers. Suppliers will have an idea of what they need to prepare for, thereby preventing over and under-production. This can save money and make the energy industry more efficient. We applied a multiple regression model and three Convolutional Neural Networks (CNNs) in order to predict Florida’s future electricity use. The multiple regression model was a time series model that included all the variables and employed a regression equation. The univariant CNN only accounts for the energy consumption variable. The multichannel network takes into account all the time series variables. The multihead network created a CNN model for each of the variables and then combined them through concatenation. For all of the models, the dataset was split up into training and testing data so the predictions could be compared to the actual values in order to avoid overfitting and to provide an unbiased estimate of model accuracy. Historical data from January 2010 to December 2017 were used. The results for the multiple regression model concluded that the variables month, Cooling Degree Days, Heating Degree Days and GDP were significant in predicting future electricity demand. Other multiple regression models were formulated that utilized other variables that were correlated to the variables in the best-selected model. These variables included: number of visitors to the state, population, number of consumers and number of households. For the CNNs, the univariant predictions had more diverse and higher Root Mean Squared Error (RMSE) values compared to the multichannel and multihead network. The multichannel network performed the best out of the three CNNs. In summary, the multichannel model was found to be the best at predicting future electricity demand out of all the models considered, including the regression model based on the datasets employed.