This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.
With the rapid development and wide application of distributed generation technology and new energy trading methods, the integrated energy system has developed rapidly in Europe in recent years and has become the focus of new strategic competition and cooperation among countries. As a key technology and decision-making approach for operation, optimization, and control of integrated energy systems, power consumption prediction faces new challenges. The user-side power demand and load characteristics change due to the influence of distributed energy. At the same time, in the open retail market of electricity sales, the forecast of electricity consumption faces the power demand of small-scale users, which is more easily disturbed by random factors than by a traditional load forecast. Therefore, this study proposes a model based on X12 and Seasonal and Trend decomposition using Loess (STL) decomposition of monthly electricity consumption forecasting methods. The first use of the STL model according to the properties of electricity each month is its power consumption time series decomposition individuation. It influences the factorization of monthly electricity consumption into season, trend, and random components. Then, the change in the characteristics of the three components over time is considered. Finally, the appropriate model is selected to predict the components in the reconfiguration of the monthly electricity consumption forecast. A forecasting program is developed based on R language and MATLAB, and a case study is conducted on the power consumption data of a university campus containing distributed energy. Results show that the proposed method is reasonable and effective.
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
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