Development and application of a gradient method for solving differential games
A technique for solving n-dimensional games is developed and applied to two pursuit-evasion games. The first is a two-dimensional game similar to the homicidal chauffeur but modified to resemble an airplane-helicopter engagement. The second is a five-dimensional game of two airplanes at constant altitude and with thrust and turning controls. The performance function to be optimized by the pursuer and evader was the distance between the evader and a given target point in front of the pursuer. The analytic solution to the first game reveals that both unique and nonunique solutions exist. A comparison between the gradient results and the analytic solution shows a dependence on the nominal controls in regions where nonunique solutions exist. In the unique solution region, the results from the two methods agree closely. The results for the five-dimensional two-airplane game are also shown to be dependent on the nominal controls selected and indicate that initial conditions are in a region of nonunique solutions.
Differential Games Treated by a Gradient–Restoration Approach
Abstract When When two competitive actors are involved in a flight path optimization, the problem can be modelled as a zero-sum game. This chapter describes a general procedure to convert the two-sided optimization problem into an optimal control problem. In addition, a numerical approach to the solution is proposed. The method is based on the joint application of an evolutionary algorithm (for providing a starting guess) and of the sequential gradient-restoration algorithm (to achieve the final solution). The homicidal chauffeur game – a classical example of zero-sum game – and an orbital pursuit-evasion game are considered to describe the method and test its effectiveness.
A Short-Term and High-Resolution Distribution System Load Forecasting Approach Using Support Vector Regression With Hybrid Parameters Optimization
This paper proposes an approach for distribution system load forecasting, which aims to provide highly accurate short-term load forecasting with high resolution utilizing a support vector regression (SVR) based forecaster and a two-step hybrid parameters optimization method. Specifically, because the load profiles in distribution systems contain abrupt deviations, a data normalization is designed as the pretreatment for the collected historical load data. Then an SVR model is trained by the load data to forecast the future load. For better performance of SVR, a two-step hybrid optimization algorithm is proposed to determine the best parameters. In the first step of the hybrid optimization algorithm, a designed grid traverse algorithm (GTA) is used to narrow the parameters searching area from a global to local space. In the second step, based on the result of the GTA, particle swarm optimization is used to determine the best parameters in the local parameter space. After the best parameters are determined, the SVR model is used to forecast the short-term load deviation in the distribution system. The performance of the proposed approach is compared to some classic methods in later sections of this paper.