A Stochastic Nonlinear Differential Game Control Method Based on Statistical Linearization

Abstract

The invention belongs to the field of non-linear differential game control, and provides a random non-linear differential game control method based on statistic linearization. The random non-linear differential game control method based on the statistic linearization comprises the following steps of: carrying out similar linearization on a system non-linear function by using a statistic linearization technology according to system state random probabilistic nature, and deriving with a random dynamic programming method to obtain analysis controller containing a statistic linearization coefficient; and meanwhile, carrying out statistic linearization on a non-linear saturation function by considering a condition that a control mount in actual engineering is limited by saturation, so as to obtain an analysis controller in a saturation limited condition. The controller consists of two parts of a system state feedback part and a statistic linear coefficient feedback part. With the adoption of the method, the two-point boundary problem caused by solving a non-linear (partial) differential equation (set) can be effectively avoided; and the random non-linear differential game control problems can be more conveniently solved on the premise that certain solving accuracy is ensured, so that multiple functions which cannot carry out the linearization by using Taylor series expansion have possibility of carrying out the linearization. The method is particularly suitable for functions, such as phase step and saturation control and digital conversion switch which are most used on aircraft, and has strong popularization and application values.

Description

technical field [0001] The invention belongs to the field of nonlinear differential strategy control, in particular to a stochastic nonlinear differential strategy control method based on statistical linearization. Background technique [0002] With the rapid development of high-tech such as aviation weapon technology, electronic technology and computer technology, the offensive and defensive confrontation is becoming more and more fierce. Because the differential game theory has obvious advantages in describing the dynamic confrontation process, its research has been widely studied by domestic and foreign scholars. Pay attention to. There are some bottlenecks in the development of differential game control. On the one hand, there are a large number of non-linear functions such as step, saturation control, and digital switch on both sides of the aircraft. Due to the interaction of players in the game, the nonlinear differential game The solution of linear unilateral optimal...

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Problems solved by technology

[0003] The present invention provides a stochastic nonlinear differential game control method based on statistical linearization, aiming to solve some bottleneck problems in the development of differential game control. For nonlinear systems, due to the interaction of people in the game, the nonlinear differential game is more complicated than the solution of nonlinear unilateral optimal control, and it is often necessary to solve the nonlinear (partial) differential equation (group) two-point boundary value problem and the actual system It is often accompanied by random noise interference. Since methods such as feedback linearization rely on accurate system models, they are not applicable to random nonlinear differential game control problems.

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