A new intelligent control system for guided bombs

The control system is the key part of the guided bomb. At present, the control systems of all guided bombs are based on a certain mathematical model and correct the ballistic error in a fixed way. Due to the existence of various unpredictable error factors, but the control method cannot be adjusted, the actual hit accuracy of the guided bomb is not high. In response to this situation, the literature [1] proposed an intelligent control system for guided bombs based on adaptive neural fuzzy inference system (ANFIS). It is not based on a mathematical model, but controls by learning training data through ANFIS. Since it fully utilizes the self-learning ability and generalization function of the neural network and combines the heuristic search ability of the fuzzy system, the intelligent control system based on ANFIS has high control accuracy and strong generalization ability. However, after a large number of experiments, it was found that since ANFIS does not have the ability to resist noise, when the training data is affected by noise, it is necessary to manually analyze the data characteristics and modify the training data to obtain appropriate inference rules, which greatly reduces the "intelligent" performance of the system. Based on this, a new guided bomb intelligent control system is proposed. The system introduces non-single-point fuzzification technology with pre-filtering characteristics. Aiming at the problem that the internal parameters of the non-single-point fuzzy inference system are difficult to adjust, a hybrid parallel learning algorithm composed of gradient descent algorithm and genetic algorithm is proposed to adjust the internal parameters of the system, so that the training data affected by noise can be automatically processed and the hit accuracy can be improved. The effectiveness of the control system is verified through computer simulation experiments and comparison with the guided bomb intelligent control system based on ANFIS.

1 Non-single-point fuzzy inference system (NSFIS)
The core of the proposed guided bomb intelligent control system is the non-single-point fuzzy inference system (NSFIS). A fuzzy inference system with n inputs and 1 output, whose fuzzy rules can be expressed as follows
The fuzzy sets on, and y∈V correspond to the system input and output variables, l=1, 2,…, M is the number of fuzzy rules.
When the central average fuzzy eliminator, product inference rule, Gaussian membership function and non-single-point fuzzification are used, the non-single-point fuzzy inference system is obtained as follows:

When , non-single-point fuzzification is equivalent to single-point fuzzification; when the input variable xk is contaminated by noise, the noise will be overcome by the factor in the non-single-point fuzzifier. If σx ≥ σFkl, the noise will be suppressed to a large extent.

2 Parameter learning algorithm of NSFIS
Fuzzy inference system is a highly nonlinear system. In the process of modeling complex systems, its internal parameters are mainly determined by training the input-output data pairs with a certain learning algorithm. At present, the learning algorithms used for fuzzy inference systems are mainly gradient descent algorithm and recursive least squares algorithm. The gradient descent algorithm is simple and easy to operate, with small amount of computation, but it converges slowly, is prone to fall into local extreme values, and has a large dependence on the spectrum of the signal; the recursive least squares algorithm converges quickly and has no dependence on the spectrum of the signal, but its structure is complex, the amount of computation is large, and there is a problem of long-term numerical stability. From an engineering perspective, because the computational complexity of non-single-point fuzzy inference systems is large in itself, the recursive least squares algorithm with a large amount of computation is not suitable for use. In order to make up for the shortcomings of the gradient descent algorithm, the genetic algorithm is introduced in this paper. The genetic algorithm is a global optimization search algorithm that simulates the biological evolution process. Its objective function does not require continuity or differentiability, but only requires that the problem be computable, and its search always covers the entire solution space, making it easy to obtain the global optimal solution. The gradient descent algorithm and the genetic algorithm are used to search the solution space in parallel and exchange information regularly. This not only avoids the disadvantage of falling into local extreme values, but also speeds up the convergence speed. Although the amount of calculation increases due to the addition of the genetic algorithm, the real-time performance of the algorithm is not reduced because the genetic algorithm and the gradient descent algorithm work in parallel. The subtractive clustering method is used to set the initial parameters, which further speeds up the convergence speed of the algorithm. The parameter learning algorithm of the non-single-point fuzzy inference system designed in this paper is as follows:
Step 1: Set the initial parameters. The subtractive clustering algorithm is used to cluster the training data [X, y] to obtain M cluster centers. Construct the initial parameters of the non-single-point fuzzy system: select each component element in the cluster center vector Xlc as the initial value of the corresponding in formula (2) ; use half of the Euclidean distance between the nearest cluster center and the nearest cluster center as the initial value of the corresponding in formula ( 2 ); when it is known that the training data contains a lot of noise, take
Step 2: (1) Use the gradient descent algorithm to adjust the parameters (the derivation process is omitted).

(2) Genetic algorithm is used to search for the best parameters at the same time
. 1) Encode the parameters. Taking the initial parameter value determined by subtractive clustering as a reference, considering that the solution space of the parameters is within the range of positive and negative s times of the initial parameter value, the solution space is converted into binary, and each parameter is cross-combined and encoded;
2) 20 individuals are randomly generated as the initial group;
3) The mathematical expectation of the criterion function E[φ(e(t))] is mapped to the fitness function.

The fitness of the individuals in the group is evaluated using this fitness function. When the fitness reaches the standard Ff,max, the evolution stops;
4) Genetic operation: The fitness ratio method is used for selection, the two-point crossover method is used for crossover, and the basic mutation operator is used for mutation.

Step 3: Information exchange between the gradient descent algorithm and the genetic algorithm. Every q generations of the genetic algorithm, the effects of the parameters obtained by the genetic algorithm and the gradient descent algorithm are compared according to the mathematical expectation of the criterion function E[φ(e(t))]. If the parameters searched by the genetic algorithm are better, they are used as the initial parameters for the next step of the gradient descent algorithm; if the parameters obtained by the gradient descent algorithm are better, they are used to replace the individual with the worst fitness in the contemporary population of the genetic algorithm.
Step 4: When the mathematical expectation of the criterion function E[φ(e(t))] reaches the standard 1-Ff,max, or when the genetic algorithm evolves g generations, the algorithm stops. In this paper, the time average of the criterion function within the time length of the training data is used instead of its mathematical expectation for calculation.

3 Simulation design of guided bomb intelligent control system based on NSFIS
According to the design idea of ​​literature [1], NSFIS is used to design the guided bomb intelligent control system in the simulation environment.
3.1 Setting of simulation environment
Assume the following simulation environment:
(1) The direction of the integrated wind speed UZ is in the horizontal plane and is a constant vector;
(2) The gravity acceleration is 9.8 m/s2, without damping;
(3) The maximum controllable acceleration max a(t) (max a(t)=maxax(t)+maxay(t)) that can be generated by the wing increases with the falling height, and the component of the acceleration a(t) generated by the wing in the vertical direction is not considered;
(4) The height H is 7 075.4 m (that is, the falling time T is 38 s), and the height space is divided into N=152 layers according to the falling distance △h every 0.25 s;
(5) The bombing method is horizontal bombing;
(6) The control process does not consider the time delay;
(7) The motion of the projectile is a particle motion.
3.2 Analysis of bomb motion equations
According to the literature [9, 10], the top view of horizontal bombing is shown in Figure 1.

(oyxz)H: aircraft heading coordinate system; Of: aircraft bombing point; Om: ground target; A: no need to adjust, can directly hit the coordinate position of bomb D0 at time t; A: need to adjust, can hit the coordinate position of bomb D1 at time t; B: need to adjust, can hit the coordinate position of bomb D1 at time t-1.
No need to adjust, can directly hit bomb D0 parameters: Vx0: bombing point aircraft airspeed; Uz0: comprehensive wind speed when bombing D0; ε0: angle between Vx0 and Uz0; Xh(t): coordinate position of bomb in xH direction at time t; Yh(t): coordinate position of bomb in yH direction at time t.
The parameters of missile D1 that need to be controlled in order to hit the target are: Vx1: the airspeed of the aircraft at the bombing point; Uz1: the comprehensive wind speed when bombing D1; ε1: the angle between Vx1 and Uz1; Axe(t): the displacement difference of the missile in the xH direction at time t and time t-1; Aye(t): the displacement difference of the missile in the yH direction at time t and time t-1; Exh(t): the component of the distance between the missile and the target Om in the xH direction at time t; Eyh(t): the component of the distance between the missile and the target Om in the yH direction at time t; Vxh(t): the component of the velocity of the missile in the xH direction at time t; Vyh(t): the component of the velocity of the missile in the yH direction at time t. Axe(t): the component of the displacement difference between missile D1 and missile D0 in the xH direction at time t; Aye(t): the component of the displacement difference between missile D1 and missile D0 in the yH direction at time f. In the simulation environment, the motion equation of missile D1 at time t is derived.

Wherein, Vax(t) is the velocity generated by the acceleration at time t-1 in the xH direction, and Vay(t) is the velocity generated by the acceleration at time t-1 in the yH direction.

3.3 Establishment of the intelligent control system of guided bombs
According to the ballistic motion equation, the control in the x and y directions is independent of each other (a(t)=ax(t)+ay(t)), so two non-single-point fuzzy subsystems (NSFISix and NSFISiy) are established for each layer of space: NSFISix controls the trajectory of the missile in the x direction, with inputs of Exh(t), Axe(t), Vxh(t), and outputs ax(t); NSFISiy controls the trajectory of the missile in the y direction, with inputs of Eyh(t), Aye(t), Vyh(t), and outputs ay(t). Fully collecting the training data of each layer, and using the learning algorithm proposed in this paper to adjust the internal parameters of NSFISix and NSFISiy, an intelligent control system of guided bombs based on NSFIS is formed, and its schematic flow chart is shown in Figure 2.

3.4 Obtaining training data
First, use the following formula to solve a(t)

radians, |Uz1|=28, 29, 30, 31 m/s, |Vx1|=319, 320, 321, 322 m/s, ε1=0.3, 0.4, 0.5, 0.6 radians; by adjusting the parameters cx and cy, 64 sets of circular error probability CEP∈(4, 5)m training data are obtained, and a certain degree of disturbance error is added to it.
3.5 Test
Assume two initial conditions for bombing:
(a) |Uz1|=30 m/s, |Vx1|=321 m/s, ε1=0.5 radians (trained initial conditions for bombing, i.e., teacher knowledge);
(b) |Uz1|=30.8 m/s, |Vx1|=319.7 m/s, ε1=0.38 radians (untrained initial conditions for bombing, i.e., non-teacher knowledge).
Using the training data containing disturbance errors, the ANFIS-based guided bomb intelligent control system and the NSFIS-based guided bomb intelligent control system are trained respectively, and bombing control tests are carried out under (a) and (b) conditions respectively. The control results of the two intelligent control systems are compared as shown in Table 1 (the data in the table are CEP, unit: m).

As can be seen from Table 1, no matter under (a) or (b) conditions, the hit accuracy of the intelligent control system based on NSFIS is very high, while the hit accuracy of the intelligent control system based on ANFIS is very low. This is because ANFIS does not have anti-noise ability, and during the training process, it also learns disturbances as experience, so its reasoning error is bound to be large and the control is inaccurate. NSFIS has strong anti-noise ability and can remove the influence of disturbances during the learning process, so its control accuracy is high. In reality, disturbances are inevitable, so the intelligent control system of guided bombs based on NSFIS has higher engineering application value.

4 Conclusion
Aiming at the disadvantage that the intelligent control system of guided bombs based on ANFIS has no anti-noise ability, a new intelligent control system of guided bombs is designed with non-single-point fuzzy inference system as the core. The pre-filtering characteristics of the non-single-point fuzzy inference system are utilized, and a hybrid parallel learning algorithm composed of gradient descent algorithm and genetic algorithm is proposed to adjust the internal parameters of the system, which solves the problem of dynamic adaptive adjustment of the internal parameters of the system. The experimental results show that when the training data contains noise, the intelligent control system of guided bombs based on NSFIS can automatically filter out the noise and achieve high-precision control. This has certain significance for the engineering implementation of the intelligent control system of guided bombs.