FLIGHT CONTROL BY MEANS OF ARTIFICIAL INTELIGENCE

Transcription

1 FLIGHT CONTROL BY MEANS OF ARTIFICIAL INTELIGENCE Ing. Michal Turčaník, PhD. NAO Litovský Mikuláš, Abstract Nonlinear redictable sstems can be controlled b recurrent neural networks (RNN). Recurrent neural network can remember revious states and use it for rediction of next state. But there is disadvantage in difficult otimalization of their arameters like neuron bias, weight etc. There are man methods to do this, so it was chosen genetic algorithm (GA). The aer deals with using RNN for modelling of nonlinear sstem - a model of manoeuvring aircraft as target of guided missile. Both aircraft and missile are controlled b recurrent neural network. The coevolution of the genetic algorithms evolves to set of arameters for each recurrent neural network. Alication also can visualize some combats for best aircraft and missile control networks.selected results of simulation of air combat are discussed in the aer. Detail algorithms are resented as well. INTRODUCTION The otimization of the artificial neural network reresents a difficult roblem. This roblem can be divided on the otimization of the toolog and arameters otimization (weights and thresholds) of the artificial neural networks. The toolog of the neural network can be determined b constructive or destructive methods (2, 7). The other methods use genetic algorithms. The back roagation algorithm is used for the determination of arameters of the artificial neural network. Genetic algorithms reresent the alternative wa for the determination of arameters of the artificial neural network. Results acquired b research and simulation of artificial neural networks are ver useful to understand function of those biological, eventuall enable use of aroriate artificial neural network in such alications, where utting human should be dangerous to his life and health, or b the influence of various factors he wouldn t be able to decide in enough short time. One of thus alications is flight control of fighter aircraft or a missile. The aer deals with the otimization of arameters of the recurrent neural network for flight control b modified genetic algorithm and coevolution of modified genetic algorithms. The modification of the using of genetic algorithms is based on the execution of two genetic algorithms, oulations of which are imacted each other. The imact of each other oulations with common fitness function is called the coevolution. The coevolution (evolution of the two or several cometitive oulations with common rate of the fitness) has some functions, which can extend the ower of the adatation of the artificial evolution

2 Figure 1 - Aircraft coordinate sstem 1 AIR COMBAT BETWEEN FIGHTER AIRCRAFT AND A MISSILE Air combat between fighter aircraft and a missile is used as fitness function for evaluating individuals in genetic algorithm. The evading aircraft and the ursuing missile, both are governed b the following 6 DOF (degree of freedom) equations of motion (8). These equations are in form after LaPlace transformation. The coordinate sstem is shown in figure Vertical lane equations 1 = + a ϑ = POM V α ( a a V a α ) POM 1 ωv V α α& ( ) ( ) ( ) ( a a V a a α ) ω m z z V m z m + z mz + a mz + α ϑ = 0 (3) (1) (2) Where: V α - a x, a x,... - measurable aerodnamic derivations (coefficients describing aircraft roerties), POM - thrust, V - itch control, - ϑ - itch angle, - V relative vertical velocit, - α - angle of attack,

3 - - vertical fl ath angle. 1.2 Horizontal lane equations γ h = Ψ = 1 = 1 γ β [ a γ + a β ] z ϖx ( + a ) mx z ϖ KV ϖs β [ amx ( Kr ) + amx ( S ) amx Ψ amxβ ] 1 s ϖx β ( ) ( ) [ a γ β ] ϖ m s am am a + m h + β Ψ = 0 (7) Where: S - aw control, Kr - roll control, - h - vertical aw angle, - γ - roll angle, - a... - aerodnamic derivations, β γ z a z - β - side sli, - Ψ - course angle. (4) (5) (6) 1.3 Simulation of the air combat Flow grah of the simulation of the air combat is shown in the figure 2. First ste of the simulation is data initialization (osition, seed, ). In the next ste there are comuted flight data for aircraft and missile. In the next is comuted inut vector for recurrent neural network. Comuted outut data from RNN are used for flight model. Condition for the end of the simulation are finishing of the duel due hit aircraft b missile or realisation of defined number of the time ste for air combat. No Yes Start Inicialization Comuting flight data for aircraft and missile Comuting inut vector for the RNN Comuting outut vector of the RNN and alication to flight model End of the simulation Start Figure 2 Flow grah of the simulation of the air combat

4 L distance to oonent ϕ - oonent direction V P oonent velocit V V own velocit - own vertical fl ath angle K - own horizontal aw angle POM - thrust V - itch control S - aw control K - roll control Figure 3 - RNN toolog 2 The toolog of the recurrent neural network It was used RNN toolog (shown in figure 3) based on Jordan toolog of recurrent neural network. Context laer can remember 10 revious outut states through the time dela blocks creating a time window. Each neuron has sigmoidal activation function and its rate of rise is art of otimalized arameters as well as weights and neuron biases. 3 GENETIC ALGORITHM Figure 4 - Chromosome reresentation Genetic algorithms are search algorithms based on the mechanics of natural selection and natural genetics. The combine survival of fittest among string structures with a structured et randomised information exchange to form a search algorithm with some of the innovative flair of

5 human search. In ever generation, a new set of artificial creatures (strings) is created using bits and ieces of the fittest of the old; an occasional new art is tried for good measure. While randomised, genetic algorithms are no simle random walk. The efficientl exloit historical information to seculate on new search oints with exected imroved erformance. Modification of standard genetic algorithm consists of chromosome reresentation alication and modification of standard genetic oerators of selection, crossover and mutation. Chromosome reresents the string of neuron arameters (shown in figure 4) and its constant length is 314 real numbers. As selection methods I used both roulette and tournament selection with elitism. This otion can be set in alication before otimalization starts. Crossover oerators are standard one oint crossover or uniform crossover with random mask. Mutation changes the genes values b random number in secified range. This range can be adated if convergence of oulation is too slow. Figure 5 3D view of air combat between aircraft and missile CONCLUSION The standard methods for otimization of the ANN are deending on one criterion function, which isn t changed. The otimization of the ANN b coevolution changes the criterion function. The criterion function is affected b external environment. In this aer there were resented methods for otimization of artificial neural networks used as flight control element in fighter aircraft and missile. Results shows, that recurrent neural networks with right otimization method can be used as control element for comlex nonlinear dnamic sstems. The advantages of genetic algorithms are simle using, imlementation and versatilit of otimization method. On the other hand the solution of comlex otimisation roblem has big time

6 comlexit. Time comlexit of the genetic algorithms can be decreased b using arallel genetic algorithms. The coevolution of the two or more oulations with the similar or oosite goals can be used for solving different roblems like otimization of the ANN. The design of the simulator for the different field of alications is a ossible roblem. The simulator is adated to the behaviour of a human, whose behaviour is successive. The results of the simulation in the next ste will be a failure, if human uses the same behaviour. The goal of the design is the simulator, for which the stereoted behaviour of a human to win can t be used. REFERENCES [1] KVASNIČKA, V., BEŇUŠKOVÁ, Ľ., POSPÍCHAL, J., TIŇO, P., FARKAŠ, I.: Úvod do teórie neurónových sietí, IRIS, Bratislava [2] GOLDBERG, David E.: Genetic Algorithms in Search, Otimization and Machine Learning, Addison-Wesle, [3] LAZAR, T.: Matematické modelovanie ozdĺžneho ohbu lietadla, VVŠL Košice, [4] HERTZ, J., KROGH, A., PALMER, R.G.: Introduction To The Theor Of Neural Comutation. Addison-Wesle Publishing Coman, [5] JORDAN, M.I.: A arallel distributed rocessing aroach, Erlbaum, Hillsdale, [6] BASAR, T., OLSDER, G.J.: Dnamic Noncooerative Game Theor, 2 nd edition, Academic Press, San Diego, [7] Turčaník, M. Líška, M. Kaloča, P.: The simulation of the coevolution of the artificial neural networks b genetic algorithms. Proceedings of the conference MATLAB 2001, Praha, October 2001, [8] LAZAR, T. a kol.: Tendencie vývoja a modelovania avionických sstémov, Vdavateľská a informačná agentúra MO SR, Bratislava, Ing. Michal Turčaník, PhD. Centrum simulačných technológií Národná akademia obran Litovský Mikuláš Slovensko turcanik@nao.sk