A neural network for N-stage optimal control problems

Abstract

Abdract-Neural nets have the potential to be a powerful tool in dealing with nonlinear systems. Different approaches about how neural nets can be incorporated in optimal control strategies have been proposed in terms of general gradient descent and back-propagation. In this paper a particular neural network t o solve discrete time N-stage optimal control problems with a direct method to assign its weights is introduced, to systematically incorporate knowledge about the system's behavior. This method is based on the Bellmann's Optimality Principle and in the interchange of information which occurs during the synaptic chemical processing among neurons. This approach presents some advantages with regard to alternative approaches because of the ausence of exaustive training. Some important applications are addressed to illustrate the usefulness of the approach proposed. I. ~N T R O D U C T I O NThe need to meet demanding control requirements in increasingly complex dynamical systems under significant uncertainties makes neural networks very attractive because of their ability t o learn, t o approximate functions, to classify patterns and because of their potential for massively parallel hardware implementation [I].A number of different approaches for training a controller have been described in the literature. They include reinforcement leariling [2]. inverse control [ll], [I41 and optimal control [9], [ll]. Optimal control problems can be solved by dynamic programming techniques. However, because of t,he large con~putational requirements of the st.andard computational algorithm a number of new procedures with reduced computational requirements have been developed. *Supported by CNPq grant # 300634/925 'Supported by CNPq grant # 300?29/863 0-7803-1901-X/94 $4.00 01994 IEEE 4508 ~ Fernando GoinideRecently, an neural network with a two-layer feedback topology for solving discrete dynamic programming problems has been proposed [5]. The learning method iniplemented by this neural-network is equivalent. to the dynamic programming algorithni. A class of fuzzy decision making problems have also been solved by this approach [GI. In both in cases, Max and Min neuron models proposed in [8] have been utilized to construct the neural network.In this paper generalized recurrent neurons models are introduced from which the Max and Min neurons of [8] can be obtained. Based on this new neuron model a modification of the approach proposed in [5] is presented.

Glide Control for Engine-Out Aircraft

“…(14-1) (14-2) tworks 13,17 . Our proposal here, has been to take profit of the amount of data generated by the reverse dynamic programming search process, considering different situations and parameters such as aircraft initial distance to landing site x; altitude z; speed V and glide path angle r, to train a neural network device designed to generate pitch angle directives (in fact the target current reference value for the pitch angle θ) at each point along the descent so that the glide trajectory leads safely to the landing location.…”

“…The drag, Ds, produced by speed , we get relations between airspeed and ground speed, and relation between ground displacement and displacement with respect to air, which are shown in Eq. (17), where V w is wind speed, V g is ground speed, and Vs is airspeed. , 3 Figure 10.…”

Dynamic programming for trajectory optimization of engine-out transportation aircraft

“…Moreover, this approach should facilitate the consideration of ground separation constraints and could make easier the consideration of the effect of wind over the glide trajectory. From equations (3) with : (15) we get:…”

“…Our proposal here, which should be developed in the near future is to take profit of the amount of data generated by the reverse dynamic programming search process, considering different situations and parameters such as aircraft initial flight level, altitude and mass, to train a neural network devise designed to generate pitch angle directives at each point along the descent so that the glide trajectory leads safely to the landing situation. Here the computational burden associated with reverse dynamic programming is taken into profit to generate the training data base for the neural network [15]. The generated pitch angle directives can be either sent to the autopilot when it is still operating or to a flight director.…”