Optimization of flying vehicle control allowing for random perturbations, restrictions and failures

N.Ye.Rodnishchev, K.G.Denisov

We are investigating the necessary conditions for optimal control of stochastic systems, random jump structure, describing the operation of aircraft with constraints that take into account the different goals and requirements for the system, perturbations randomly spread in the parameters, the effect of the additive and multiplicative noise as well as a random flow of failures of the subsystems. The problem of withdrawal of aircraft on a circular orbit given the refusal of one of two sections of parallel engines is considered

Determination of the optimal control aircraft without reliability factors can lead to poor value of the probability of failure of control systems and aircraft in general, and in case of failure may be unsatisfactory in terms of probability of success of the flight task in the different implementations of failure.

Taking into account of reliability in the optimization of traffic leads to a change of known management programs and optimal parameters, which indicates the relevance of optimization of stochastic systems, aircraft, taking into account failures.

Let's consider nonlinear stochastic system at the moment when a malfunction occurs l from n₀ a concurrent identical subsystems with failure rateљ with some probability.

We are should determine optimal control v=(u, a), which minimize considered functional, characterizing the effectiveness of control for initial system. And we taken in consideration also k following failures that make up on the time interval [t₀, t_f] ordinary flow of random events with some probabilities.

Controls targets v=(u, a) and different requirements for the system, described mixed constraints such as equality and inequality on the parameters of the system management functions and phase coordinates.

For illustration of developed method was studied the problem of interorbital flight according with engines refuses. Let us consider the problem of transfer of a material point moving in the central force field from one orbit to another by the use of reactive force of the propulsion unit consisting of two simultaneously working engine sections. At random moments used engines can be refusing.

The movement of aircraft is carried out in the plane of a large circle of the earth's sphere, taking into account the parametric noise rejection section of the power plant.

We are need to determine optimal control v=(x₁₀, x₂₀, x₃₀, u, t_f), which provides the outљ of aircraft from the passive section along the trajectory on a circular orbit and provides a view of the erosive burning of fuel and engine-out section of the maximal mass, defined here. Given that the maximal mass of the aircraft provided the minimal time of transition from the passive section of a circular orbit, we solve the problem for the optimal control v=(x₁₀, x₂₀, x₃₀, u, t_f).