Pham

One of the main difficulties of analysis and synthesis of control in stochastic systems is the need of operation in multi-dimensional abstract spaces which are typically infinite-dimensional and difficult to interpret physically. A method was proposed to solve the problem of synthesis of control in stochastic systems using generalized polynomial chaos. The method allows to transform the original problem with a stochastic model into a problem with a deterministic model of high-dimensional state space of a dynamical system. This problem can be solved by known numerical methods.

 The authors formulate a problem of control systems synthesis for dynamic objects with random initial values. It was proposed for the synthesis to modify functionals of quality to form sum of values with weights for each initial value. Weights determine probabilities of initial values.  It was proposed to use the numerical network operator technique for solving the synthesis problem. An example of control system synthesis for an aircraft at the descend stage is presented in the article.