Control of a linear stochastic system by a probability functional
The authors study the problem of maximization of the probability that the terminal state of a discrete-time linear stochastic system reaches a given terminal set, namely, a parallelepiped the faces of which are parallel to the coordinate axes. At each instant a suboptimal control is searched by solving a linear programming problem with parameters depending on current values of the state vector of the system. The dynamics of a linear stochastic system is described by the equation \[ x_{n+1}= A_n x_n+ B_nu_n+ \zeta_n,\quad 0\leq n\leq N<\infty, \] where \(x_n\) is the state vector of the system, \(u_n\) is a control vector, \(\zeta_n\) are normally distributed. Actually, the authors maximize the lower bound of a ``terminal'' probability, so the solution to the problem is suboptimal. Benders' decomposition is used for searching a suboptimal positional control. Numerical experiments demonstrate good effectiveness of the proposed algorithm with the probability criterion; it is better in comparison with the mean-square criterion.
scientific article; zbMATH DE number 1279855