Design of Trajectory Optimization Approach for Models with Unobservable Variables in Intelligent Systems

We present an Off-data approach to solving a finite-horizon linear quadratic (LQ) problem for a time-invariant discrete-time system with a graph dynamics matrix. Unlike the regulation problem, stability and complete controllability are not assumed. The construct of optimal control is assumed in the complete absence of data on the dynamics of the system. The design of the control trajectory is controlled by the direction of the increase in the change in the state of variables over the small number of steps, which is determined by the conditional principal eigenvector of the adjacency matrix of the graph model. An important difference from the standard discrete control problem is that the control model has been modified to estimate changes in the state of variables under the controls transmitted through the dynamics matrix. We have introduced a new interpretation of the mathematical construction of the system dynamics matrix in the standard finite-horizon discrete control problem, which can be used to design any controlled dynamic system with unobservable (by its very nature) parameters. The proposed Off-data algorithm (ODGA) using the graph dynamics matrix implements recurrent computations of dynamic equations and adjoint equations, as well as the Powell method for solving a system of linear equations (SLE).