Two-point boundary optimization problem for bilinear control systems

This paper presents a new approach to the optimization problem for the bilinear system (Formula presented.) based on the well-known method of continuous parametric group reconstruction using of its structure constants defined by the Brockett equation (Formula presented.) Here x is the system state vector, (˙,˙) are the Lie brackets, z = (x, y), y is the vector of cojoint variables, ω = A −1z is the control vector, A is the inertion matrix. The quadratic control functional has to reach an extremum at the optimal solution of the equation (2) and the boundary optimization problem is to find such z 0 that solution (2) makes evolution from the state x(t 0) = x 0 up to the final state x(t 1) = x 1 during the time delay T = t 1−t 0. Therefore it is necessary to define a transformation group of the state space which is parametrized by components of the vector and then to solve the Cauchy problem for an arbitrary smooth curve joining x(t 0) with x(t 0). © 1997 Taylor & Francis Group, LLC.