Disturbance rejecting optimal regulation of hyperbolic systems
Optimal regulation of the hyperbolic system \[ {d^2 y\over dt^2}+ Ay= Bu+ C\nu,\quad t\in I\equiv (0, T),\quad y(0)= y_0,\quad y_t(0)= y_0' \] with the cost function \[ \widetilde J(u, \nu, w)= {(q_1/2) \int_I |y- y^d|^2_H dt+ (q_2/2) \int_I |y_t- y^d_t|^2_H dt+ (r_1/2) \int_I |u|^2_H dt\over (s_1/2) |y_0|^2_H+ (s_2/2) |y_0'|^2_H+ (r_1/2) \int_I |\nu |^2_H dt}, \] where \(s_1\), \(s_2\), \(q_1\), \(q_2\), \(r_1\), \(r_2\) are scalar weighting factors, and, \(y^d\), \(y^d_t\) are desired trajectories, respectively, in the presence of unknown exogenous and initial disturbances is considered. Necessary conditions for determining the optimal control that tracks a desired trajectory in the presence of disturbances are developed. The fact that these necessary conditions have the form of a two-point boundary value problem along with certain equality and inequality conditions is stated. An \(H_\infty\)-like control method for hyperbolic systems is presented. The main results are related to the \(H_\infty\) control problem.
scientific article; zbMATH DE number 881724
scientific article