Design of linear regulators with energy constraints

In the usual design of linear quadratic optimal control systems, the regulator performance is obtained for several different values of the constant Lagrange multiplier q. The Lagrange multiplier determines the amount of control energy expended. If the energy is to be constrained, then the value of q must be found such that the energy constraint is satisfied. In this paper a method is described for determining simultaneously the optimal trajectory and the value of q which satisfies the energy constraint.