Optimal Continuous/Impulsive LQ Control With Quadratic Constraints

In this paper, the optimal continuous/impulsive linear quadratic (LQ) control problem with quadratic constraints is thoroughly solved for the first time. The main contributions of this paper can be stated as in the following. First, the maximum principle is developed by using the variational method. Then, by using the Lagrange duality principle, the optimal continuous/impulsive control can thus be obtained via decoupling the forward and backward differential/difference equation (FBSDE). Finally, the optimal parameter can be calculated by using the gradient-type optimization algorithm.