An explicit solution to a class of constrained optimal control problems

Optimal control problems that admit closed form solutions are rare so that numerical methods have to be used to obtain an approximate solution in most cases. This paper derives an explicit solution to a class of constrained optimal control problem that arises in the investigation of nonlinear L₂-gain properties. The optimal control problem is a nonlinear problem in ℝ₂ even for linear systems in ℝ due to the presence of an L₂-norm constraint on the input signals. The solution to the optimal control problem considered is obtained via connection to the parameterized linear ℌ_∞-control solutions in ℝ which are explicitly solvable.