Dualization and discretization of linear-quadratic control problems with bang–bang solutions

摘要: We consider linear-quadratic (LQ) control problems, where the variable appears linearly and is box-constrained. It well-known that these problems exhibit bang–bang singular solutions. assume solution of type, which computationally challenging to obtain. employ a quadratic regularization LQ problem by embedding \(L^2\)-norm into cost functional. First, we find dual guided methodology Fenchel duality. Then prove strong duality saddle point property, together ensure primal can be recovered from solution. propose discretization scheme for problem, under diagram depicting relations between their commutes. The commuting ensures that, given convergence results discrete variables, variables also converge with similar error bound. demonstrate via simple but illustrative example significant computational savings achieved solving dual, rather than primal, problem.