A parametrization of the solutions of the Hamiltonian system for stabilizable pairs

摘要

In this note, a simple method is proposed for the solution of the finite-horizon LQ problem, which does not require the integration of the Riccati differential equation. Precisely, the problem is tackled by parametrizing the set of trajectories solving the Hamiltonian system in finite terms, under the assumption of stabilizability of the underlying system. In this way, it is possible to determine closed-form expressions for the state and control functions, as well as for the optimal cost in terms of the assigned state at the end-points.