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Keywords:
finite-horizon LQ problems; Hamiltonian system; Riccati differential equation; algebraic Riccati equation; optimal value of the quadratic cost
finite-horizon LQ problems; Hamiltonian system; Riccati differential equation; algebraic Riccati equation; optimal value of the quadratic cost
Summary:
This short paper deals with the classical finite-horizon linear-quadratic regulator problem with the terminal state constrained to be zero, for both continuous and discrete-time systems. Closed-form expressions for the optimal state and costate trajectories of the Hamiltonian system, as well as the corresponding control law, are derived through the solutions of two infinite- horizon LQ problems, thus avoiding the use of the Riccati differential equation. The computation of the optimal value of the performance index, as a function of the initial state, is also presented.
References:
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