## A simple solution to the finite-horizon LQ problem with zero terminal state.(English)Zbl 1249.49048

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 Riccati differential equations. The computation of the optimal value of the performance index, as a function of the initial state, is also presented.

### MSC:

 49N10 Linear-quadratic optimal control problems 93C15 Control/observation systems governed by ordinary differential equations
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### References:

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