The non-iterative solution of the discrete-time finite-horizon linear quadratic optimal control problem with fixed terminal state derived by means of the Moore-Penrose inverse of an appropriately defined matrix is intrinsically subject to a constraint on the maximal length of the control time interval which can be considered. In fact, this is a consequence of the limitation on the computational power available for processing the matrix generalized inverse. This article introduces a computational framework where the dimensionality restriction is completely removed. The core of the proposed algorithm consists of a procedure where the time interval taken into account doubles at each step. This routine guarantees a fast convergence to the solution. Moreover, an arbitrarily accurate solution of the corresponding infinite-horizon problem can be retrieved by setting the final state to zero and welding a sufficient number of finite time intervals satisfying the original dimensionality constraint. It is worth noting that the procedure presented in this work returns an arbitrarily accurate solution of the infinite-horizon problem, with no additional complications, also when the to-be-controlled system is non-left-invertible.

An improved computational algorithm for the non-iterative solution of the DTFH LQ optimal control problem with fixed terminal state / E. Zattoni. - In: INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS. - ISSN 1311-8080. - STAMPA. - 37:(2007), pp. 227-238.

An improved computational algorithm for the non-iterative solution of the DTFH LQ optimal control problem with fixed terminal state

ZATTONI, ELENA
2007

Abstract

The non-iterative solution of the discrete-time finite-horizon linear quadratic optimal control problem with fixed terminal state derived by means of the Moore-Penrose inverse of an appropriately defined matrix is intrinsically subject to a constraint on the maximal length of the control time interval which can be considered. In fact, this is a consequence of the limitation on the computational power available for processing the matrix generalized inverse. This article introduces a computational framework where the dimensionality restriction is completely removed. The core of the proposed algorithm consists of a procedure where the time interval taken into account doubles at each step. This routine guarantees a fast convergence to the solution. Moreover, an arbitrarily accurate solution of the corresponding infinite-horizon problem can be retrieved by setting the final state to zero and welding a sufficient number of finite time intervals satisfying the original dimensionality constraint. It is worth noting that the procedure presented in this work returns an arbitrarily accurate solution of the infinite-horizon problem, with no additional complications, also when the to-be-controlled system is non-left-invertible.
2007
An improved computational algorithm for the non-iterative solution of the DTFH LQ optimal control problem with fixed terminal state / E. Zattoni. - In: INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS. - ISSN 1311-8080. - STAMPA. - 37:(2007), pp. 227-238.
E. Zattoni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/51034
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