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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1 On the Value Functions of the Discrete-Time
 

Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1
On the Value Functions of the Discrete-Time
Switched LQR Problem
Wei Zhang, Jianghai Hu, and Alessandro Abate
Abstract--In this paper, we derive some important properties for the fi-
nite-horizon and the infinite-horizon value functions associated with the
discrete-time switched LQR (DSLQR) problem. It is proved that any fi-
nite-horizon value function of the DSLQR problem is the pointwise min-
imum of a finite number of quadratic functions that can be obtained re-
cursively using the so-called switched Riccati mapping. It is also shown that
under some mild conditions, the family of the finite-horizon value functions
is homogeneous (of degree 2), is uniformly bounded over the unit ball, and
converges exponentially fast to the infinite-horizon value function. The ex-
ponential convergence rate of the value iterations is characterized analyti-
cally in terms of the subsystem matrices.
Index Terms--Discrete-time switched LQR (DSLQR).
I. INTRODUCTION
Optimal control of switched systems is a challenging problem that
has received much research attention in recent years [1][4]. Compared
with traditional optimal control problems [5], the distinctive feature

  

Source: Abate, Alessandro - Faculty of Mechanical, Maritime and Materials Engineering, Technische Universiteit Delft

 

Collections: Engineering