On the Value Functions of the Discrete-Time Switched LQR Problem Export

@article{citeulike:6038540, abstract = {<para> In this paper, we derive some important properties for the finite-horizon and the infinite-horizon value functions associated with the discrete-time switched LQR (DSLQR) problem. It is proved that any finite-horizon value function of the DSLQR problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the so-called <emphasis emphasistype="italic">switched Riccati mapping</emphasis>. 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 exponential convergence rate of the value iterations is characterized analytically in terms of the subsystem matrices. </para>}, author = {Zhang, W. and Hu, J. and Abate, A.}, citeulike-article-id = {6038540}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TAC.2009.2031574}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5288566}, day = {16}, doi = {10.1109/TAC.2009.2031574}, journal = {Automatic Control, IEEE Transactions on}, keywords = {control-optimal, control-switching, dp, switching}, month = {October}, number = {11}, pages = {2669--2674}, posted-at = {2009-10-30 00:31:13}, priority = {2}, title = {On the Value Functions of the Discrete-Time Switched LQR Problem}, url = {http://dx.doi.org/10.1109/TAC.2009.2031574}, volume = {54}, year = {2009} }

TY - JOUR ID - citeulike:6038540 L3 - citeulike-article-id:6038540 N2 - <para> In this paper, we derive some important properties for the finite-horizon and the infinite-horizon value functions associated with the discrete-time switched LQR (DSLQR) problem. It is proved that any finite-horizon value function of the DSLQR problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the so-called <emphasis emphasistype="italic">switched Riccati mapping</emphasis>. 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 exponential convergence rate of the value iterations is characterized analytically in terms of the subsystem matrices. </para> IS - 11 JF - Automatic Control, IEEE Transactions on EP - 2674 TI - On the Value Functions of the Discrete-Time Switched LQR Problem VL - 54 SP - 2669 KW - control-optimal KW - control-switching KW - dp KW - switching AU - Zhang, W AU - Hu, J AU - Abate, A PY - 2009/10/16/ UR - http://dx.doi.org/10.1109/TAC.2009.2031574 ER -