1,091 research outputs found
Max-plus fundamental solution semigroups for a class of difference Riccati equations
Recently, a max-plus dual space fundamental solution semigroup for a class of
difference Riccati equation (DRE) has been developed. This fundamental solution
semigroup is represented in terms of the kernel of a specific max-plus linear
operator that plays the role of the dynamic programming evolution operator in a
max-plus dual space. In order to fully understand connections between this dual
space fundamental solution semigroup and evolution of the value function of the
underlying optimal control problem, a new max-plus primal space fundamental
solution semigroup for the same class of difference Riccati equations is
presented. Connections and commutation results between this new primal space
fundamental solution semigroup and the recently developed dual space
fundamental solution semigroup are established.Comment: 17 pages, 3 figure
Switching Quantum Dynamics for Fast Stabilization
Control strategies for dissipative preparation of target quantum states, both
pure and mixed, and subspaces are obtained by switching between a set of
available semigroup generators. We show that the class of problems of interest
can be recast, from a control--theoretic perspective, into a
switched-stabilization problem for linear dynamics. This is attained by a
suitable affine transformation of the coherence-vector representation. In
particular, we propose and compare stabilizing time-based and state-based
switching rules for entangled state preparation, showing that the latter not
only ensure faster convergence with respect to non-switching methods, but can
designed so that they retain robustness with respect to initialization, as long
as the target is a pure state or a subspace.Comment: 15 pages, 4 figure
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