On the uniqueness of promotion operators on tensor products of type A crystals

The affine Dynkin diagram of type $A_n^{(1)}$ has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type $A_n$ crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type $A_n$ crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara's conjecture that all `good' affine crystals are tensor products of Kirillov-Reshetikhin crystals.Comment: 31 pages; 8 figure

Graceful Degradation of the Quality of Control through Data Drop Policy

International audienceSharing a network link in a networked control system (NCS) may result in the network overload leading to the non respect of the specified periodicity of control system, this may cause an unpredictable performance degradation of the system. In this paper, we consider an overload management technique which selectively drops the data packets of the NCS to avoid network overload. The investigated problems are: how to design the controller under packet drops and how to distribute the packet drops in a packet delivery sequence so that the quality of control (QoC) is optimized. The paper first gives the optimal LQ-controller using the conventional technique to reduce the deterioration in QoC due to packet drops. Then, the paper proposes a methodology for deriving a distribution of the packet drops in the packet delivery sequence so that the QoC is optimal. Finally, an efficient algorithm is given to reduce the computation complexity of the proposed methodology. This proposal contributes to the co-design of the controller and the resource performance management process at the implementation level

Optimal LQ-controller Design and Data Drop Distribution under (m,k)-firm constraint

The share of the network link in a networked control system (NCS) may result in the network overload where the periodicity of control system could be infected, causing an unpredictable performance degradation in control system. In this paper, we consider an overload management technique which selectively drops the data packets of the NCS to avoid the network overload. The problems investigated are: how to design the controller under packet drops and how to distribute the packet drops in a packet delivery sequence so that the quality of control (QoC) is optimized. The paper first gives the optimal LQ-controller by using the conventional technique to reduce the deterioration in QoC due to packet drops. Then, the paper proposes a methodology for deriving the distribution of the packet drops in the packet delivery sequence so that the QoC is optimal. To reduce the computation complexity of the proposed methodology, a computationally cheaper algorithm is also given. This proposal contributes to the co-design of the controller and the resource performance management process at the implementation level