8 research outputs found
Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems
We consider the problem of designing distributed controllers to ensure
passivity of a large-scale interconnection of linear subsystems connected in a
cascade topology. The control design process needs to be carried out at the
subsystem-level with no direct knowledge of the dynamics of other subsystems in
the interconnection. We present a distributed approach to solve this problem,
where subsystem-level controllers are locally designed in a sequence starting
at one end of the cascade using only the dynamics of the particular subsystem,
coupling with the immediately preceding subsystem and limited information from
the preceding subsystem in the cascade to ensure passivity of the
interconnected system up to that point. We demonstrate that this design
framework also allows for new subsystems to be compositionally added to the
interconnection without requiring redesign of the pre-existing controllers.Comment: Accepted to appear in the proceedings of the American Control
Conference (ACC) 201
INVALS: An Efficient Forward Looking Inventory Allocation System
We design an Inventory Allocation System (INVALS) that, for each item-store
combination, plans the quantity to be allocated from a warehouse replenishing
multiple stores using trailers, while respecting the typical supply-chain
constraints. We formulate a linear objective function which when maximised
computes the allocation by considering not only the immediate store needs, but
also its future expected demand. Such forward-looking allocation significantly
improves the labour and trailer utilisation at the warehouse. To reduce
overstocking, we adapt from our objective to prioritise allocating those items
in excess which are sold faster at the stores, keeping the days of supply (DOS)
to a minimum. For the proposed formulation, which is an instance of Mixed
Integer Linear Programming (MILP), we present a scalable algorithm using the
concepts of submodularity and optimal transport theory by: (i) sequentially
adding trailers to stores based on maximum incremental gain, (ii) transforming
the resultant linear program (LP) instance to an instance of capacity
constrained optimal transport (COT), solvable using double entropic
regularization and incurring the same computational complexity as the Sinkhorn
algorithm. When compared against the planning engine that does the allocation
only for immediate store needs, INVALS increases on an average the labour
utilization by 34.70 and item occupancy in trailers by 37.08. The DOS
distribution is also skewed to the left indicating that higher demand items are
allocated in excess, reducing the days they are stocked. We empirically
observed that for ~ 90% of replenishment cycles, the allocation results from
INVALS are identical to the globally optimal MILP solution
Mixed Voltage Angle and Frequency Droop Control for Transient Stability of Interconnected Microgrids with Loss of PMU Measurements
We consider the problem of guaranteeing transient stability of a network of
interconnected angle droop controlled microgrids, where voltage phase angle
measurements from phasor measurement units (PMUs) may be lost, leading to poor
performance and instability. In this paper, we propose a novel mixed voltage
angle and frequency droop control (MAFD) framework to improve the reliability
of such angle droop controlled microgrid interconnections. In this framework,
when the phase angle measurement is lost at a microgrid, conventional frequency
droop control is temporarily used for primary control in place of angle droop
control. We model the network of interconnected microgrids with the MAFD
architecture as a nonlinear switched system. We then propose a
dissipativity-based distributed secondary control design to guarantee transient
stability of this network under arbitrary switching between angle droop and
frequency droop controllers. We demonstrate the performance of this control
framework by simulation on a test 123-feeder distribution network.Comment: American Control Conference (ACC), 202
A scalable solution for the extended multi-channel facility location problem
We study the extended version of the non-uniform, capacitated facility
location problem with multiple fulfilment channels between the facilities and
clients, each with their own channel capacities and service cost. Though the
problem has been extensively studied in the literature, all the prior works
assume a single channel of fulfilment, and the existing methods based on linear
programming, primal-dual relationships, local search heuristics etc. do not
scale for a large supply chain system involving millions of decision variables.
Using the concepts of sub-modularity and optimal transport theory, we present a
scalable algorithm for determining the set of facilities to be opened under a
cardinality constraint. By introducing various schemes such as: (i) iterative
facility selection using incremental gain, (ii) approximation of the linear
program using novel multi-stage Sinkhorn iterations, (iii) creation of
facilities one for each fulfilment channel etc., we develop a fast but a tight
approximate solution, requiring
instances of optimal transport problems to select k facilities from m options,
each solvable in linear time. Our algorithm is implicitly endowed with all the
theoretical guarantees enjoyed by submodular maximisation problems and the
Sinkhorn distances. When compared against the state-of-the-art commercial MILP
solvers, we obtain a 100-fold speedup in computation, while the difference in
objective values lies within a narrow range of 3%