This paper proposes a novel adaptive model reduction method for multi-input multi-output (MIMO) linear time-invariant (LTI) systems. The method integrates the Takenaka-Malmquist (TM) systems with the Multiple Signal Classification (MUSIC) algorithm. First, a novel frequency-domain sampling scheme preserving conjugate symmetry is introduced, which enables seamless integration of TM basis functions with the MUSIC algorithm. Second, the MUSIC algorithm is reinterpreted from direction-of-arrival (DOA) estimation to dominant pole selection. In this framework, source directions correspond to pole positions, and the number of sources corresponds to the reduced order. This enables adaptive, non-iterative pole selection, automatic order determination via eigenvalue energy ratio, and real-valued computation via persymmetrization. Moreover, when the dominant poles appear in complex conjugate pairs, the corresponding coefficient matrix exhibits conjugate symmetry, ensuring that the resulting reduced-order model has real coefficients. Theoretical guarantees of stability, steady-state preservation, and H_2 space membership are provided without state-space conversion. Numerical examples demonstrate high accuracy, efficiency, and robustness.
We extend an existing mixed-integer linear programming model that determines a cost-minimal set of conventional and renewable technologies and their corresponding dispatch at hourly fidelity to include: (i) multiple years of electrical demand, (ii) multiple investment opportunities, and (iii) technology degradation. Solving the monolithic formulation proves to be computationally inefficient. We utilize a Lagrangian decomposition methodology in which yearly subproblems are solved individually (and in parallel). An upper bound derived via optimization-based heuristics assesses solution quality against a linear-programming-based lower bound. Across twelve case studies involving decades-long planning horizons and projected electrical loads in distributed-generation (college campus) settings, the decomposed model achieves objective values within 0.5
Effective channel assignment is essential to optimising satellite communication networks. Although traditionally modelled as a graph colouring or disjunctive scheduling problem, such approaches fall short of addressing contemporary user demands and the increasing complexity of operations in congested electromagnetic environments. This paper extends the standard channel assignment problem by introducing cumulative interference constraints arising from overlapping frequency intervals with heterogeneous bandwidths and non-symmetric interference powers. The model represents a flexible, digitally channelised satellite communication network employing a single-channel-per-carrier waveform. To address the challenges posed by this extension, we integrate constraint programming and operations research techniques to develop matheuristic algorithms that exploit problem-specific relaxations and decompositions. Through experimental analysis, we evaluate the effectiveness of our algorithms and examine the relative strengths and limitations of each approach, providing a foundation for future research into resource allocation in large-scale, complex satellite communication constellations.
The conductance problem and its special cases—the Cheeger constant and graph expansion—are NP-hard graph partitioning problems. Hochbaum, Hochbaum (2024), recently introduced the Incremental Parametric Cut (IPC) algorithm, which solves a relaxation of the conductance problem, the conductance* problem, as well as other “monotone” ratio problems, in the complexity of a single minimum cut on a related graph. IPC is not only theoretically efficient but also very fast in practice, as demonstrated here and in a previous experimental study for the densest subgraph problem. A large number of other heuristic techniques have been proposed for the conductance problem and its special cases. These include spectral methods Fiedler Sweep, PR-Nibble Sweep, and ACL Sweep; flow-based refinement approaches such as MQI, Flow Improve, and the Simple Local algorithm; and graph partitioning methods that construct a partition with a small balanced cut value, such as the one provided by METIS. We present the first publicly available implementation of IPC for conductance*, together with an extensive experimental study comparing its performance against state-of-the-art techniques, including several spectral method implementations, several flow-based methods, and METIS. The study demonstrates that IPC achieves dramatically faster running times than any competing method, while also producing new best-known conductance values for many benchmark graphs.
We consider the problem of operating a battery in a home connected to the grid to minimize electricity cost, which combines an energy charge and a tiered peak power charge based on the average of the N largest daily peak powers in each billing month. With perfect foresight of loads and prices, the minimum cost is the solution of a mixed-integer linear program (MILP), which provides a lower bound on the cost of any implementable policy. We propose a model predictive control (MPC) policy that uses simple forecasts of loads and prices and solves a small MILP at each time step. Numerical experiments on one year of data from a home in Trondheim, Norway, show that the MPC policy attains a cost within 1.7% of the prescient bound, and saves close to three times as much as the best rule-based policy we consider.
