Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2204.01084

On Polynomially Solvable Constrained Input Selections for Fixed and Switched Linear Structured Systems

Yuan Zhang·Yuanqing Xia·Shenyu Liu·Zhongqi Sun
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the inputs of the smallest possible cost with a bound on their cardinality, all to ensure system structural controllability. Those problems have attracted much attention recently; unfortunately, they are NP-hard in general. In this paper, it is found that, if the input structure satisfies certain `regularizations', which are characterized by the proposed restricted total unimodulairty notion, those problems can be solvable in polynomial time via linear programming (LP) relaxations. Particularly, the obtained characterizations depend only on the incidence matrix relating the inputs and the source strongly connected components (SCC) of the system structure, irrespective of how the inputs actuate states within the same SCC. They cover all the currently known polynomially solvable cases (such as the dedicated input case), and contain many new cases unexploited in the past, among which the source-SCC separated input (SSSI) constraint is highlighted. Further, for switched systems, the obtained polynomially solvable condition (namely the joint SSSI constraint) does not require each of the subsystems to satisfy the SSSI constraint. We achieve these by first formulating those problems as equivalent integer linear programmings (ILPs), and then proving total unimodularity of the corresponding constraint matrices. This property allows us to solve those ILPs efficiently via LP-relaxation. We also discuss solutions obtained via LP-relaxation and LP-rounding in the general case. Several examples are given to illustrate the obtained theoretical results.

Explore related subjects

eess.SYcs.SY

Keep this discovery

BibTeXRIS

Yuan Zhang, Yuanqing Xia, Shenyu Liu, Zhongqi Sun. 2022-04-03. On Polynomially Solvable Constrained Input Selections for Fixed and Switched Linear Structured Systems. https://arxiv.org/abs/2204.01084

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Structured Stochastic Representations of Integrated Dynamic Strategies

Dynamic allocation decisions couple present resource use to evolving internal conditions, delayed returns, and future costs. We represent this interaction by four probability localizations linked through regime-indexed, graph-constrained column-stochastic operators. Pre-action state or context selects a locally affine model, while action-dependent changes update subsequent regimes, yielding a causal switched representation of nonlinear evolution. We characterize operator identifiability relative to the graph, the stochastic constraints, and the sampled embedding, separating coefficient recovery from predictive equivalence on the decision domain. Decision making is then formulated through implementable return--cost acceptability regions. Finite-horizon error propagation supplies conservative classification margins, and simultaneous intervals distinguish model-relative near-optimality from certified $\epsilon$-optimality over a declared finite policy class. Regime-indexed stochastic feedback is admitted when it satisfies the same certification test. Reproducible synthetic laboratories for personal preparation, supplier participation, and customer retention illustrate exact, operator-supplied, and noisy feedback cases. Multinomial experiments show improving recovery of the feedback function and fewer unresolved decisions with increasing sample size, while unrestricted off-policy recovery remains limited. The contribution is a structure-preserving representation--identification--decision workflow, not a domain-specific physiological or commercial calibration.

eess.SY↗
arXiv2026

Fusion Estimation in Multi-sensor Systems for Data Packets with Disrupted Identities

In this paper, we explore the problem of fusion estimation for a multi-sensor system where the identity of the data packet received by each sensor may be disrupted or incorrect due to confusion in device identity allocation, communication protocol defects, or the lack of a clear sensor identifier. This can result in a random shuffle of the data components during the fusion estimation process, compromising the performance of the fusion estimation. To address this issue, we introduce the concepts of permutations and symmetry groups to describe this phenomenon as data packet permutation. We construct statistics to simplify the information set, developing two algorithms: a Bayesian approach, which performs fusion using posterior arrangement probabilities, and a greedy approach, which effectively improves estimation performance by guessing the likely data arrangement. We compare these two algorithms and demonstrate that both are expectation error-bounded. We improve algorithms for information-scarce scenarios. By employing the expectation-maximization algorithm, we fill in the prior information of data arrangement where the correct convergence is proven. Finally, we present numerical simulations to validate our results.

eess.SY↗
arXiv2026

Quantifying the Reality Gap for RL-Based UAV Placement at mmWave and Sub-THz

Reinforcement learning (RL) policies for unmanned aerial vehicle (UAV) placement in mmWave and sub-terahertz networks are typically trained on simplified analytical channels. We quantify the resulting sim-to-real gap on a real urban map of Doha, Qatar, at carriers {28, 140, 183, 300} GHz and altitudes {50, 75, 100, 125} m, evaluating three channel pipelines: an analytical model (FSPL + atmospheric absorption + cuboid LoS), full Monte-Carlo ray tracing in Sionna RT with ITU-R P.676-13 absorption, and a deterministic-LoS hybrid that reuses Sionna's mesh under a closed-form path-gain expression. We formalize the gap on the spatial SNR distribution via four metrics, namely bias, RMSE, Jensen-Shannon divergence, and optimum-deployment displacement. Three findings emerge: at 28/140 GHz, $\sim$70% of the apparent -5.6/-4.8 dB Sionna bias is Monte-Carlo undersampling and shrinks to -1.7/-1.5 dB after mitigation; at 183 GHz a -9.2 dB residual isolates the atmospheric absorption / ITU-R P.676 line-shape disagreement; at 300 GHz the stochastic ray tracer agrees with the analytical model only coincidentally, with a +3.8 dB structural offset exposed by the deterministic-LoS pipeline. Across all carriers the linear-domain regret of the analytical-trained policy stays $\geq$ 0.93, indicating practical near-optimality but with a carrier-resolved SNR bias that warrants explicit reporting.

eess.SY↗