Search Results (71)

The increasing computational demands of artificial intelligence (AI) inference at the edge require hardware accelerators capable of overcoming the von Neumann bottleneck while operating under power constraints. Conventional digital architectures based on multiply–accumulate (MAC) units are limited in energy efficiency and scalability for resource-constrained applications. This work presents a proof-of-concept AI accelerator based on analog frequency–domain computation implemented within a semi-systolic array architecture. The proposed approach exploits frequency mixing to perform multiplication and accumulation operations in hardware, enabling the execution of matrix–matrix operations, which constitute the General Matrix Multiplication (GEMM) methods that dominate the computational workload of convolutional and fully connected neural networks. The proposed system consists of a custom printed circuit board controlled by an ATmega328P microcontroller(Microchip Technology Inc., Chandler, AZ, USA) and a software stack designed to interface with standard machine learning frameworks such as PyTorch. The software layer enables neural network operations, including convolutional and fully connected layers, to be mapped onto hardware-executed matrix–matrix computations through an abstraction analogous to the General Matrix Multiplication (GEMM) functionality provided by Level-3 Basic Linear Algebra Subprograms (BLAS). Matrix multiplication and accumulation are partly performed directly by the hardware processing elements, while the software control unit coordinates data movement and computation scheduling. Although bias operations are not implemented in the current prototype, their comparatively low computational cost makes them less critical to the overall acceleration strategy. A quantization-aware mapping methodology constrained by analog-to-digital and digital-to-analog converter specifications is introduced to translate neural network operations into frequency–domain computations. The paper further describes the hardware architecture, communication protocols, software stack organization, and interactions between system components. In addition, the effects of analog nonidealities and error sources associated with frequency–domain multiplication are investigated, and simulations of the proposed processing elements are presented to evaluate the computational approach. Experimental and simulation results demonstrate the feasibility of performing dense linear algebra operations through analog frequency–domain processing and validate the operation of the processing elements. The study further explores converter resolution, frequency interference, and analog component nonidealities and provides a comparison with conventional digital and other low-power accelerator approaches. The results indicate that exploiting the inherent parallelism of analog computation offers a promising pathway toward ultra-low-power AI inference, making the proposed architecture a potential alternative for energy-constrained edge applications. Full article

Embedded systems increasingly require on-device deep learning, yet their processors must simultaneously handle real-time sensing, networking administration, and data control. Existing Field-Programmable Gate Array (FPGA) accelerators typically target peak per-operator throughput without addressing concurrent execution demands of real-time embedded platforms. This paper presents a systolic array-based accelerator prototype implemented on the Zynq-7000 SoC integrated directly into PyTorch, enabling dense linear algebra to be delegated to the FPGA chip while Cortex-A9 continues executing the software stack uninterrupted. Unlike traditional accelerators optimized for peak per-operator speed, this design prioritizes asynchronous co-executionbetween the processing system (PS, the dual-core Cortex-A9) and the programmable logic (PL): The PL performs tiled matrix multiplication, while the PS executes preprocessing, orchestration, and I/O data concurrently, increasing effective end-to-end throughput regardless of the relative isolated performance of CPU and FPGA. The proposed module includes high-level-synthesis (HLS)-based matrix multiplication, activation functions, and Advanced eXtensible Interface (AXI)-Stream Direct Memory Access (DMA) interfaces, wrapped as custom PyTorch kernels under the PetaLinux operating system. The results obtained on the PYNQ-Z2 board show that, once the DMA transfer time is included in the measurement, the FPGA path does not surpass Cortex-A9 in isolated per-operator latencies across the evaluated range; the benefit lies instead in delegating the matrix compute to the fabric at low incremental power while the host CPU cores stay available for concurrent tasks. A concurrent workload sweep across matrix sizes from $8\times 8$ to $256\times 256$ confirms that the co-execution mode sustains 98–99% of available PS compute throughput compared with a constant ≈50% in single-core blocking mode; the difference is statistically significant for all evaluated sizes (see Mann–Whitney U: $U=25$, $p=3.97\times {10}^{-3}$, perfect discrimination, $n=5$). A fair dual-core CPU-only baseline attains comparable PS availability, so this figure reflects the dual-core scheduling that co-execution enables rather than a per-operator advantage of the fabric; the accelerator’s distinct role is to perform the matrix arithmetic off the general-purpose cores at low incremental power. The design occupies only 8% of available look-up tables (LUTs) and 5% of digital signal processing (DSP) blocks, maintains 1.69 W power with a junction temperature of 44.5 °C, and achieves 96.10% MNIST accuracy under fixed-point arithmetic. Full article

Continuous-time orthogonal basis functions play a fundamental role in system identification, signal approximation, model reduction, and control, where compact and numerically efficient representations of dynamical systems are required. Most existing constructions are based on predefined frequency-domain basis functions and their associated pole configurations. This paper introduces a novel state-space framework for the construction of continuous-time orthogonal and biorthogonal systems by characterizing orthogonality directly through the dynamics of stable linear systems. The central result shows that orthogonality can be enforced by a Lyapunov-type matrix condition linking the system matrix and the initial state, thereby enabling the systematic generation of orthogonal basis functions as state trajectories. The proposed framework naturally encompasses the classical Laguerre and Kautz systems as special cases while providing substantially greater design flexibility through the independent parametrization of system matrices and initial conditions. It is further extended to output-orthogonal, state-biorthogonal, and output-biorthogonal systems, yielding a unified state-space formulation of orthogonal and dual functional representations. In addition, new algebraic formulations of convolution and signal decomposition are derived, leading to explicit coefficient relations expressed through Lyapunov and Sylvester matrix equations. The applicability of the proposed framework is demonstrated through numerical examples in system identification, model reduction, and optimal control. The results show that the additional parametrization freedom enables orthogonal representations that are better adapted to oscillatory and weakly damped dynamics while preserving the computational advantages of orthogonal-function-based approaches. Full article

Turbofan engines exhibit complex nonlinear dynamics across the entire flight envelope, which cannot be captured by explicit mathematical models, posing significant challenges for engine controller design. Traditional control designs often rely on multiple linearized models covering the entire operating range, which require designing multiple linear controllers and gain-scheduling strategy to switch these sub-controllers. This article aims to establish a global nonlinear affine model-based feedforward control method for turbofan engines, and the control input can be efficiently obtained through simple algebraic calculations with given reference signal. In this method, the nonlinear affine model via a multi-layer perceptron (MLP) combined with polynomial feature expansion is constructed based on engine model simulation data. With this affine model, the need for the cumbersome design process of multiple linear controllers and their sub-controller switching can be avoided. Additionally, a Proportional–Integral (PI) feedback controller is integrated with the feedforward controller to eliminate tracking errors caused by model mismatches and disturbances. Numerical simulation results verify that the proposed MLP model has high identification accuracy, and the composite control strategy can simplify the control design. During the acceleration/deceleration process between intermediate and idle state, the high-pressure rotor speed overshoot is less than 0.01%, and the settling time is less than 2.6 s, outperforming the 4.1 s of the gain-scheduled PI controllers. Full article

This paper proposes a construction of algebraically stabilizing blocks for quantized and finite-precision neural networks. The approach is based on linear transformations defined by integer-valued matrices satisfying a condition of the form $W^k=I+\mu D$, which specifies algebraically controlled $k$-step behavior and modular periodicity in the integer-valued setting. The proposed property is invariant under conjugation, allowing the stabilizing construction to be transferred across equivalent linear representations. The resulting module can be integrated locally into existing neural architectures without requiring the algebraic structure to be imposed globally. The theoretical results concern algebraic and modular stabilization of the linear block and do not constitute a general guarantee of classical spectral or asymptotic stability in real-valued space. The approach is evaluated experimentally under multi-component harmonic, impulsive, and noisy inputs in both floating-point and INT8-quantized settings. Across several experimental configurations, the proposed block reduces output energy, component-wise variation, selected amplitude-related measures, and finite-precision deviation relative to floating-point reference trajectories. Norm-matched control experiments further suggest that the observed effects are not attributable solely to a reduction in operator magnitude, but may also reflect structural properties of the algebraically constructed operator. The proposed construction is particularly relevant to neural systems operating under limited numerical precision, including FPGA-, ASIC-, and edge-oriented implementations. It provides a structural approach for incorporating formally specified algebraic properties into the design of neural-network architectures. Full article

The increasing integration of wind power reduces the equivalent inertia of power systems, leading to lower frequency nadirs and higher rate of change of frequency following disturbances. In Type-4 wind turbine systems, conventional maximum power point tracking (MPPT) may counteract the additional inertial power command during frequency support and cause secondary frequency dips during rotor-speed recovery. To address these issues, this paper proposes a virtual-inertia rate-of-change-of-frequency (VI-RoCoF) frequency-modulated Andronov-Hopf oscillator (AHO)-based adaptive inertia enhancement method together with an adaptive MPPT coordination strategy. The proposed method constructs a frequency-support demand from frequency deviation and VI-filtered RoCoF and embeds it into the instantaneous angular-frequency evolution of the AHO. Different from a conventional linear virtual-inertia controller that directly converts frequency-deviation and RoCoF signals into an algebraic power command, the proposed method realizes the additional support through a bounded limit-cycle frequency-forming process, thereby preserving phase continuity and nonlinear amplitude self-regulation during frequency modulation. Meanwhile, the adaptive MPPT strategy adjusts the power reference in stages to suppress the counteractive effect of conventional MPPT on inertial support and to ensure a smooth transition back to maximum power point tracking. Theoretical analysis shows that the proposed modulation maintains the limit-cycle stability of the AHO under bounded control constraints while improving the equivalent inertia and damping characteristics of the system. Simulation results, including both averaged-model and switching-level SPS simulations, demonstrate that, compared with conventional AHO-based, fixed-inertia AHO-based, and linear VI-RoCoF benchmark schemes without AHO dynamics, the proposed AHO-MPPT coordinated control strategy increases the frequency nadir, reduces the peak RoCoF, improves recovery-stage frequency dynamics, mitigates secondary frequency dips, maintains bounded AHO internal variables, and preserves DC-link voltage stability. Full article

We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation as a geometry induced by a self-adjoint positive semidefinite operator acting on a latent Hilbert space. A system is represented as a triple $(\mathcal{H},\mathsf{\Pi },O),$ where $\mathcal{H}$ denotes a latent representation space, $\mathsf{\Pi }⪰0$ is an observation operator, and $O\left(v\right)=⟨v,\mathsf{\Pi }v⟩$ defines an induced scalar observable. The framework characterizes observability through the quotient geometry $\mathcal{H}/ker\left(\mathsf{\Pi }\right),$ which represents equivalence classes of latent states that are indistinguishable under observation. From this perspective, observable behavior is governed not by latent representations themselves, but by the geometry induced through the observation operator. We show that both quantum measurement and representation inference under linear observation models can be formulated within this common operator-theoretic structure while differing in the algebraic properties of their observation operators. Within this perspective, quantum measurement serves primarily as a mathematically canonical example of projection-mediated observability. The correspondence developed in PPS is therefore structural rather than physical. Within the same framework, representation transfer and knowledge distillation can be interpreted as approximate preservation of observable geometry through the intertwining condition $\mathsf{\Phi }{\mathsf{\Pi }}_T\approx {\mathsf{\Pi }}_S\mathsf{\Phi }.$ PPS further reveals a structural limitation of output-based interpretability: latent components contained in $ker\left(\mathsf{\Pi }\right)$ are fundamentally inaccessible from observables generated through the induced observation process. Accordingly, attribution and explanation methods inherit intrinsic constraints imposed by the observation geometry itself. We provide controlled empirical validations demonstrating kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. Overall, PPS provides a mathematically explicit characterization of observability through operator-induced quotient geometry, offering a unified perspective on representation accessibility, interpretability, and representation transfer. Full article

This paper presents a novel optimal control-based beamforming framework for phased antenna arrays, targeting advanced wireless communication and radar applications, including 5G systems. Unlike conventional beamforming techniques, such as Fourier-based methods and adaptive algorithms (e.g., LMS and RLS), the proposed approach formulates the beam synthesis problem as a discrete-time optimal control problem. The antenna array is modeled using a state-space representation, and a quadratic cost function is introduced to jointly minimize the deviation from a desired radiation pattern and the excitation power. The optimal excitation weights are derived using the Linear Quadratic Regulator (LQR) framework by solving the discrete-time algebraic Riccati equation. This formulation enables an effective trade-off between sidelobe suppression, main lobe accuracy, and power efficiency. Simulation results demonstrate that the proposed method achieves a well-focused main beam, significantly reduced sidelobe levels, and improved directivity compared to conventional approaches. Furthermore, the framework offers robustness and computational efficiency, making it a promising candidate for future FPGA and embedded implementations. Overall, the proposed optimal control-based beamforming approach provides a flexible, robust, and computationally efficient solution for next-generation antenna systems in 5G, beyond-5G (B5G), and radar applications. Full article

The Linear Equivalence Signature Scheme (LESS) is a code-based post-quantum candidate in the National Institute of Standards and Technology’s (NIST) standardization process for additional digital signatures. In this paper, we present an area-efficient FPGA accelerator for the Reduced Row Echelon Form (RREF) kernel of LESS, designed for embedded RISC-V SoCs where resource overhead is the primary constraint. Our architecture targets the scheme’s primary computational bottleneck: the linear-algebra core responsible for RREF processing. By implementing an optimized pivot-reuse workflow, our design significantly reduces redundant row-reduction operations across related computations. The accelerator features a matrix-oriented execution engine paired with a streaming control interface to minimize synchronization overhead. Implementation on a Xilinx Artix-7 FPGA shows that despite its compact footprint, the accelerator achieves up to 21× speedup over the embedded software RREF baseline. By prioritizing a minimalist footprint, our design requires only 1.38 to 8.7 KeSlice, depending on the targeted security level. By covering all LESS security levels and providing comparisons with existing post-quantum cryptographic hardware, this work establishes a performance baseline for a signature scheme that has remained largely unexplored in the hardware domain. Full article

The concept of an extended PID controller is introduced. This controller combines the properties of two well-known variants of the classical PID controller. The extended PID controller includes two additional parameters in addition to the three parameters of the classical PID controller. Its properties are examined using the yaw channel of a rocket angular stabilization system equipped with an extended PID controller. Linearized equations of motion for the yaw channel of the rocket angular stabilization system with the extended PID controller are formulated. The transfer function of the rocket angular stabilization system and its characteristic polynomial are obtained. Stability and performance indices of the rocket angular stabilization system are introduced. These indices are determined from the coefficients of the characteristic polynomial and are expressed directly in terms of the parameters of the extended PID controller of the stabilization system. Based on sufficient conditions for stability and performance of the stabilization system, systems of algebraic inequalities are derived with respect to the required values of the control-law parameters that satisfy the stability and performance requirements of the stabilization system. It is shown that the set of their solutions is nonempty. It is demonstrated that the introduction of additional extension parameters into the classical PID controller makes it possible to vary the zeros of the transfer function of the stabilization system. This enables the stability and performance requirements of the rocket angular stabilization system to be satisfied independently of one another. At the same time, by varying the additional parameters, the zeros of the transfer function of the stabilization system can be made equal to its poles. This changes the structure of the transfer function by reducing its order by two. Numerical experimental studies of the dynamics of the rocket angular stabilization system are carried out using the technical characteristics of the developed test bench for the rocket angular stabilization system. The results confirm the high effectiveness of the extended PID controller: (1) the transient response retains an aperiodic character, which follows directly from the form of the transfer function of the extended PID controller, and (2) the settling time is reduced by a factor of 7.53 compared with the classical PID controller. Full article

Large language models (LLMs) built upon the Transformer architecture have achieved remarkable performance in natural language understanding, text generation and logical reasoning, while their internal working mechanisms remain poorly interpreted. This paper establishes a systematic mathematical analysis framework tailored for decoder-only Transformer LLMs, based on linear algebra, tensor analysis, probability theory, information theory, optimization dynamics and geometric deep learning. We conduct rigorous mathematical modeling and theoretical deduction on core modules including word embedding, position encoding, self-attention, feed-forward networks, training optimization and generalization reasoning, and explore the mathematical nature of semantic representation, contextual correlation, knowledge storage and logical inference within models. In this paper, we strictly distinguish between classic established Transformer theories and our original mathematical derivations and conclusions. Distinct from existing fragmented theoretical studies, this work presents six targeted novel contributions beyond conventional Transformer theories: (1) we construct the first full-process unified mathematical framework covering all core modules and the entire lifecycle of Transformer-based LLMs; (2) we provide strict mathematical proof to verify that single-head self-attention is essentially a kernel weighted average operation in reproducing kernel Hilbert space and derive the low-rank and sparse properties of attention weights; (3) we establish a high-dimensional non-convex optimization dynamics model for pre-training and mathematically prove that model training converges to flat local minima; (4) we derive a tighter upper bound of generalization error and quantify the quantitative relationship among model parameters, sequence length, training data scale and generalization performance; (5) we characterize the latent space as a low-curvature smooth Riemannian manifold and model logical reasoning as geometric transformation on this manifold; (6) we design multi-group controlled experiments on mainstream datasets to quantitatively validate all above theoretical conclusions. This paper further summarizes the inherent mathematical limitations of current Transformer LLMs and proposes feasible theoretical optimization paths, referring to state-of-the-art research published from 2021 to 2026. The outcomes of this research can provide solid mathematical theoretical support for improving model interpretability, optimizing network structures and boosting practical performance, and facilitate the transition of LLM research from empirical engineering practice to theory-driven development. Full article

Efficient task assignment for mobile robots is a crucial challenge in modern intralogistics. This paper presents an integrated cyber-physical framework combining predictive tree search on switching max-plus linear systems with a physical IoT-based dispatch interface. The scheduling problem is modelled as a discrete event system, where standard max-plus algebra captures robot synchronization, and a switching mechanism represents alternative resource assignments. To address real-world operational disturbances, the predictive model is enhanced with a fault-tolerant control (FTC) mechanism that dynamically estimates and adapts to non-stationary transport delays. The resulting decision space, which grows exponentially with the prediction horizon, is explored via a predictive tree search algorithm utilizing a quadratic cost function to penalize excessive and uneven transport times. The physical dispatch layer is realized using KIS.BOX IoT devices acting as operator-controlled stations, communicating with the central controller via a WebSocket/STOMP event stream and a lightweight REST API. Simulation results obtained in a Blender 3D environment demonstrate that the proposed FTC predictive strategy significantly reduces the variance of task completion times under fault conditions compared to a baseline First-In-First-Out approach. Furthermore, the IoT integration successfully simulates and validates the feasibility of human-in-the-loop task injection within a realistic, stochastic scenario. Full article

Modeling and controlling multilayer complex network dynamics is challenging under coexisting crosslayer interactions, higher-order couplings, and decentralized strategic decisions. Most existing schemes focus on graph-based pairwise structures and overlook topological cavities, mesoscale loops, and layered self-interested actions. This paper presents TopoGame-MND, an algebraic-topological and game-theoretic framework for multilayer network dynamics. We first build a filtration-driven simplicial lifting to unify pairwise and higher-order interactions into a weighted multilayer simplicial complex. A topological state operator using generalized Hodge Laplacians and persistent homology is then constructed to characterize cross-scale diffusion, circulation, and structural inconsistency. A distributed potential-game mechanism is developed with a topology-aware utility, followed by a proximal mirror-best-response algorithm with consensus correction. We prove Nash equilibrium existence and uniqueness, global potential monotone descent, linear convergence, computational complexity, and input-to-state robustness. Simulations on multiplex and interdependent networks validate that TopoGame-MND outperforms baselines in regulation speed, oscillation energy, failure resilience, and robustness, providing a unified way to connect higher-order topology and distributed decision optimization. Full article

Unmanned Aerial Vehicles (UAVs) are complex nonlinear systems characterized by high dimensionality. They are prone to aerodynamic effects, structural dynamics, actuation constraints, and networked interactions, requiring advanced mathematical models and precise control. Their governing equations involve nonlinear rigid-body dynamics coupled with fluid and elasticity models, while modern architectures introduce redundancy that creates constrained mappings between generalized forces and actuator inputs. Coordinated UAV teams add another layer of mathematical structure through graph-based interaction models that determine consensus, formation keeping, and distributed stability. These characteristics give rise to several interconnected challenges. High-fidelity aerodynamic and aeroelastic solvers provide accurate results; however, these are computationally intensive, motivating the development of reduced-order models and data-driven approximations that preserve dominant physical behavior. Methods for quantifying uncertainty support robustness assessments by characterizing the effects of parametric variation and model form error. At the actuation level, control allocation problems rely on constrained linear algebra, convex optimization, and dynamic formulations to ensure feasible and stable realization of command forces and moments. In multi-agent systems, the spectral properties of adjacency and Laplacian matrices govern convergence and cooperative behavior. This article reviews the state of the art in these areas, highlights the mathematical foundations that relate them, and provides a coherent perspective on the methods that enable reliable modeling and control of modern UAV systems. Full article

Under the dual carbon strategy and the sweeping tide of digital transformation in education, higher education confronts an urgent imperative: cultivating talent equipped with interdisciplinary skills and sustainable decision-making capabilities. To meet this critical challenge, this study pioneers the PAMD (Patient Capital–Accounting–Matrix–Development) interdisciplinary teaching framework. Rooted firmly in Education for Sustainable Development (ESD) principles, PAMD uniquely weaves together patient capital, carbon asset accounting, and linear algebra matrix modeling. Utilizing a quasi-experimental design with undergraduate business students, we implemented “Carbon Asset Accounting and Low-Carbon Transition Investment Analysis” as a case study. We rigorously evaluated teaching effectiveness across academic performance, competency, and cognitive attitude dimensions using Welch’s t-test, Hedges’ g, and ANCOVA. After controlling for baseline scores, the experimental group significantly surpassed the control group in comprehensive decision-making (81.22 vs. 72.41, g = 0.71) and matrix modeling competency (3.74 vs. 3.22, g = 0.77). The experimental cohort also demonstrated consistent gains in carbon accounting reporting precision and data representation clarity. Cognitive assessments revealed moderate effect sizes for both low-carbon investment literacy and interdisciplinary learning interest. These compelling results demonstrate that embedding a long-term value orientation into accounting representation and matrix modeling powerfully cultivates students’ ability to transfer interdisciplinary knowledge and make sound sustainable decisions within complex contexts. This study offers a robust, evidence-based, and replicable pathway for driving sustainability-oriented interdisciplinary reform within business education. Full article