This paper introduces a novel 2D fractional sine-cosine (2D-FSC) hyperchaotic map and its application in a robust image encryption scheme. Through comprehensive dynamic analysis including bifurcation diagrams, Lyapunov exponents, butterfly effect, Shannon entropy, and phase space visualization, it is demonstrated the map's superior chaotic characteristics compared to conventional 1D chaotic systems. The proposed encryption framework employs a three-stage diffusion-permutation-confusion architecture enhanced by two key innovations: (1) a genetic algorithm optimizing diffusion and confusion processes to maximize entropy (7.998 +/- 0.002) and minimize correlation coefficients (|cc| < 0.004) of the encrypted image, and (2) a novel chaos-based pixel fusion technique for efficient bit-level permutation. Hardware implementation on a Cyclone IV FPGA (6057 logic elements, 34.29 MHz max frequency) validates the practical feasibility of the chaotic map. Security analysis confirms resistance against brute-force (key space > 2(750)), statistical (chi(2) < 184.2), differential (NPCR 99.61 +/- 0.04 %, UACI 33.46 +/- 0.09 %), and noise/clipping attacks. The algorithm processes 256x 256 images in 0.32 s which is 28-42 % faster than comparable schemes, while maintaining consistent performance across grayscale, color, and edge-case images. These advancements establish a new benchmark for chaos-based cryptosystems in applications requiring both high security and computational efficiency.
Conventional fault-tolerant control (FTC) schemes typically assume the exponent of the faulty input to be 1, overlooking its impact on actuator power. In this article, we propose a novel FTC strategy that extends the exponent to any positive odd integer, thus capturing higher-order fault effects. In addition, by integrating a Gaussian function to modify the constraint boundaries, a novel suction-cup-type prescribed performance function is proposed. Unlike existing prescribed performance functions, this design uses a suction cup module to regulate output overshoot without requiring asymmetric design. This design is globally effective, eliminating the initial feasibility conditions. Simulation results validate the effectiveness of the proposed scheme.
We study inequalities involving convex functions and positive linear operators and interpret them within the framework of convex stochastic order <=(cx). Our approach is operatorial in nature and provides a unified view of such inequalities involving several classical approximation processes. By considering a broad class of positive linear operators, we obtain new inequalities that describe dominance between the corresponding induced measures. In addition to the direct problem, showing that the convexity of a function f implies inequalities of the type L(n)f >= M(n)f, we also consider the inverse problem: given f and a suitable family of measures mu <=(cx) nu satisfying integral f d mu <= integral f d nu, does it follow that f must be convex? This inverse problem is particularly challenging. As an illustrative example, we ask whether, for f is an element of C[0, infinity), the condition S(t)f <= V(t)f for all t > 0, where S-t and V-t denote the Szasz-Mirakjan and classical Baskakov operators respectively, necessarily implies the convexity of f.
Resource-constrained Internet of Things (IoT) devices are increasingly deployed in critical domains but remain vulnerable to stealthy attacks that can bypass conventional defenses. At the same time, privacy constraints limit centralized data collection and processing, complicating anomaly detection. This systematic review surveys methods for privacy-preserving anomaly detection in resource-constrained IoT and introduces a five-dimension taxonomy covering deployment paradigms, resource constraints, real-time requirements, protection techniques, and communication constraints. We review how the literature measures and reports resource and privacy costs and identify three major gaps: (1) a shortage of co-designed detector-plus-privacy solutions tailored to constrained hardware, (2) inconsistent reporting of resource and privacy trade-offs, and (3) limited robustness against adaptive attackers and realistic deployment noise. We conclude with actionable recommendations and a prioritized research roadmap. Furthermore, the multi-dimensional taxonomy we introduce provides a structured framework to guide design choices and systematically improve the comparability, deployability, and overall trustworthiness of anomaly detection systems for constrained IoT.
Fractional order controllers are more frequently encountered in industrial applications due to their robustness and the improved performance they offer to the system. A large majority of research papers focus on methods for tuning controllers that are robust to gain variations. A novel approach to the design of a robust fractional order PID controller to variations in the time constant is studied in this manuscript. The procedure mentioned is developed for a first order plus time delay system. The robustness criterion used in the control algorithm is based on partial derivatives. The nonlinear system of equations obtained from all the imposed performance criteria is solved using the graphical method. To prove the efficiency of the proposed strategy, numerical simulations and experimental validation of the resulting controller are performed on a model of the DC servo system. The experimental results explicitly prove that the controller is robust to time-constant variations within the range of ±70%.
