Overhead crane systems, which are inherently nonlinear and underactuated, demand controllers that simultaneously achieve precise trolley positioning, payload swing suppression, and disturbance robustness, yet existing Takagi–Sugeno fuzzy approaches suffer from an exponential growth in the number of fuzzy rules that severely limits their practical scalability. However, conventional Takagi–Sugeno (T–S) fuzzy approaches are fundamentally constrained by the exponential growth of fuzzy rules, causing the number of Linear Matrix Inequality (LMI) constraints and decision variables to increase as 2 r with the number of premise variables r . This paper addresses this limitation by exploiting the affine structure of the crane dynamics to derive an exact polytopic representation with only 2 × r submodels, avoiding both approximation errors and excessive computational burden. Based on the resulting RC–TS representation, a parallel distributed compensation (PDC) tracking controller is synthesized by solving a convex semidefinite optimization problem subject to LMI constraints derived from a quadratic Lyapunov function, guaranteeing closed-loop asymptotic stability with a prescribed decay rate. An L ∞ performance constraint is incorporated to bound the worst-case tracking error, while an Equal-Time-and-Magnitude (ETM) input shaper is integrated to attenuate residual oscillations. Simulation results demonstrate that the RC–TS model preserves the dynamics of the conventional T–S formulation while reducing the number of fuzzy rules from 2 6 = 64 to 2 × 6 = 12 . Five scenarios evaluate model equivalence, tracking and input shaping, disturbance rejection under collocated and non-collocated disturbances, and benchmark performance, demonstrating accurate tracking, oscillation suppression, and disturbance attenuation. Validation is limited to numerical simulations, and experimental verification remains for future work.
Antimicrobial resistance represents a critical global healthcare emergency, with carbapenem resistant Klebsiella pneumoniae (CRKP) standing as a leading pathogen responsible for severe clinical infections. This study develops a fractional-order susceptible–resistant–persister (SRP) mathematical model under the Caputo fractional derivative framework to characterize CRKP dynamics across three distinct bacterial subpopulations. The formulation accounts for memory-dependent fractional orders, nonlinear transmission, saturated antibiotic efficacy, plasmid-mediated resistant dynamics, and environmental bacterial influx. Analytical proofs using Mittag-Leffler functions and the Banach fixed-point theorem establish the positivity, boundedness, existence, and uniqueness of the system solutions. The effective reproduction number is derived, governing the global stability thresholds between the resistant-free and endemic steady states. Numerical simulations using the Adams–Bashforth-Moulton predictor–corrector method illustrate how variations in the fractional order alter resistant distribution and system memory. Furthermore, an optimal control framework is established using two intervention variables: infection prevention and treatment enhancement. The optimization aims to minimize the resistant CRKP population while balancing operational expenses. The optimal control analysis reveals that lower fractional-order values yield a higher averted resistant bacterial burden. Due to inherent memory characteristics, the system requires more intensive control efforts during the initial phase of the intervention, with all cost-effective strategies maintaining a low incremental cost-effectiveness ratio.
We formulate and analyse a Caputo fractional-order model of HIV/AIDS transmission that distinguishes oral from injectable pre-exposure prophylaxis and follows individuals through diagnosis, antiretroviral treatment, viral suppression, and treatment failure. The model extends an integer-order care-continuum structure by an undiagnosed infectious class, a treated-AIDS class, formulation-specific prophylaxis failure, and a single fractional order that encodes the memory of past exposure and treatment history, with every rate expressed in dimensionally consistent units. We prove non-negativity, boundedness, and existence and uniqueness of solutions, and we obtain the control reproduction number R0 in closed form from a next-generation matrix that includes the relapse loops of the care continuum; the expression does not contain the fractional order and, at the calibrated values, attributes about ninety-five percent of transmission to undiagnosed infection. The disease-free equilibrium is locally asymptotically stable when R0<1 and globally asymptotically stable under a condition that coincides with R0≤1 up to the baseline prophylaxis coverage, a unique endemic equilibrium exists exactly when R0>1, and a centre-manifold computation shows that the bifurcation at R0=1 is forward under an explicit condition satisfied with a wide margin, so that no bistable window exists and R0=1 is the operational elimination threshold. A fractional optimal control problem for PrEP promotion and adherence support is solved through Pontryagin’s principle with right Riemann–Liouville adjoints and a forward–backward sweep; the solution front-loads PrEP promotion and sustains adherence support over the planning horizon. Variance-based sensitivity analysis with a sparse polynomial chaos surrogate, a convergence study of the predictor–corrector scheme, and Bayesian calibration by Hamiltonian Monte Carlo with identifiability, prior-sensitivity, and model-comparison checks round off the study. The posterior of the fractional order excludes the integer-order value, and scenario analysis indicates that expanding injectable PrEP with sustained adherence support averts considerably more infections than expanding oral PrEP alone.
Hyperparameter optimization is widely used to improve deep-learning models, yet its practical benefits can be difficult to separate from noisy configuration selection and computational search cost. This study evaluates these issues for long short-term memory (LSTM), gated recurrent unit (GRU), and bidirectional LSTM (BiLSTM) architectures in turbofan remaining useful life prediction using the NASA C-MAPSS FD001 and FD003 subsets. Each architecture–subset pair received a nominal 50-evaluation Bayesian optimization (BO) budget under a frozen leakage-free preprocessing pipeline, followed by ten-seed evaluation. Additional analyses examined validation-objective sensitivity, candidate-selection noise, and an equal-budget random-search benchmark. BO reduced mean test RMSE relative to literature-derived baselines in five of six pairs, but none of these improvements remained significant after Holm correction. Although BO attained lower observed validation objectives than random search in five of six searches, the only statistically detected test-RMSE difference between optimizers favored random search for FD001 LSTM (Holm-adjusted p = 0.038). BO-selected configurations reduced mean per-run training time in all six pairs (approximately 26–76% in five pairs and 5.5% in the remaining pair). However, random-search selections were faster than BO-selected configurations in four of six pairs, and the six BO searches required approximately 14.74 hours of recorded training expenditure. The findings demonstrate that validation design, selection noise, and search cost materially affect the interpretation of hyperparameter optimization. Reliable RUL model comparisons therefore require multi-seed evaluation and explicit separation of predictive performance, selection uncertainty, and computational expenditure.
