Jinzhong Zhang

To address the challenges of lumped model uncertainties and tracking error constraints in biomimetic rehabilitation robot control, this paper proposes a novel high-order integral barrier function to construct an adaptive neural tracking control scheme. Radial basis function neural networks (NNs), inspired by the receptive field mechanism of motor neurons, feature local activation and can accurately approximate the nonlinear dynamics of such bionic rehabilitation devices. Distinct from traditional integral barrier Lyapunov functions, the presented high-order integral barrier function can accommodate both time-varying and time-invariant error constraints, while simplifying the controller derivation and ensuring full differentiability of virtual control laws throughout the backstepping framework. Supported by the derived barrier function theorems, the tracking error of the robot is theoretically proven to stay within predefined safe boundaries and converge exponentially to a compact neighborhood of the origin. Finally, comparative numerical simulations on a biomimetic rehabilitation robot validate the effectiveness of the proposed theorem and constrained adaptive neural control strategy.

The input layer, hidden layer, and output layer constitute the feedforward neural networks (FNNs) with unidirectional propagation and no feedback loop connection. The FNNs exhibit pivotal properties of nonlinear fitting ability, flexible structure, multitasking adaptability, easy implementation, strong compatibility and composability. The FNNs can independently tackle classification and regression tasks and support the construction of complex networks. The red-billed blue magpie optimization (RBMO) is constructed on the collective collaborative exploration and sophisticated hunting proficiency of the red-billed blue magpies. The RBMO emulates searching for food sources, chasing and attacking prey, and hoarding superfluous food to balance extensive global exploration and meticulous local exploitation, and to ascertain the fittest solution. In this paper, the RBMO is proposed to train FNNs, the motivation is to measure the dissimilarity between anticipated and actual outputs, quantify the training efficiency and classification precision of the sample datasets, and fabricate the connection weights and biases. The RBMO exhibits the distinctive advantages of extensible adaptability and flexibility, accelerated convergence speed, heightened calculation accuracy, decreased control parameters, remarkable robustness and stability, and diminished computational complexity. Seventeen sample datasets are utilized to authenticate the applicability and practicality, the RBMO is compared with SFOA, FLO, APO, HEOA, EGO, BKA, WO, HO, IAO, NRBO, ETO and PO. The experimental results demonstrate that the RBMO can dynamically alternate between exploration and exploitation to strengthen stability and robustness, intensify training efficiency and classification precision, promote convergence speed and solution quality.

The input, hidden and output layers cultivate a hierarchical framework of the feedforward neural networks (FNNs) characterized by unidirectional information flow and feedback feedback-free loop connection, the network highlights attributes of fortified scalability and adaptability, elevated parallel computation and training efficiency, uncluttered structure and easy implementation. The blood-sucking leech optimization (BSLO) is predicated on the foraging patterns of blood-sucking leeches in rice paddies, which incorporates exploration, exploitation, switching mechanism of directional leeches, recherche mechanism of directionless leeches, and re-tracking mechanism to accomplish global coarse discovery and local elaborated extraction, and ascertain the fantastic solution. To expedite solution efficiency and reinforce mining precision, this paper proposes an enhanced BSLO with the simplex method (SBSLO) to train the FNNs, the objective is to quantify the discrepancy between anticipated output and realistic output, assess training efficacy and classification accuracy of prediction samples, and establish the fantastic connection weights and bias thresholds. Simplex method not only strengthens directional exploration precision and bolsters population diversity to mitigate premature convergence and facilitate escape from local optimum but also advances constraint processing capability and emphasizes noteworthy robustness and generalization to reinforce convergence procedure and elevate solution quality. The stability and dependability of the SBSLO are validated by seventeen sample datasets, and the SBSLO is compared with KOA, NRBO, HLOA, IAO, WO, PKO, EGO, HEOA, APO, FLO, PO and BSLO. The experimental results demonstrate that the SBSLO amalgamates the collective cooperative exploration of the BSLO with the refined directional exploitation of the simplex method to leverage complementary advantages, alleviate local search stagnation, boost training efficiency and prediction precision, strengthen stability and robustness, and foster convergence speed and solution quality.

The greater cane rat algorithm (GCRA) is a swarm intelligence algorithm inspired by the discerning and intelligent foraging behavior of the greater cane rats, which facilitates mating during the rainy season and non-mating during the dry season. However, the basic GCRA exhibits serious drawbacks of high parameter sensitivity, insufficient solution accuracy, high computational complexity, susceptibility to local optima and overfitting, poor dynamic adaptability, and a severe curse of dimensionality. In this paper, a hybrid nonlinear greater cane rat algorithm with sine–cosine algorithm named (SCGCRA) is proposed for resolving the benchmark functions and constrained engineering designs; the objective is to balance exploration and exploitation to identify the globally optimal precise solution. The SCGCRA utilizes the periodic oscillatory fluctuation characteristics of the sine–cosine algorithm and the dynamic regulation and decision-making of nonlinear control strategy to improve search efficiency and flexibility, enhance convergence speed and solution accuracy, increase population diversity and quality, avoid premature convergence and search stagnation, remedy the disequilibrium between exploration and exploitation, achieve synergistic complementarity and reduce sensitivity, and realize repeated expansion and contraction. Twenty-three benchmark functions and six real-world engineering designs are utilized to verify the reliability and practicality of the SCGCRA. The experimental results demonstrate that the SCGCRA exhibits certain superiority and adaptability in achieving a faster convergence speed, higher solution accuracy, and stronger stability and robustness.

In this study, an appointed-time tracking controller is devised for the marine surface vessel based on the novel mathematical methods. The novel mathematical methods include that (i) a new high-order integral barrier function is proposed to deal with the symmetric and asymmetric constraints of the high-order systems; (ii) an appointed-time performance function is given to make the performance-constrained error converge to residual domains within the user-designated time; (iii) an integral term is introduced into the disturbance observer to improve estimation accuracy. The rationality of the proposed mathematical method has been proven through theorems. Finally, simulation experiments on a fully actuated surface vessel with three degrees of freedom are used to confirm the efficacy of the trajectory tracking controller developed using the high-order integral barrier function, appointed-time performance function, and disturbance observer.

This paper proposes a dual-mode thermal analysis framework for the composite cage rotor bearingless induction motor (CCR-BIM), which combines lumped parameter thermal network (LPTN) and finite element thermal model (FETM) methods with experimental verification. The CCR-BIM, an advanced motor design combining torque and suspension windings within a single stator core, offers significant advantages in high-speed and high-precision applications. However, accurate thermal management remains a critical challenge due to its complex structure and increased losses. An LPTN model tailored to the unique thermal characteristics of the CCR-BIM is proposed, and detailed FETM simulations and experimental tests are validated. The LPTN model employs a meshing method to discretize the motor into orthogonal thermal nodes, enabling the rapid and accurate calculation of steady-state temperatures. The FETM further verifies the LPTN results by simulating the transient and steady-state temperature fields. Experimental validation using a 2 kW CCR-BIM test platform confirms the effectiveness of both models, with temperature predictions closely matching measured values. This study provides a reliable thermal analysis method for CCR-BIM.

This article proposes a time-synchronized fault-tolerant convergence control method for n-degree-of-freedom robotic manipulators. The main challenge lies in driving the tracking errors of all joints to converge simultaneously, especially in the presence of system faults, external disturbances, and model uncertainties. We introduce a normalized sign function that guarantees the property of ratio persistence for all joints and plays a crucial role in time-synchronized convergence control. A time-synchronized convergence observer is proposed that not only adopts a time-synchronized convergence control framework but also overcomes the lumped uncertainty term, which includes the system fault components, external disturbances, and system uncertainties. A salient feature of this method is that, regardless of the initial state and various uncertainties, each component of the robot manipulator system can simultaneously converge to an equilibrium point. Simulations conducted on a two-link robotic manipulator demonstrate the notable benefits of the designed time-synchronized control method, as evidenced by the comparative results.

The black-winged kite algorithm (BKA) constructed on the black-winged kites’ migratory and predatory instincts is a revolutionary swarm intelligence method that integrates the Leader tactic with the Cauchy variation procedure to retrieve the expansive appropriate convergence solution. The essential BKA exhibits marginalized resolution efficiency, inferior assessment precision, and stagnant sensitive anticipation. To foster aggregate discovery intensity and advance widespread computational efficacy, an innovative complex-valued encoding BKA (CBKA) is presented to resolve the global optimization. The complex-valued encoding manipulates the dual-diploid configuration to encode the black-winged kite, and the actual and fictitious portions are inserted into the BKA, which transforms dual-dimensional encoding into a single-dimensional manifestation. With the inherent parallelism and consistency, the actual and fictitious portions are renewed separately for each search agent, which reinforces population pluralism, restricts discovery stagnation, extends identification area, promotes estimation excellence, advances information resources, and fosters collaboration efficiency. The CBKA not only showcases abundant flexibility and compatibility to accomplish supplementary advantages and sharpen resolution precision but also incorporates localized exploitation and universal exploration to forestall exaggerated convergence and cultivate desirable solutions. The function evaluations, engineering layouts, and adaptive infinite impulse response system identification are executed to certify the suitability and affordability of the CBKA. The experimental results manifest that the computational accomplishment and convergence productivity of the CBKA are superior to those of other comparison algorithms, the CBKA delivers noteworthy stabilization and resilience to explore superior assessment precision and swifter convergence efficiency.

This work presents a rat optimization algorithm (ROA), which simulates the social behavior of rats and is a new nature-inspired optimization technique. The ROA consists of three operators that simulate rats searching for prey, chasing and fighting prey, and jumping and hunting prey to deal with optimization issues. The Levy flight strategy is introduced into the ROA to keep the algorithm from running into issues with slow convergence and local optimums. The ROA is tested with four real-world engineering optimization issues and twenty-two benchmark functions. Experiments show that the ROA is particularly effective at solving real-world optimization problems compared to other well-known optimization techniques.