In recent decades, missile guidance and control have advanced significantly, with methods like pure pursuit (PP), command to line-of-sight (CLOS), and proportional navigation (PN) enabling accurate target interception in uncertain environments through line-of-sight (LOS) tracking. In this work, we propose a novel 3D sliding pure pursuit guidance (3DSPP) law for controlling a surface-to-air missile against a maneuvering target. The algorithm is compared with established guidance laws such as zero-effort miss distance “ZEM-PN” and “3D-PP”, with performance metrics including the miss distance $M_d$ and time of closest approach $t_{cap}$. The results demonstrate that the 3DSPP outperforms the conventional methods by achieving the lowest $M_d=$ 0.1497 m and the fastest $t_{cap}=$ 7.3853 s, ensuring more precise and rapid interception. The algorithm also exhibits superior robustness to noise and efficient energy management, making it a promising solution for real-world missile guidance systems.

This paper introduces a robust neural adaptive MIMO control strategy to improve the stability and adaptability of bipedal locomotion amid uncertainties and external disturbances. The control combines nonlinear dynamic inversion, finite-time convergence, and radial basis function (RBF) neural networks for fast, accurate trajectory tracking. The main novelty of the presented control strategy lies in unifying instantaneous feedback, real-time learning, and dynamic adaptation within a multivariable feedback framework, delivering superior robustness, precision, and real-time performance under extreme conditions. The control scheme is implemented on a 5-DOF underactuated $\mathrm{R}\mathrm{A}\mathrm{B}\mathrm{B}\mathrm{I}\mathrm{T}$ robot using a $\mathrm{d}\mathrm{S}\mathrm{P}\mathrm{A}\mathrm{C}\mathrm{E}\mathrm{D}\mathrm{S}1103$ platform with a sampling rate of $∆t=1.5 \mathrm{m}\mathrm{s} (667 \mathrm{H}\mathrm{z})$. The experimental results show excellent performance with the following: The robot achieved stable cyclic gaits while keeping the tracking error within $e=\pm 0.04 \mathrm{r}\mathrm{a}\mathrm{d}$ under nominal conditions. Under severe uncertainties of trunk mass variations ${∆m}_{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{n}\mathrm{k}}=+100\%$, limb inertia changes ${∆I}_{\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{b}}=\pm 30\%$, and actuator torque saturation at $\tau =\pm 150 \mathrm{N}\mathrm{m}$, the robot maintains stable limit cycles with smooth control. The performance of the proposed controller is compared with classical nonlinear decoupling, non-adaptive finite-time, neural-fuzzy learning, and deep learning controls. The results demonstrate that the proposed method outperforms the four benchmark strategies, achieving the lowest errors and fastest convergence with the following: $\mathrm{I}\mathrm{A}\mathrm{E}=1.36$, $\mathrm{I}\mathrm{T}\mathrm{A}\mathrm{E}=2.43$, $\mathrm{I}\mathrm{S}\mathrm{E}=0.68$, $t_{ss}=1.24 \mathrm{s}$, and $M_p=2.21\%$. These results demonstrate evidence of high stability, rapid convergence, and robustness to disturbances and foot-slip.

In this paper we are going to introduce a new control design algorithms based on the theory of matrix polynomials. The first procedure is called Block decoupling control which is based on the spectral factors of the denominator of the right matrix fraction description (RMFD), the advantages of this control are the non-interacted behavior, simplicity in control design and low order controller is obtained due to the cancellation property of the proposed algorithm. The second control is called MIMO PID controller design via the placement of Block roots with the help of Diophantine equation resolution, the later systematic procedure retains both regulation and tracking objectives with small gains and minimum error.

This work outlines a novel intelligent predictive control method for Multi-Input Multi-Output (MIMO) systems based on solving matrix Diophantine equations. By embedding maximum likelihood identification into an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictive control scheme, this method achieves effective control of a stochastic two-wheeled self-balancing robot, even when system parameters are unknown. The robot’s dynamics were modeled via Newton–Euler equations and linearized around the upright position. The controller regulates tilt angle and rotational speed while adapting to 7% model uncertainty. It efficiently rejects \(\:0.1\)-magnitude disturbances under 0.05-noise, achieving a \(\:0.92\:\text{s}\) settling time and Integral of Absolute Error (IAE) of \(\:0.061\). Compared to existing controllers, simulation results demonstrate superior convergence, disturbance rejection, and robust tracking, validating the robot’s use as a mobile transport platform.

This paper introduces a novel recursive algorithm for inverting matrix polynomials, developed as a generalized extension of the classical Leverrier–Faddeev scheme. The approach is motivated by the need for scalable and efficient inversion techniques in applications such as system analysis, control, and FEM-based structural modeling, where matrix polynomials naturally arise. The proposed algorithm is fully numerical, recursive, and division free, making it suitable for large-scale computation. Validation is performed through a finite element simulation of the transverse vibration of a fighter aircraft wing. Results confirm the method’s accuracy, robustness, and computational efficiency in computing characteristic polynomials and adjugate-related forms, supporting its potential for broader application in control, structural analysis, and future extensions to structured or nonlinear matrix systems.