Atmospheric optical communication links represent a promising solution for long-distance information transmission, including classical and quantum communication systems. However, their performance is limited by wavefront distortions caused by atmospheric turbulence.

This work presents experimental approaches to improving transmission efficiency in atmospheric optical channels through adaptive wavefront correction. The experimental setup involved focusing a laser beam with a diameter of 45 mm by means of a bimorph mirror through apertures of 20 μm and 10 μm, simulating signal reception conditions in free-space optical communication systems. The photodiode current, proportional to the transmitted optical energy, was used as the objective function for optimization. Maximization of this signal provided an indirect measure of the effectiveness of wavefront correction and energy concentration in the focal spot.

Two different optimization algorithms were implemented. The first approach was a deterministic hill-climbing algorithm aimed at sequentially increasing the energy density in the far-field focal spot. The optimization process lasted approximately 8 minutes and consisted of 5800 control steps. As a result, a maximum signal value of 25,823 was achieved, compared to a theoretically attainable value of 27,472. This corresponds to a transmission efficiency of 94% through the 20 μm aperture. For the 10 μm aperture, the efficiency achieved was approximately 90%.

The second approach was based on a stochastic algorithm employing random control voltages distributed according to a Bernoulli distribution. It demonstrated a significantly faster convergence rate: the optimization process required approximately 10 seconds and involved 500 iterations. The maximum recorded signal value was 23,200, corresponding to about 90% energy transmission through the 20 μm aperture and approximately 82% through the 10 μm aperture.

A comparative analysis indicates that the deterministic hill-climbing algorithm provides higher correction accuracy, while the stochastic method offers a substantial advantage in terms of optimization speed. The obtained experimental results confirm the effectiveness of adaptive optics algorithms for compensating for atmospheric wavefront distortions and demonstrate their potential application in optical communication systems.

Introduction:

Reachability is a key property of linear systems in control theory and plays a central role in system analysis. The minimum energy control problem is closely linked to reachability: in a reachable system, there typically exist multiple admissible controls capable of driving the system from a given initial state to a desired final state within a specified time interval. Singular (or descriptor) systems, which commonly appear in applications such as electrical circuits, constrained mechanical systems, and economic models, introduce additional challenges due to algebraic constraints and the potential non-uniqueness of solutions.

Method:

The proposed approach is based on transforming the minimum energy control problem of a singular continuous-time linear system with rectangular input matrices into its canonical form using the Weierstrass–Kronecker decomposition of matrix pencils. This decomposition allows the separation of the dynamic and algebraic components of the system. The minimum energy control problem is then formulated and solved. We derive explicit conditions for the existence of admissible controls and construct an optimal control law. The analytical results are established using techniques from linear algebra and system theory.

Result:

The derived conditions provide a systematic procedure for computing the optimal input and the corresponding minimum value of the performance index. The effectiveness of the proposed approach is illustrated through a numerical example, demonstrating its applicability to various classes of singular systems.

Conclusion:

This work presents a systematic method for the optimal control of singular systems based on the Weierstrass–Kronecker decomposition. The approach simplifies the analysis of constrained dynamics and provides explicit control strategies.

Reinforcement learning (RL) can achieve strong performance in nonlinear control, but exploration often violates safety constraints, which limits deployment in safety-critical systems. Koopman-based control offers a promising bridge between nonlinear dynamics and linear control tools, yet practical success depends on explicitly accounting for approximation errors; recent Koopman control theory highlights that bilinear surrogate models with finite-data, proportional error bounds enable rigorous closed-loop guarantees.

We propose a safe actor–critic framework in which a Koopman surrogate model is learned from data together with an error certificate that upper-bounds one-step prediction mismatch as a function of the lifted state and input magnitudes. Using this certificate, we construct a robust safety layer that computes, at every step, the nearest admissible action to the actor’s proposed action such that state and input constraints are satisfied for all model errors consistent with the bound. This safety layer is formulated as a tractable convex projection problem, guaranteeing constraint satisfaction whenever the certified safe action set is nonempty.

We interpret the safety layer as an additional “safety critic”. The filter’s intervention (the difference between proposed and applied actions) provides a direct learning signal that penalizes reliance on the filter, encouraging the actor to produce intrinsically safe actions while the standard critic optimizes task reward.

Simulation results on a nonlinear controlled system with intentional model mismatch show that robust projection eliminates training-time safety violations compared to unshielded and nominally shielded baselines. Moreover, incorporating the safety-critic signal substantially reduces safety interventions while maintaining achieved performance, demonstrating safe learning and improved policy self-safety without sacrificing control quality.

This paper addresses the fixed-time adaptive stabilization issue for a category of underactuated mechanical systems regulated by Euler–Lagrange dynamics, characterized by aligned parametric uncertainties. Unlike traditional adaptive control schemes that only guarantee asymptotic convergence and usually assume stable internal dynamics, a new framework is created that guarantees global fixed-time convergence and explicitly proves that the zero dynamics caused by underactuation are stable. The suggested controller combines partial feedback linearization with a recursive fixed-time backstepping design and an online parameter adaptation law that keeps the structural properties of Euler–Lagrange systems. A new composite Lyapunov function is presented to address the coupled dynamics of actuated and unactuated coordinates and to formulate a differential inequality of the following form, ?˙ ≤ −??^? − ??^?, where 0 < α < 1 and β > 1. This structure guarantees global fixed-time convergence with a clear upper limit on the settling time that is not affected by the starting conditions. A Lyapunov certificate for the internal (zero) dynamics is also created and shown to work with the adaptive outer-loop design. This means that minimum-phase assumptions are no longer needed. A thorough analysis shows that all closed-loop signals are globally bounded and that the system is robust against matched uncertainties. Numerical simulations of typical underactuated systems show the theoretical properties and show how fixed-time performance compares to asymptotic adaptive controllers. The results lay a systematic groundwork for the fixed-time adaptive control of underactuated mechanical systems and facilitate further advancements towards robustness and constrained control.

Learning from Demonstrations (LfD) has the capability to transfer human expertise on repetitive tasks into robotic systems, thus avoiding the need for highly technical knowledge to program such systems. A common formulation for modeling human demonstrations as non-linear trajectories, as well as for ensuring robustness against perturbations, is state-dependent dynamical systems (DSs). Recent DS-based LfD approaches learned the complex dynamics of motion and provided stability guaranties; however, most of them followed the next integral curves of the DS to reach their target. These approaches are unsuitable for applications that require precise tracking of the robot's trajectory. To address this drawback, this study proposes a neuroadaptive control approach to enhance the tracking fidelity of learned trajectories, which provides performance guarantees online in a DS-based LfD approach. Furthermore, a constrained optimization problem based on the Gaussian Mixture Model (GMM) and the Control Lyapunov Function (CLF) is used to generate the reference trajectory offline. The proposed approach has been experimentally validated on the LASA dataset and on real trajectories coming from the Unmanned Surface Vessel (USV) Vendaval. Preliminary results confirm that the novel DS-based LfD approach proposed in this study significantly improves trajectory tracking when the system is disturbed; moreover, these results outperform existing approaches in terms of tracking fidelity.

This work presents a comprehensive investigation into the free vibration behavior of nonhomogeneous nanobeams, particularly axially functionally graded (AFG) nanobeams, incorporating spatially varying nonlocal effects. The nanobeam is modeled using the Euler–Bernoulli beam theory, while small-scale phenomena are captured through Eringen’s nonlocal elasticity theory. Unlike conventional approaches that assume a constant nonlocal parameter, the present work considers a varying nonlocal parameter along the axial direction, enabling a more realistic representation of nonlocal effects. The material properties of the nanobeam are assumed to vary continuously along the beam’s axis according to a power-law distribution, reflecting the functional gradation of the structure. The governing equations are formulated and solved using the Rayleigh–Ritz method to obtain the frequency parameters. A convergence study is conducted to demonstrate the numerical stability and accuracy of the proposed solution methodology. The obtained results are further validated through comparisons with existing solutions available in the literature for specific limiting cases. Parametric analyses are performed to examine the effects of the power-law exponent and the variable nonlocal parameter on the first four frequency parameters. The results indicate that increasing the power-law exponent or the nonlocal parameters results in a noticeable reduction in the frequency parameters, highlighting the significant roles of material gradation and small-scale effects in the dynamic response. Overall, the study demonstrates that incorporating a spatially varying nonlocal parameter provides enhanced predictive capability for the vibration analysis of AFG nanobeams, offering valuable insights for the design and optimization of advanced nanostructures.

A predictive adaptive control system for multi-joint robotic manipulators is proposed, leveraging Long Short-Term Memory (LSTM) neural networks for trajectory tracking error prediction. The method is designed to mitigate dynamic uncertainties and external perturbations without explicit system identification, thus enabling robust and model-agnostic control.

The key finding of this study is that an encoder–decoder LSTM network, trained on joint angle increments (in delta-space), is capable of making accurate multi-step forecasts, ensuring smooth trajectory continuation. Delta-space representation is emphasized as a crucial factor for maintaining physical consistency, effectively eliminating discontinuities commonly encountered in absolute-value predictions.

In order to establish a theoretical basis, this work incorporates concepts derived from functional analysis, particularly the generalized Hölder-type conditions, which are formalized through the notion of a local modulus of continuity. These concepts serve as a promising framework for examining the approximation properties and stability of the predictor.

These mathematical instruments provide a structured framework for future rigorous analysis, encompassing the derivation of error bounds and guarantees for preserving smoothness. The discussion emphasizes how these analytical approaches can inform the selection of architecture and the regularization of training and ultimately contribute to enhancing the reliability of data-driven predictive controllers in real-time robotic applications and deployment scenarios.

Introduction
Cancer treatment increasingly relies on combination therapies to improve patient outcomes while reducing toxicity. Chemotherapy directly kills tumor cells, whereas immunotherapy enhances the body’s immune response. Determining optimal dosing schedules for both therapies remains a major challenge. This study develops an optimal control framework to investigate combined chemotherapy and immunotherapy strategies that minimize tumor burden while controlling treatment cost and side effects.

Methods
We consider a nonlinear system of ordinary differential equations describing interactions among tumor cells, immune cells, and chemotherapeutic drug concentration. Two time-dependent control variables are introduced: chemotherapy dosage and immunotherapy input. Pontryagin’s Maximum Principle is applied to derive necessary optimality conditions for minimizing an objective functional that balances tumor reduction, immune preservation, and treatment cost. The optimality system is solved numerically using a forward–backward Runge–Kutta method. In addition, normalized local sensitivity analysis is performed to evaluate the robustness of the optimal strategy to parameter uncertainty.

Results
Numerical simulations compare chemotherapy, immunotherapy, and combined therapy. Chemotherapy is most effective in weak immune environments, while immunotherapy success depends strongly on immune proliferation and lifespan. Combined therapy reduces tumor burden more efficiently than single therapies, although chemotherapy contributes more strongly to tumor elimination. Sensitivity analysis shows that tumor growth rate, immune proliferation, and drug efficacy are the most influential parameters. The optimal strategies remain stable under small parameter perturbations.

Conclusions
The proposed dual-control framework demonstrates how optimal scheduling of chemotherapy and immunotherapy can improve treatment effectiveness while limiting drug usage. The results provide quantitative insight into combination therapy design and highlight the importance of treatment timing and immune dynamics in cancer therapy optimization.

The control performance of permanent magnet brush (PMB) DC motors, which are vital components in electric vehicles (EVs), is fundamental to ensuring the smooth, efficient, and safe operation of these vehicles under varying working conditions. This study investigates intelligent control of fractional-order nonlinear systems (FONSs) subject to full-state error constraints, mismatched disturbances, and actuator failure, with the electromechanical dynamics of PMB DC motors serving as a representative application. An error-dependent transformation is proposed to reformulate the constrained tracking control problem into an equivalent unconstrained formulation with deferred error bounds, thereby eliminating the requirement that initial state errors satisfy predefined constraints. Unlike conventional backstepping-based approaches, the proposed strategy avoids the computation of higher-order derivatives of the reference trajectory, which significantly reduces implementation complexity and practical limitations. To compensate for unknown mismatched disturbances, an adaptive estimation law is developed to online approximate their unknown upper bounds in real time. Based on the transformed fractional-order system, a recursive intelligent control scheme is systematically constructed. By employing Lyapunov stability theory in conjunction with Barbalat’s lemma, it is rigorously proven that all state errors enter a prescribed bounded region within finite time and asymptotically converge to zero. The simulation results conducted on a PMB DC motor model demonstrate improved transient performance, enhanced robustness, and reliable constraint satisfaction compared with existing barrier Lyapunov function-based and adaptive control methods.

The non-linear dynamics of robotic arm manipulators impose considerable barriers to control and stabilization. The proposed study will help to close the gap between theory and applicationin physics by comparing mathematical modeling with simulations of physical 3D mechanical systems of a manipulator working as a simple double pendulum. The study uses SolidWorks to design the 3D of the first stage and MATLAB to simulate the changes in physical parameters on oscillatory motion. The method included the derivation of the Lagrange equations of a 2-DoF system, creation of the MATLAB/Simulink blocks in mathematical analysis, and execution of a simulation using MATLAB/Simscape Multibody in the 3D visualization. Four models of robots were analyzed, and the numerical results indicated that sine waves were always generated by the mathematical simulation. The sine wave peaked at 57.9 in the case of Franka Emika. By comparison, the 3D model simulation of the same reached the highest point of 56.9 at a definite time delay, highlighting the influence of physical models. The most important results showed that mathematical models are more appropriate for deriving a transfer function but the behavior of robots with similar dimensions and weights was closed when 3D simulation was used. An effective control parameter development of robotic hardware is presented by this dual-modeling methodology, which enables all theoretical designs that are developed to be tested against mechanical realities.