Efficient nonlinear homogenization of bones using a cluster-based model order reduction technique.

We present a reduced order model for efficient nonlinear homogenization of bones, accounting for strength difference effects and containing some well-known plasticity models (like von Mises or Drucker-Prager) as special cases. The reduced order homogenization is done by using a cluster-based model order reduction technique, called cluster-based nonuniform transformation field analysis. For an offline phase, a space-time decomposition is performed on the mesoscopic plastic strain fields, while a clustering analysis is employed for a spatial decomposition of the mesoscale RVE model. A volumetric-deviatoric split is additionally introduced to capture the enriched characteristics of the mesoscopic plastic strain fields. For an online analysis, the reduced order model is formulated in a unified minimization problem, which is compatible with a large variety of material models. Both cortical and trabecular bones are considered for numerical experiments. Compared to conventional FE-based RVE computations, the developed reduced order model renders a considerable acceleration rate beyond 10 3 , while maintaining a sufficient accuracy level.

Neural Network-Based Nonconservative Predefined-Time Backstepping Control for Uncertain Strict-Feedback Nonlinear Systems.

To handle the tracking problem of uncertain strict-feedback nonlinear systems with matched and mismatched composite disturbances, this article studies a predefined-time backstepping controller by resorting to a Lyapunov-based predefined-time dynamic paradigm, a regulation function, and neural networks (NNs). Moreover, an adding-absolute-value (ADV) technique is adopted in the design process to remove the control singularity. Theoretical analyses prove the boundedness of all closed-loop system signals and the predefined-time convergence of the tracking error into an arbitrarily small vicinity of the origin. The proposed controller exhibits four advantages: 1) the actual convergence time is precisely predefined by only one design parameter irrespective of the initial conditions, and the control energy is economized; 2) no unbounded terms are adopted for predefining the actual convergence time, thus avoiding numerical overflow problem under limited memory space and gaining strong noise-tolerant ability; 3) the peaking tracking error and control input magnitude can be effectively reduced by appropriately setting parameters of the regulation function; and 4) the controller is continuous and nonsingular everywhere. Finally, a practical example of a single-link manipulator is presented to validate the efficacy and superiority of our predefined-time controller.

Quantized predefined-time control for heavy-lift launch vehicles under actuator faults and rate gyro malfunctions.

The quantized control problem for a heavy-lift launch vehicle (HLV) under actuator faults and rate gyro malfunctions is addressed in this paper. A predefined-time observer (PTO) is designed to reconstruct the immeasurable time derivative of attitude tracking errors with the settling time precisely predefined by one design parameter. Thus, parameter tuning for temporal demands is more straightforward and less conservative for the PTO than for fixed-time observers. Using the reconstructed state, a quantized controller is developed to render attitude tracking errors to a small neighborhood of the origin within a predefined time interval (physically realizable) under actuator faults. The controller has three characteristics (1) An unswitched singularity-avoidance layer is derived to ensure the boundedness of control signals. (2) A hysteresis quantizer is used to discretize control signals for applications on the digital onboard platform and reduce communication burden. (3) The settling time of attitude tracking errors is predefined by two design parameters under discretized control signals without using performance functions, avoiding the risks of violating performance functions and sudden controller collapse suffered by the existing quantized predefined-time controllers. Furthermore, stability analysis is impelled using a nonsmooth analysis method and a Lyapunov method. Finally, numerical simulations on an HLV demonstrate the efficiency of the proposed control system.

Fractional-order sliding mode control with a predefined-time observer for VTVL reusable launch vehicles under actuator faults and saturation constraints.

For vertical takeoff vertical landing (VTVL) reusable launch vehicle (RLV) with actuator faults and saturation constraints, this paper presents a composite control system including a high-order predefined-time extended state observer (HO-PTESO), a predefined-time anti-saturation compensator (PTASC), and a fractional-order practical predefined-time sliding mode control law (FO-PPTSMC). The HO-PTESO accomplishes the precise estimation of disturbance in a time interval predefined by only one design parameter, resulting in a simple and weakly conservative parameter tuning process for temporal demands. Moreover, the peaking value problem is well addressed. The PTASC serves to ensure the stability of the saturated system. Auxiliary variables of the PTASC remain bounded during the saturation process and vanish within the predefined time interval after the saturation process ends, avoiding long-term impacts on the attitude tracking that are common concerns for existing ASCs. Using the estimated disturbance, the FO-PPTSMC enforces unsaturated system states to a predefined residual set of the origin in a chattering-alleviated manner within the predefined time interval. Two parameters respectively predefine the convergence range and time, resulting in a considerably simplified synthesis procedure. Ultimately, numerical simulations on the double integrator system and VTVL RLV model validate the efficiency of the proposed control system.