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In this article, we propose a robust high-order control barrier functions (HoCBFs)-based optimal control method for nonlinear systems with state constraints to achieve safety-stability perspectives. First, a kind of HoCBFs is presented for constrained nonlinear systems to address state constraints with high relative degrees. Second, the robustness property of the HoCBFs is analyzed based on the asymptotic stability of the forward invariant set. Specifically, a robust HoCBFs-based Lyapunov function is constructed to prove the uniform asymptotic stability of the set associated with the HoCBFs. In this way, a new sufficient condition is obtained for the stability analysis of the forward invariant set by using the inequalities of high-order derivatives of Lyapunov function. Third, a robust HoCBFs-based optimal control scheme is proposed for the constrained nonlinear system to achieve the safety-stability perspectives of constraints satisfaction and system stabilization, where the robust HoCBFs are combined with control Lyapunov functions (CLFs) to satisfy the small control property (SCP) in solving a quadratic program (QP). Furthermore, the proposed optimal control scheme is shown to be Lipschitz continuous and has no initial condition restrictions. Finally, two examples are presented to demonstrate the control performance of the proposed scheme. Note to Practitioners—The motivation of this article is that constraints exist widely in actual control systems, and the lack of constraint satisfaction in control systems may inevitably lead to safety defects, which usually degrade the control performances or even damage the entire system. In this article, a robust HoCBFs-based optimal control scheme is proposed for constrained nonlinear systems. The theoretical derivation demonstrates that the proposed control scheme can achieve safety-stability perspectives, which ensure system stabilization and task-oriented performance without violating the state constraints. The satisfactory control performances of the simulation on a constrained robotic manipulator show the potential practical application on a real robotic system.

A coupled thermo-hydro-mechanical-damage model considering anisotropic stiffness degradation of rock after shear damage is developed for the first time, and the coupling mechanism and failure behaviour of caprock in steam assisted gravity drainage (SAGD) operations are systematically investigated using analytical and numerical approaches. New insights into the failure characteristics of caprock were obtained. The damage of caprock is mostly induced by shear and initiates near the interface directly opposite the well pair in the earliest stage of SAGD production and propagates rapidly to form a main crack. The vertical and zigzag main crack may penetrate the caprock, while the secondary cracks on both sides are mostly inclined and straight that they cannot penetrate the caprock. Failure modes of caprock are observed including penetrating crack, non-penetrating crack and interface damage. This study will be helpful in accurately evaluating the caprock integrity and efficiently breaking interbedded shale or mudstone layers in thermal recovery reservoirs. [Received: June 2, 2023; Accepted: February 13, 2024]

This brief concerns with the tracking control problem for time-varying input-output linearizable systems with output constraints under only measurable output signals. To prevent constraint violation, a high-order control barrier function (HoCBF) is introduced. Furthermore, a continuously differentiable auxiliary reference signal function is constructed to reduce the chattering at the safe boundaries and avoid the constraint violation at the switching time when the constraints become active or inactive. Based on that, blending a time-varying coordinate transformation and the HoCBF conditions, a safety-based dynamic output feedback tracking control method is proposed in an explicit form such that the output is driven to track the reference signal to a small neighborhood and ensured within the constrained region simultaneously. Consequently, it is unnecessary to solve the quadratic program (QP) problem online, which avoids the undesirable infeasibility problem, and facilitates the stability analysis in a closed form by the proposed controller. The effectiveness of the proposed control approach is illustrated by a numerical example.

The aim of this study is to investigate risk factors for external root resorption (ERR) of second molars (M2) associated with impacted third molars (M3), and to develop a prediction model that can offer dentists a reliable and efficient tool for predicting the likelihood of ERR.