Suboptimal Safety-Critical Control for Continuous Systems Using Prediction-Correction Online Optimization

This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using more efficient online algorithms by the time-varying optimization method. The idea of the algorithms is that when quadratic programming (QP) or other convex optimization algorithms needed in the CBF-based method is not computation affordable, the alternative suboptimal feasible solutions can be obtained more economically. By using the barrier-based interior point method, the constrained CBF-QP problems are transformed into unconstrained ones with suboptimal solutions tracked by two continuous descent-based algorithms. Considering the lag effect of tracking and exploiting the system information, the prediction method is added to the algorithms, which achieves exponential convergence to the time-varying suboptimal solutions. The convergence and robustness of the designed methods as well as the safety criteria of the algorithms are studied theoretically. The effectiveness is illustrated by simulations on the anti-swing and obstacle avoidance tasks

6-Chloro-2-phenyl-3-(2-phenyl­ethyn­yl)quinoxaline

In the title compound, C22H13ClN2, the quinoxaline ring system is close to planar [maximum deviation = 0.061 (2) Å]. The phenyl ring at the 2-position and the phenyl ring of the phenyl­ethynyl substituent make dihedral angles of 49.32 (7) and 11.99 (7) °, respectively, with the quinoxaline mean plane. The two phenyl rings are inclined to one another by 61.27 (9)°. In the crystal, mol­ecules are linked by C—H⋯π and π–π inter­actions [centroid–centroid distances = 3.6210 (12) and 3.8091 (12) Å]

Aqua­[6-carboxyl­ato-N′-(pyridin-2-yl­methyl­idene)pyridine-2-carbohydrazidato]copper(II) trihydrate

In the title compound, [Cu(C13H8N4O3)(H2O)]·3H2O, the complex molecule, except for the aqua ligand, is essentially planar [r.m.s. deviation = 0.034 (2) Å]. The coordination polyhedron of the Cu2+ cation is a square-pyramid, with the aqua ligand at the apex. The compound exhibits a three-dimensional structure, which is is stabilized by O—H⋯O and O—-H⋯N hydrogen bonds and π–π inter­actions [centroid–centroid distance = 2.987 (3) Å]