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This article proposes a new terminal cooperative guidance law to control both impact time and impact angle in three-dimensional engagement. The presented guidance law employs on and normal line-of-sight accelerations to control the impact time and angle together. Two parts are included in this guidance law, that is, the guidance laws with impact time constraint and impact angle constraint. The first is designed based on fixed-time consensus theory to fulfill the salvo attack of the target, and the second is developed based on fixed-time nonsingular fast terminal sliding mode control method to achieve the desired impact angles. The stability analysis of this guidance law based on Lyapunov theory is also presented in detail. Moreover, the maneuvering target can be intercepted successfully with the presented guidance law, and the fixed-time stability and less control energy are well ensured. Additionally, the effectiveness and applicability of the proposed guidance scheme are explicitly verified through simulation tests.

In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception.

Anodic oxidation of catechols 1a–e in the presence of 5-methyl-2-mercapto-1,3,4-thiadiazole 2 has been studied in acetate buffer solution by cyclic voltammetry and controlled-potential electrolysis techniques. The effects of various electrolytic conditions (amount of passed charge, anodic materials, pH of the electrolytic solution, applied potential, and concentration of substrates) on the yield have also been investigated. The results showed that the position of the initial substituent of the starting catechol derivatives dominated the formation of monothiadiazol-2-ylthio-substituted or/and dithiadiazol-2-ylthio-substituted products. For 4-substituted catechols 1a–b, monothiadiazol-2-ylthio-substituted products (3a–b) were exclusively produced in high to excellent yields. However, in the cases of catechol itself (1c) and 3-substituted catechols (1d–e), both monothiadiazol-2-yl-substituted (3c–e and 5d–e) and dithiadiazol-2-ylthio-substituted products (4c–e) were isolated. In addition, the nature of the initial substituent of the starting 3-substituted catechols (1d and 1e) affected the relative ratio of the two monothiadiazol-2-ylthio-substituted isomers (3d–e vs 5d–e).

Electrochemical synthesis of o -benzoquinone derivatives and their in situ transformation are one of the versatile approaches for the synthesis of derivatized catechols. In the present work, electrochemical oxidation of catechols 1a – 1d in the presence of a unique nucleophile, 4-amino-3-methyl-5-mercapto-1,2,4-triazole 3 , bearing two nucleophilic groups (–NH 2 and –SH), have been studied in phosphate buffer solutions using cyclic voltammetry and controlled-potential electrolysis (CPE) methods. The results show that only the mercapto group participated selectively in the Michael addition reaction and led to the formation of catechol substituted products of types 4 and 5 , bearing a free amino group, potentially useful for further chemical modifications, e.g. of interest in biomedical applications. Various electrolytic conditions, such as the nature of anode material, amount of passed charge, pH of the electrolytic solution and cell configuration (divided or undivided cell), were also investigated to optimize the yields of corresponding products.

The electrochemical synthesis of 5-purin-6′-ylthiocatechols was carried out by anodic oxidation of catechol derivatives 1a–1d in the presence of 6-mercaptopurine (2) in aqueous solution. Results of cyclic voltammetry and controlled-potential electrolysis indicated that the starting catechols were first oxidized to the corresponding o-benzoquinone, which underwent further Michael addition with 6-mercaptopurine to produce titled products 3a–3d following an EC (E=electrochemical and C=chemical step) mechanism. Such work further demonstrates the versatility of the anodic oxidation of catechols and their in-situ transformation for the synthesis of derivatized catechols.

An novel and convenient electrochemical approach was developed for the synthesis of indole derivatives from catechols and α-oxoheterocyclic ketene N,O-acetals. This method provides an environmentally benign access to fused indole derivatives containing active hydroxyls and carbonyl under mild reaction conditions.

The electrochemical synthesis of 5-purin-6′-ylthiocatechols was carried out by anodic oxidation of catechol derivatives 1a–1d in the presence of 6-mercaptopurine (2) in aqueous solution. Results of cyclic voltammetry and controlled-potential electrolysis indicated that the starting catechols were first oxidized to the corresponding o-benzoquinone, which underwent further Michael addition with 6-mercaptopurine to produce titled products 3a–3d following an EC (E=electrochemical and C=chemical step) mechanism. Such work further demonstrates the versatility of the anodic oxidation of catechols and their in-situ transformation for the synthesis of derivatized catechols.

As the maneuverability of targets has been further increased in recent years, it is highly desirable to improve the performance of an interceptor’s guidance law. The ‘‘hit-to-kill’’ scenarios of a kinetic kill vehicle (KKV) require a centimeter-level miss distance, and control of impact angle can considerably increase the KKV’s lethality. Two forms of linear quadratic differential game (LQDG) guidance laws for the KKV are proposed in this paper. The first can achieve only zero terminal miss distance, and the second can achieve a specified impact angle as well as zero terminal miss distance. The LQDG guidance laws are obtained by solving a two-sided linear quadratic optimization problem. In game theory, the adversaries are considered as two independent controlled objects. A major advantage is that the LQDG guidance laws make no assumption of the target’s future maneuver strategy. Simulation results show that the two guidance laws can meet the requirements of the KKV and that the centimeter-level miss distance does not lead to a large guidance command near the terminal time.