Impact Angle Control Guidance to Intercept Moving Targets by Virtual Target Technique

To solve the problem regarding the impact angle of the missile, this paper proposes a novel guidance law, which can control the missile to hit the target at the desired angle. The key of the guidance law is selecting a moving point on the collision line as the virtual target, and the tactical requirements can be fulfilled by the missile directly pursuing the virtual target. The Lyapunov stable theory is used to prove the convergence of the proposed guidance law. The guidance command is generated by a PID controller to make the missile towards the virtual target. The proposed guidance law makes the lateral acceleration of the missile converge to zero, which leads the angle of attack to zero, and it theoretically guarantees the flight path angle equals the attitude angle. Numerical simulations demonstrate this impact angle control guidance law is very accurate and robust. Regardless of whether the initial heading error is large or small, the missile which employs the proposed guidance law can always hit the target from the preset direction and the guidance process is smooth.

Implementation of Adaptive Fault-Tolerant Tracking Control for Robot Manipulators with Integral Sliding Mode

This paper addresses an adaptive fault-tolerant tracking control for robot manipulators. By fully considering the effects of uncertainties and actuator effectiveness faults (UAEFs), a robust fault-tolerant tracking control combining with an auxiliary function and an integral sliding manifold is first developed for uncertain robot manipulators. Then, an adaptive law for unknown parameters of the upper bounded uncertainties is constructed to obtain a robust fault-tolerant approach with the elimination of the reaching phase of sliding mode control (SMC). The stability of the proposed approaches is accomplished by Lyapunov stable theory. The key contributions of the proposed approach are as follows: i) the reaching phase of SMC is removed in the control design and then the sliding mode starts at very beginning; (ii) the nominal control term is eliminated in the design of integral sliding surface and then the algebraic loop problem is also avoided in the proposed approach for robot manipulators; (iii) the simple control structure with an adaptive law is obtained for improving chattering-restraining ability of the proposed approach and then the effects of time delay and computational burden are also restrained from the proposed approach. Simulation and experimental comparisons have been accomplished for verifying the effectiveness of the proposed approach.

Realism, Physical Meaningfulness, and Molecular Spectroscopy

Although the realism debate has focused on the work of Jean Perrin on Brownian motion, this chapter claims that the best place to look for a resolution of this debate is the period after the late 1920s, when stable theory-mediated measurement of molecular parameters first became possible through the application of quantum mechanics to spectroscopy. The chapter first examines how stable measurement of the molecular parameters of diatomic molecules was achieved in spectroscopy and then gauges what evidence there is that this stable measurement is giving spectroscopists access to the real properties and structure of molecules. It argues that an evaluation of the latter question requires a distinction to be made between physically meaningful representations and those that are not, and a full answer requires the deployment of that distinction in the analysis of scientific research on atoms and molecules in the period after 1950.

Event-Triggered Fixed-time Adaptive Fuzzy Control for State-constrained Stochastic Nonlinear Systems Without Feasibility Conditions

The problem of event-triggered fixed-time control for state-constrained stochastic nonlinear systems is discussed in this article. Different from the Barrier Lyapunov Function (BLF)-based and Integral BLF-based schemes which rely on feasibility conditions (FCs), by introducing nonlinear state-dependent functions , the asymmetric time-varying state constraints are handled without FCs .Combining with the fixed-time stable theory and dynamic surface control technique with fixed-time filter, the fixed-time stability in probability of the closed-loop system is ensured and the problems of “explosion of complexity” and “singularity” are overcome. Furthermore, the novel fixed-time error compensation signals are designed to compensate filtering errors, and event-triggered control technique is used to save network resources. Simulations also illustrate the effectiveness of the proposed method.

COUNTABLE MODELS OF THE THEORIES OF BALDWIN–SHI HYPERGRAPHS AND THEIR REGULAR TYPES

We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11].

GROUPOIDS AND RELATIVE INTERNALITY

In a stable theory, a stationary type $q \in S\left( A \right)$ internal to a family of partial types ${\cal P}$ over A gives rise to a type-definable group, called its binding group. This group is isomorphic to the group $Aut\left( {q/{\cal P},A} \right)$ of permutations of the set of realizations of q, induced by automorphisms of the monster model, fixing ${\cal P}\,\mathop \cup \nolimits \,A$ pointwise. In this article, we investigate families of internal types varying uniformly, what we will call relative internality. We prove that the binding groups also vary uniformly, and are the isotropy groups of a natural type-definable groupoid (and even more). We then investigate how properties of this groupoid are related to properties of the type. In particular, we obtain internality criteria for certain 2-analysable types, and a sufficient condition for a type to preserve internality.

A New Method of Porous Space Reconstruction Using Multipoint Histogram Technology

Pore-scale modeling is becoming a hot topic in overall reservoir characterization process. It is an important approach for revealing the flow behaviors in porous media and exploring unknown flow patterns at pore scale. Over the past few decades, many reconstruction methods have been proposed, and among them the simulated annealing method (SAM) is extensively tested and easier to program. However, SAM is usually based on the two-point probability function or linear-path function, which fails to capture much more information on the multipoint connectivity of various shapes. For this reason, a new reconstruction method is proposed to reproduce the characteristics of a two-dimensional (2D) thin section based on the multipoint histogram. First, the two-point correlation coefficient matrix will be introduced to determine an optimal unit configuration of a multipoint histogram. Second, five different types of seven-point unit configurations will be used to test the unit configuration selection algorithm. Third, the multipoint histogram technology is used for generating the porous space reconstruction based on the prior unit configuration with a different calculation of the objective function. Finally, the spatial connectivity, patterns reproduction, the local percolation theory (LPT), and hydraulic connectivity are used to compare with those of the reference models. The results show that the multipoint histogram technology can produce better multipoint connectivity information than SAM. The reconstructed system matches the training image very well, which reveals that the reconstruction captures the geometry and topology information of the training image, for instance, the shape and distribution of pore space. The seven-point unit configuration is enough to get the spatial characters of the training image. The quality of pattern reproduction of the reconstruction is assessed by computing the multipoint histogram, and the similarity is around 97.3%. Based on the LPT analysis, the multipoint histogram can describe the anticipated patterns of geological heterogeneities and reproduce the connectivity of pore media with a high degree of accuracy. The two-point correlation coefficient matrix and a new construction theory are proposed. The new construction theory provides a stable theory and technology guidance for the study of pore space development and multiphase fluid flow rule in the digital rock.

Three-dimensional path following control of underactuated autonomous underwater vehicle based on damping backstepping

This article addresses the problem of three-dimensional path following control for underactuated autonomous underwater vehicles in the presence of ocean current. Firstly, three-dimensional path following error model was established based on virtual guidance method. The control law is developed by building virtual velocity errors and backstepping method, which can simplify the virtual control input and avoid the singular problem induced by initial state constraints. Considering the curvature and torsion characteristics of the three-dimensional desired path, the approaching angle is introduced to guarantee fast convergence of error. Nonlinear damping term is introduced to offset the effects of dynamic uncertainties and external disturbances. The controller stability was proved by Lyapunov stable theory. Finally, simulations were conducted and the results indicate the effectiveness and robustness to parameter uncertainties and external disturbances of the proposed approach.