A new type of CGO solutions and its applications in corner scattering

We consider corner scattering for the operator ∇ · γ(x)∇ + k2ρ(x) in R2, with γ a positive definite symmetric matrix and ρ a positive scalar function. A corner is referred to one that is on the boundary of the (compact) support of γ(x) − I or ρ(x) − 1, where I stands for the identity matrix. We assume that γ is a scalar function in a small neighborhood of the corner. We show that any admissible incident field will be scattered by such corners, which are allowed to be concave. Moreover, we provide a brief discussion on the existence of non-scattering waves when γ − I has a jump across the corner. In order to prove the results, we construct a new type of complex geometric optics (CGO) solutions.

Alcohol Use in China: Unrecorded and Recorded Bai Jiu in Three Rural Regions

In China, approximately 70% of beverage alcohol is consumed in the form of spirits. An estimated 25% of all alcohol consumed is unrecorded, mostly spirits (bai jiu), produced outside regulatory systems in small neighborhood distilleries, mostly in rural areas. Unrecorded bai jiu drinkers are generally older, male, prefer higher-strength bai jiu, and drink daily and mostly at home. To explore possible regional differences, researchers used interview data from 2919 bai jiu drinkers in rural areas in Hebei, Anhui, and Hubei provinces in China. Results confirmed that patterns varied by province. The sample in Hubei preferred unrecorded bai jiu with a more stable preference to alcohol type, tended to drink less frequently, and reported experiencing less drinking pressure, suggesting lower-risk drinking patterns in this region. The Hebei and Anhui sample reported higher frequency and greater amount of alcohol consumption, were more likely to experience drinking pressure, indicating higher-risk patterns in alcohol use in these two regions. The results provide needed details about regional differences in unrecorded bai jiu drinking patterns that are not evident in aggregated data and suggest variations in drinking patterns that may reflect local geography, local values, traditions, and ethnic differences.

Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation

This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.

Adaptive sliding tracking control for nonlinear uncertain robotic systems with unknown actuator nonlinearities

This study is concerned with the tracking control problem for nonlinear uncertain robotic systems in the presence of unknown actuator nonlinearities. A novel adaptive sliding controller is designed based on a robust disturbance observer without any prior knowledge of actuator nonlinearities and system dynamics. The proposed control strategy can guarantee that the tracking error eventually converges to an arbitrarily small neighborhood of zero. Simulation results are included to demonstrate the effectiveness and superiority of the proposed strategy.

Finite-time tracking control for nonstrict-feedback nonlinear systems with unknown time delays and input saturation

In this article, the problem of adaptive finite-time control is studied for a category of nonstrict-feedback nonlinear time-delay systems with input saturation and full state constraints. The fuzzy logic systems are applied to model the unknown nonlinear terms in the systems. Then, a novel tan-type barrier Lyapunov function is adopted to overcome the problem of full state constraints. By utilizing the finite-time control theory and the backstepping technique, a finite-time fuzzy adaptive controller is designed. The controller can guarantee that the tracking error is adjusted around zero with a small neighborhood in a finite time and all the signals in the closed-loop system are bounded. Finally, two simulation examples are included to verify the validity and feasibility of the control scheme.

PARAMETRIC SYNTHESIS OF A MOVING OBJECT STABILIZER

The problem of choosing the variable parameters of a stabilizer of an object which minimize an additive quadratic integral functional reflecting the complex of requirements for a closed stabilization system is considered. To solve the problem a combined method of parametric synthesis of the stabilizer, which is a sequential combination of the Sobol grid method and the Nelder-Mead method, is proposed. At the first stage of the method by applying the Sobolev grid method a working point of the closed system in the pace of its variable parameters is transferred into a neighborhood of the quality functional global minimum point. Then at the second stage the Nelder-Mead method is used to relocated the working point into a small neighborhood of the global minimum. The method proposed comprises a particular algorithm for choosing the weight coefficient of the additive quality functional as well as makes use of the stabilization object state vector main coordinates, which provide the most adequate description of its dynamic features. The properties of a mathematical model of controlled system with discontinuous stabilization process control are studied numerically. The analysis of the plots in the dynamical system state phase space indicates non-spiral approach of the system to its equilibrium state. The synthesized control is realized in the form of a sequence of switchovers.

MODELING AND INVESTIGATION OF THE REGULATOR WORKING IN THE POINTWISE SLIDING MODE

The main disadvantage of the classic sliding mode is that the control signal is made of high frequency variations. In the recommended pointwisesliding mode the frequency of the variations decreases, since the control signal makes jumps at the isolated points. At the same time, the trajectory remains in a small neighborhood of the plane of switching. In the finish mode, the trajectories that start over the sliding plane reach simultaneously the equilibrium point. It is possible to assume that these regulators will expand the implementation scope of the sliding (quazisliding) modes.

Adaptive Fixed-time Control for Nonlinear Systems Against Time-varying Actuator Faults

The adaptive fixed-time control problem for nonlinear systems with time-varying actuator faults is investigated in this paper. A novel adaptive fixed-time controller is designed via combining the Lyapunov stability theory with the backstepping method. It can be adapted to both system uncertainties and unknown actuator faults. Compared with the existing fault-tolerant control schemes subject to actuator faults, the adaptive fixed-time neural networks control scheme can make sure that the tracking error is convergent in a small neighborhood of the origin within a fixed-time interval, and it does not depend on the original states of the system and actuator faults. In light of the control scheme proposed in this paper, the fixed-time stability of the closed-loop system can be guaranteed by theoretical analysis, and a numerical example is provided to verify the effectiveness of obtained theoretical results.

Classes of Dynamic Systems with Various Combinations of Multipliers in Their Reciprocal Polynomial Right Parts

A family of differential dynamic systems is considered on a real plane of their phase variables x, y. The main common feature of systems under consideration is: every particular system includes equations with polynomial right parts of the third order in one equation and of the second order in another one. These polynomials are mutually reciprocal, i.e., their decompositions into forms of lower orders do not contain common multipliers. The whole family of dynamic systems has been split into subfamilies according to the numbers of different reciprocal multipliers in the decompositions and depending on an order of sequence of different roots of polynomials. Every subfamily has been studied in a Poincare circle using Poincare mappings. A plan of the investigation for each selected subfamily of dynamic systems includes the following steps. We determine a list of singular points of systems of the fixed subfamily in a Poincare circle. For every singular point in the list, we use the notions of a saddle (S) and node (N) bundles of adjacent to this point semi trajectories, of a separatrix of the singular point, and of a topo dynamical type of the singular point (its TD – type). Further we split the family under consideration to subfamilies of different hierarchical levels with proper numbers. For every chosen subfamily we reveal topo dynamical types of singular points and separatrices of them. We investigate the behavior of separatrices for all singular points of systems belonging to the chosen subfamily. Very important are: a question of a uniqueness of a continuation of every given separatrix from a small neighborhood of a singular point to all the lengths of this separatrix, as well as a question of a mutual arrangement of all separatrices in a Poincare circle Ω. We answer these questions for all subfamilies of studied systems. The presented work is devoted to the original study. The main task of the work is to depict and describe all different in the topological meaning phase portraits in a Poincare circle, possible for the dynamical differential systems belonging to a broad family under consideration, and to its numerical subfamilies of different hierarchical levels. This is a theoretical work, but due to special research methods it may be useful for applied studies of dynamic systems with polynomial right parts. Author hopes that this work may be interesting and useful for researchers as well as for students and postgraduates. As a result, we describe and depict phase portraits of dynamic systems of a taken family and outline the criteria of every portrait appearance.

Full-State-Constrained Adaptive Control for a Class of UAVs Suffering from Coupled Uncertainties Using the HOBLF

Nowadays, the practical tasks of UAVs are becoming more and more complicated and diversified. In the practical flight process, the large-scale changes of the flight environment, the modeling errors, and the external disturbances may induce the instability of the UAV flight system. Meanwhile, the constraints of the UAV attitudes also have to be guaranteed during the flight process. However, most existing control methods still have limitations in handling the constraints and the multisource disturbances simultaneously. To address this problem, in this paper, we focus on the actual output tracking control for the UAV systems with full-state constraints and multisource disturbances. Firstly, a high-order tan-type barrier Lyapunov function (HOBLF) has been constructed for the UAV to maintain the full-state constraints. Secondly, by combining the adaptive backstepping technique and the fuzzy logic systems, the modeling errors and the unknown nonlinearities of the UAV attitude control system can be handled. Moreover, by properly constructing several adaptive laws, the time-varying disturbances existing in the UAV attitude control system can be suppressed. Finally, the full-state-constrained antidisturbance controller is formed, ensuring that the tracking error approaches arbitrarily to small neighborhood and does not violate the given constraints. The simulation results illustrate the feasibility and the advantages of the proposed method.