General Stability Criterion Research Articles

NN-Based Fixed-Time Attitude Tracking Control for Multiple Unmanned Aerial Vehicles with Nonlinear Faults

This paper focuses on the fixed-time fault-tolerant attitude tracking control problem for multiple unmanned aerial vehicles (MUAVs) with nonaffine nonlinear faults. First, the command filter and neural networks (NNs) are employed to characterize unknown nonlinearities in MUAVs, and the update law of NN is developed via convex optimization technique. Second, the algebraic loop problem caused by nonaffine nonlinear faults is adequately solved by introducing the Butterworth low-pass filter. Then, the curve-fitting method is utilized to construct a piecewise virtual control signal to avoid the singularity problem in fixed-time control. Furthermore, based on the Lyapunov stability theory, a general fixed-time stability criterion is adopted to prove that the designed fault-tolerant attitude controller can guarantee the stability of MUAVs in fixed time. Finally, the effectiveness of the proposed control design method is verified via illustrative examples.

Relativistic Dynamical Stability Criterion of Multiplanet Systems with a Distant Companion

Abstract Multiplanetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N-body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.

Dying AdS Schwarzschild black hole

The criteria for thermal stability of a most general quantum black hole derived by us appeared in the form of a series of inequalities connecting second-order derivatives of black hole mass with respect to its parameters, which determine the mass of the black hole. These nullify the concept of positivity of specific heat as the sole criteria for thermal stability. Using this most general stability criterion, we prove here that AdS Schwarzschild black holes are no longer stable anywhere in their parameter space if cosmological constant is allowed to vary. We also calculate the fluctuations of both horizon area and cosmological constant of this black hole. We calculate specific heat of it and compare this with Hawking’s prediction.

Time‐triggered intermittent control of continuous systems

AbstractFor intermittent control, its control signal is updated in a continuous manner on control time intervals. To overcome the limitation, time‐triggered intermittent control (TIC) is presented for the first time in this article. In our work, based on a new time‐triggered mechanism, the mathematical description of TIC is put forward and a TIC system is modeled. Different from the traditional time‐triggered mechanism, the new time‐triggered mechanism just allows the partial sampled data to be transmitted. Due to different structures of the TIC system, a mixed Lyapunov functional is introduced to obtain a general stability criterion. As a result, a stabilization criterion of continuous systems with TIC is deduced and two methods to design TIC are proposed. Further, comparisons between TIC and sampled‐data control (SC) are made. Finally, an example is given for illustration.

Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

In this paper, we are concerned with the problem of reachable set estimation for uncertain Markovian jump systems with time-varying delays and disturbances. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set of Markovian jump system as small as possible. Based on an augmented Lyapunov–Krasovskii functional, by dividing the time-varying delay into two nonuniform subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. An optimized integral inequality which is based on distinguished Wirtinger integral inequality and reciprocally convex combination inequality is used to deal with the integral terms. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

МАКРОЭКОНОМИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЗАИМОСВЯЗИ ЦЕНОВЫХ И ОТРАСЛЕВЫХ ПРОПОРЦИЙ

The article aims to examine one of the most interesting, in the authors’ opinion, applications of the two-sector model of social technology to identify the relationship between the trajectories of the relative price and the relative share of the product in the total output based on the concept of Pareto optimal, or “efficient”, trajectories of economic growth (i.e. trajectories, each point of which belongs to the surface of production opportunities). Within the framework of this concept, the ratio of prices of individual products corresponds to the marginal rates of these products’ substitution. The rates depend on the product (sectoral) structure of GDP, on the one hand, and on the available labor resources and production assets, on the other. The relationship between the investment component of the output and the growth of funds gives rise to a family of efficient trajectories, in the sense indicated above. Each of the trajectories is characterized by the joint dynamics of industry and price proportions; therefore, the main problem of the study is to examine the general properties of such trajectories. The main feature of the model under consideration is the nonlinear production functions of industries. Even the simplest Cobb–Douglas specification generates the dynamics of the main variables of the model described by a nonlinear differential equation of the second order, which cannot be integrated in general form. Therefore, the analysis of the properties of effective trajectories (at least when specific parameters of trajectories are of interest, and not just general criteria for existence and stability) required the development of a program of numerical experiments on a computer, designed for a fairly extensive test of hypotheses and the convenience of presenting and analyzing the results. To begin with, a variant of the twosector model was chosen, in the future it is planned to expand it to a significantly larger number of sectors. The properties of effective trajectories with constant parameters were analyzed: the marginal rate of product substitution (constant price ratio), constant marginal rate of resource substitution (constant ratio of factor payment rates), constant ratio of net output of industries, constant share of investments in GDP, etc. General conclusions are obtained about the conditions for the convergence of such “iso-trajectories” to trajectories with a constant GDP growth rate and about the characteristics of stationary trajectories. Of greatest interest, in the author’s opinion, is the conclusion that the existence and stability of stationary trajectories is determined by the intersectoral ratio of the elasticities of the output with respect to the funds of the sectors under consideration: for an industry producing investment products, this parameter should be of lesser importance. The derived equation, which can be interpreted as an expression of a trend that determines the form of the relationship between the proportions of industry outputs and prices in the economy, opens the way to a meaningful macroeconomic analysis of the relationships between these proportions, depending on the configuration of the parameters of social technology Ai, αi, aij, B and scenarios of their changes over time.

Experimental Study on Weather Criterion Applied to South Sulawesi Traditional Wooden Boats

The general stability criteria of International Maritime Organization (IMO) seem to be difficult to apply to the South Sulawesi traditional wooden boats because the down-flooding angle of most traditional wooden boats was smaller than 30 degrees. The weather criterion may be used to assess the stability of traditional wooden boats because limitation of heel angle depending only on the down-flooding angle. However the criterion was developed based on geometric characteristics of ships different from the South Sulawesi traditional wooden boats. In this paper, the hydrodynamics factors correspond to the parameters of weather criterion are determined by model experiments consist of roll decay test and test in regular beam waves. The critical metacentric height for different wave steepness is determined by using the weather criterion with parameters values based on model experiments. The damping factor due to breadth-to-draught ratio was larger than that provide in the weather criterion for corresponding breadth-to-draught ratio of 4.28. The effective wave slope coefficients for wave steepness of 0.004 and 0.006 are smaller than that obtained by the formula of weather criterion. However, a larger value was obtained for wave steepness of 0.008 and 0.01. The bilge keels position with slope of 15 degrees provided the largest damping moment. The South Sulawesi traditional wooden boats comply with the weather criterion when the wave steepness smaller than 0.08. The weather criterion can be applied to the traditional wooden boats if the parameters values of weather criterion formula have been developed.

A Note on Sampled-Data Synchronization of Memristor Networks Subject to Actuator Failures and Two Different Activations

This brief is concerned with the drive-response synchronization problem of memristor networks subject to actuator failures and two different activations via sampled-data (SD) control strategy. By using δ-matrix measure method and Halanay inequality technique, the sufficient conditions for global exponential synchronization of driving-response memristor systems are obtained. Unlike the existing works, the common Lyapunov functionals are not employed, but two simple and general stability criteria are derived. Particularly, the established criteria are easier to demonstrate and execute in practice than the relevant results. And in order to verify the validity and superiority of the proposed theoretical results, a numerical simulation is finally provided.

Fuzzy Adaptive Fixed-Time Consensus Tracking Control of High-Order Multiagent Systems

This article discusses the consensus tracking issue for multiagent systems, and the purpose is to develop a fixed-time consensus proposal by fuzzy adaptive method. To this end, we first set up a more general fixed-time stability criterion. By using the proposed stability criterion, a backstepping design procedure is presented to construct the fixed-time fuzzy adaptive controller. The suggested fuzzy adaptive control protocol guarantees that 1) for each agent, its closed-loop signals keep bounded; 2) the consensus tracking error tends to a small region around origin in fixed time. In addition, the virtual control signals are constructed to be the piecewise functions to prevent the singularity of their derivatives. Curve fitting method is used such that the designed virtual control signals are derivable at the point of partition. Finally, numerical simulation further checks the validity of the suggested control strategy.

Generalized stability criterion for exploiting optimized mechanical properties by a general correlation between phase transformations and plastic deformations

Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures, which are closely determined by the processing routes, such as phase transformations. However, the direct connection between phase transformations and mechanical properties remains largely unexplored. Here, we propose a new concept of generalized stability (GS) to correlate phase transformations with plastic deformations in terms of the trade-off relationship that exists between thermodynamics and kinetics. We then suggest that, to achieve structured materials with excellent strength–plasticity combinations, phase transformations and/or plastic deformations with high GS, thermodynamic driving force (ΔG), and kinetic activation energy (Q), are highly expected. We verify the GS concept against a phase transformation-modulated nanostructured Fe alloy, for which an ultrahigh yield strength of 2.61 GPa and an ultimate compressive strength of 3.32 GPa while having a total strain to failure of 35% are achieved via multiple strengthening and hardening mechanisms. A theoretical analysis, in combination with microstructural characterization, indicates that the desired thermo-kinetic parameter triplets (i.e., high GS-high ΔG-high Q) could be inherited from the phase transformation to the plastic deformation, which ultimately yields good mechanical performance. The proposed concept can be regarded as the first theoretical criterion or a general rule that correlates phase transformation with plastic deformation, and can assist in the rapid selection of phase transformations to facilitate superior mechanical properties.

Phase transition in decaying black holes

We had earlier derived the most general criteria for thermal stability of a quantum black hole, with arbitrary number of parameters, in any dimensional spacetime. These conditions appeared in form of a series of inequalities connecting second order derivatives of black hole mass with respect to its parameters. Some black holes like asymptotically flat rotating charged black holes do not satisfy all the stability criteria simultaneously, but do satisfy some of them in certain region of parameter space. They are known as “Quasi Stable” black holes. In this paper, we will show that quasi stable black holes although ultimately decay under Hawking radiation undergo phase transitions. These phase transitions are different from phase transition in ADS Schwarzschild black hole. These are marked by sign changes in certain physical quantities apart from specific heat of the black hole. We will also discuss the changes in the nature of fluctuations of the parameters of these quasi stable black holes with different phases.

A Dropout Compensation ILC Method for Formation Tracking of Heterogeneous Multi-Agent Systems with Loss of Multiple Communication Packets

In this paper, the formation tracking problem for heterogeneous multi-agent systems with loss of multiple communication packets is considered using the iterative learning control (ILC) method. A dropout compensation ILC method is presented to construct effective distributed iterative learning protocols. The convergence conditions are given based on the frequency-domain analysis by using the general Nyquist stability criterion and Greshgorin’s disk theorem. The results show that the multi-agent system with different packet loss rate can achieve formation tracking without reducing the convergence speed. Numerical simulation results show the effectiveness of the proposed dropout compensation ILC method.

A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method

In this paper, we propose a new General Stability Criterion (GSC) for the stability analysis of the nonlinear fractional-order systems(FOs) with time delay at all levels based on the deduction of Wirtinger inequality, Integral mean value theorem(IMVT), fractional-order Lyapunov method, and our initiated general Lemma (WILL Deduction Method). This proposed WILL-Deduction method initiates a general lemma to simplify the construction of the GSC. Therefore, the GSC prevails over the previous criteria in that it solves the stability puzzle of all FOs, including all kinds of time-delay with greater flexibility. For all the fractional-order parametersα∈0,1, the GSC is effective. In conclusion, the initially proposed GSC has generality and universality with more efficiency. Finally the numerical simulations have proved the correctness and universality of GSC .

The state of agrolandscapes of the forest-steppe zone of the Krasnoyarsk Territory

The landscape concept should give a fundamental assessment of the intensification extent of agricultural prospects. A detailed agroecological examination of all components of the natural-territorial complex, the creation of simulation models of their dynamics and the adoption of optimal decisions based on the results of forecasts should be carried out. The purpose of landscape analysis of natural resources is a comprehensive assessment of climatic, soil, plant and animal factors, establishing the relationship of landscape components with farming systems. Any landscape in the process of its development is exposed to impacts, and its stability has its limits. The stability threshold, expressed through the preservation by the landscape of its parameters and properties, and the critical impact quantities are determined in each case. General criteria for the natural stability of geosystems are their high organization, intensive functioning and geosystems functions balance, including biological productivity and renewability of vegetation cover. These qualities are determined by the optimum ratio of heat and moisture and are expressed by the development of soil cover, and ultimately, soil fertility. Landscape-ecological analysis of the territory makes it possible to establish the composition of agricultural and non-agricultural land, taking into account the heterogeneity and stability of a particular landscape, the occurrence of geochemical and biological processes in it, as well as to link the system of agriculture, land reclamation and specialization of the agricultural organization. The main element of Novosyolovo district landscape is agricultural land; the lands of the forest fund are the second largest area of natural geosystems. The degree of change in agrolandscapes is estimated on the basis of the existing structural and functional organization of agricultural lands, their quality state. It was established that plowing is low and it does not exceed the allowable limit, the forest cover of the district is close to optimal.

A general stability criterion for multidimensional fractional-order network systems based on whole oscillation principle for small fractional-order operators

The research on the fractional-order network system (FONS, The derivative model of network system is fractional-order) has seen fruitful achievements, but ignores whether the fractional-order operator (The order of fractional derivatives α ) in the FONS will affect its stability and dynamic characteristics . To tackle this problem, this paper adopts a new method to study the effect of fractional-operators in gamma functions on the dynamic state of the gamma function. This new method helps us to derive a novel dynamic principle of multidimensional FONS. We define it as the Whole Oscillation Principle. According to this principle, the choice of fractional operator reflects the dynamic oscillation characteristic of the multidimensional FONS in two dimensions of time and system state, thus better optimizing the complex case of the fractional-order system research process in the future. Furthermore, based on the auxiliary function-based integral inequality, the paper derives a new stability criterion for all dimensional FONS in the general form. Finally, the validity and correctness of the above theories are verified through numerical simulation to its good effect.

Control Design and Stability Analysis of Power Converters: The MIMO Generalized Bode Criterion

Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, complex vector theory and transfer function matrices are commonly applied, obtaining multiple-input multiple-output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist generalized stability criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design; however, the Bode stability criterion is not applicable to MIMO systems. In this article, the MIMO generalized Bode criterion is proposed. Since this stability criterion is based on the Nyquist generalized stability criterion, it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in this article for two common applications: the current control loop of a power converter, a 2 × 2 system, and the current control loop of two independent power converters in parallel, a 4 × 4 system.

Mean-Square Exponential Input-to-State Stability of Stochastic Gene Regulatory Networks with Multiple Time Delays

This paper is concerned with the input-to-state stability of stochastic gene regulatory networks with multiple time delays. It is well acknowledged that stochastic systems can accurately describe some complex systems with random disturbances. So it is significant that stochastic systems are applied to model gene regulatory networks because of the complex relationship between genes and proteins from a micro perspective. Considering the differences between stochastic differential equations and ordinary differential equations, we introduce the new stability criterion which is different from the general stability criteria. Making use of Lyapunov functionals, It$$\hat{o}$$ formula and Dynkin formula, we present sufficient conditions to guarantee that the proposed system is mean-square exponentially input-to-state stable. Moreover, numerical examples are given to illustrate validity and feasibility of the obtained results.

Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.

Stability analysis of switched systems on time scales with all modes unstable

In this paper, global uniform asymptotic stability problems of switched systems on time scales with all modes unstable are considered. First, a more general stability criterion is proposed for nonlinear switched systems on time scales, in which the value of Lyapunov function at some switching instants may not necessarily decrease. Second, based on the discretized Lyapunov function technique, a sufficient condition is derived for stability analysis of linear switched systems with all subsystems unstable on a special kind of time scale (the graininess function is constant). It is shown that this approach does not require the system matrix of one subsystem must commute with the one of the other subsystem, which is essential for stability analysis of linear switched systems on non-uniform time domains by the eigenvalue based approach in the existing results. Moreover, the idea of this paper not only provides a unified approach to study continuous switched systems and their discrete counterparts simultaneously, but also is effective to investigate stability problems of other systems on uniform or non-uniform time domains. Two examples are given for illustrating the effectiveness of the proposed results.

Formation Tracking via Iterative Learning Control for Multiagent Systems with Diverse Communication Time-Delays

In this paper, we consider the formation tracking problem for multiagent systems with diverse communication time-delays by using iterative learning control (ILC) method based on the frequency domain analysis. A first-order ILC law for multiagent systems with diverse communication time-delays is first proposed and its convergence conditions are given by the general Nyquist stability criterion and Gershgorin’s disk theorem. Then, in order for the system to track accurately, a second-order ILC law is presented. The conditions for system tracking with zero error are established. Numerical simulations show that the proposed ILC laws for multiagent systems with diverse communication time-delays are able to achieve effectively formation tracking. And the convergence speed remains the same as the learning control algorithm without communication delay.