Lyapunov Exponential Stability Research Articles

Time-Coordinated Path Following for Multiple Agile Fixed-Wing UAVs with End-Roll Expectations

This paper presents a control strategy for multiple unmanned aerial vehicle systems (multi-UAVs) time-coordinated path following with desired endpoint roll attitudes. It utilizes the strong maneuvering capabilities of agile fixed-wing UAVs and incorporates an end-roll expectation. The strategy consists of four steps: time-coordinated control, position control, roll angle planning and attitude control. The position and attitude controllers exhibit Lyapunov exponential stability. The time-coordinated controller addresses the synchronization problem by adjusting the speed based on the coordinated state to achieve progress adjustment. The position controller operates based on the cross-track error and altitude error in the Gravity-Referenced Moving frame. By employing an optimization approach and designing a penalty function, the roll angle sequence is computed. The attitude inner-loop control operates in the [Formula: see text] space and allows for control of large deviations. High-fidelity simulation validates the effectiveness of the proposed method, with normalized coordination error and following error controlled within 2% and 1.2[Formula: see text]m.

Substability and Substabilization: Control of Subfully Actuated Systems.

The region of attraction of the Lyapunov asymptotic stability at the origin is defined to be a ball centered at the origin, which is clearly simply connected and also bounded in the local case. In this article, the concept of substability is proposed, which allows "gaps" and "holes" in the region of attraction of the Lyapunov exponential stability, and also allows the origin to be a boundary point of the region of attraction. The concept is meaningful and useful in many practical applications, but is particularly made so with the control of single- and multi-order subfully actuated systems. Specifically, the singular set of a sub-FAS is first defined, and a substabilizing controller is then designed such that the closed-loop system is a constant linear one with an arbitrarily assignable eigen-polynomial, but with its initial values restricted within a so-called region of exponential attraction (ROEA). Consequently, the substabilizing controller drives all the state trajectories starting from the ROEA exponentially to the origin. The introduced concept of substabilization is of great importance because, on the one side, it is often practically useful since the designed ROEA is often large enough for certain applications, while on the other side, Lyapunov asymptotically stabilizing controllers can be further easily established based on substabilization. Several examples are given to demonstrate the proposed theories.

Work sharing as a metric and productivity indicator for administrative workflows

A mathematical method was developed to generate an indicator on the productivity of administrative complex workflows. The indicator can roughly and steadily reveal the definition of productivity as a state of endosectoral (among internal sector agents) and exosectoral (among external sector agents) administrative services sharing. The indicator can be used by public and private managers to measure human resource efficiency in proportion to work requests/inputs of all administrative services occurring in a given workflow. Defining administrative workflow events as a nonlinear dynamics that assume a random ordered or disordered growth rate of information processing, a method has been proposed for large-scale administrative systems defined as structures of hybrid system variables (continuous or discrete), iterated and composed of fixed-point attracted events at which for all possible metric spaces solutions, the modeling of variables from Lyapunov exponential stability point of view allows the projection of system performance to be oriented, that is in other words, the relationship between the number of agents and the number of administrative services within an administrative workflow environment. This definition differs from traditional or differentiated key performance indicators (KPI), such as working hours, medical certificate, per capita productivity, among others and the proposed methodology is only suitable for large-scale administrative activities that have a wide range of activities as well as the number of agents that perform them. For system management purposes, it is possible to view the possibility of administrating system discretization, computerization and monitoring in order to be able to predict and validate the exponential function as a valid indicator of nonlinear systems where the results were defined by the amount of work sharing effect.

A Novel Multimode Hybrid Control Method for Cooperative Driving of an Automated Vehicle Platoon

A multimode hybrid automaton is proposed for setting vehicle platoon modes with velocity, distance, length, lane position, and other state information. Based on a vehicle platoon shift movement under different modes, decisions are made based on key conditional actions, such as sudden acceleration changes because of vehicle distance changes, emergency braking to avoid collisions and free-lane changing choices adapted to various traffic conditions, so as to ensure effortless movement and safety in the multimode shift. With a 3-degree (longitudinal, lateral, and yaw directions) of the freedom coupled model, a hybrid vehicle platoon controller is proposed using nonsingular terminal sliding-mode control to ensure fast and steady tracking on the hybrid automaton outputs during the multimode shift process. The convergence of the hybrid controller in finite time is also analyzed with the Lyapunov exponential stability. The analysis result proves that the proposed controller not only ensures the stability of the individual vehicle and the vehicle platoon but also ensures the stability of the multimode shift movement system. The proposed cooperative driving strategy for vehicle platoon is evaluated using simulations, where varying traffic conditions and the influence of cutting off are considered in conjunction with demonstration simulations of a vehicle platoon's cruising, following, lane changing, overtaking, and moving in/out of garage functions.

Global Exponential Stability of Memristive Neural Networks With Mixed Time-Varying Delays.

This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.

Adaptive Aperiodically Intermittent Synchronization for Complex Dynamical Network with Unknown Time-Varying Outer Coupling Strengths

In this paper, exponential synchronization problem of complex dynamical networks with unknown periodically coupling strengths was investigated. An aperiodically intermittent control synchronization strategy is proposed. Based on Lyapunov exponential stability theory, inequality techniques, and adaptive learning laws design, some sufficient exponential synchronization criteria for complex dynamical network with unknown periodical coupling weights are obtained. The numerical simulation example is presented to illustrate the feasibility of theoretical results.

Robust tracking system design for a synchronous reluctance motor – SynRM based on a new modified bat optimization algorithm

This paper discusses optimal controller structure design for a Synchronous Reluctance Motor (SynRM). Optimization of controller parameters is based on a new modified BAT optimization algorithm (mBAT). SynRM is represented with a nonlinear dynamic model of a synchronous machine. All gathered nonlinearities of SynRM are taken into account in the controller’s design and optimization procedure with mBAT. A novel SynRM controller structure with a modified robust disturbance observer (mRDO) is presented. The modified mRDO ensures a higher level of stability margin, efficient disturbance rejection, and enables transparent controller parametrization and optimization. Controller synthesis is based on robust ℋ∞ pole-placement technique. The ℋ∞ robust criteria are presented in the form of spectral polynomials and their strong positivity conditions. Spectral polynomials (SP) can be directly used as objective functions in the mBAT optimization procedure. The mBAT algorithm, in terms of the derived SP introduces a novel approach to adaptive weighting function selection and modification of BAT velocity in the position formula. The new modification of the BAT algorithm is inspired by feedback control theory and Lyapunov exponential stability property. The proposed modification of the mBAT significantly increases the efficiency of the given optimization problem.

Global exponential convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects

In this paper, the global exponential convergence of T–S fuzzy complex-valued neural networks with time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and matrix inequality technique, we analyze a type of activation functions with Lipschitz function, and sufficient conditions in terms of complex-valued linear matrix inequality are obtained to ensure the global exponential convergence. Moreover, the framework of the exponential convergence ball in the state space of the considered neural networks and the exponential convergence rate index are also given out. Here, the existence and uniqueness of the equilibrium points need not be considered and the results improve existing results on the Lyapunov exponential stability as special cases. Finally, one numerical example with simulations is given to illustrate the effectiveness of our theoretical results.

Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws

Explicit boundary dissipative conditions are given for the exponential stability in L 2 -norm of one-dimensional linear hyperbolic systems of balance laws ∂ t ξ + Λ ∂ x ξ − M ξ = 0 over a finite interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint–Venant–Exner equations.

Lyapunov exponential stability of linear hyperbolic systems of balance laws

AbstractExplicit boundary dissipative conditions are given for the exponential stability in L2-norm of one-dimensional linear hyperbolic sytems of balance laws ∂tξ+Λ∂xξ-Mξ=0 over a finite space interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint-Venant-Exner equations.

The Converse Theorem of Lyapunov Exponential Stability Theorem

The dynamical behavior for nonautonomous is complicated.So, even if some basic concepts in the dynamical theory for nonautonomous systems are still undergoing investigations and need to be further developed. And Lyapunov functions play an important role in the study of the stability theory and control theory. In the view of the use of Lyapunov method, this paper is concerned with a converse theorem of Lyapunov exponential stability theorem. First, we show the content of the theorem, and then the proof is given.

Exponential Stability Based Design of Constrained Fuzzy Predictive Control

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Three new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasibility of the finite-horizon optimization problem with the added constraints is ensured based on off-line solution of a set of linear matrix inequalities (LMIs). Third, the proposed method is extended to observer-based feedback case. The novel stability method, which we call First Point Constraint Method, is compared to existing methods, such as the techniques based on the end-point constraints (Terminal Constraint Set), and the robust stability techniques based on the small gain theory. The proposed method ensures Lyapunov exponential stability, can be used for open loop unstable plants, and doesn’t need an auxiliary controller. Illustrative examples including the predictive control of a highly nonlinear continuous stirred tank reactor (CSTR) and the observer-based predictive control of a steam generator are discussed.

LMI based design of constrained fuzzy predictive control

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Two new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasibility of the finite-horizon optimization problem with the added constraints is ensured based on an off-line solution of a set of LMIs. The novel stability method is compared to the existing methods, such as the techniques based on the end-point constraints (terminal constraint set), and the robust stability techniques based on the small gain theory. The proposed method ensures Lyapunov exponential stability, does not need an auxiliary controller and can be used with any feasible controller parameters. Illustrative examples including the predictive control of a highly nonlinear chemical reactor (CSTR) are discussed.

An improved indirect field-oriented controller for the induction motor

In this paper, the standard indirect field-oriented controller (IFOC) commonly used in current-fed induction motor drives is modified to achieve global exponential rotor velocity/rotor flux tracking. The modifications to the IFOC scheme, which involve the injection of nonlinear terms into the current control input and the so-called desired rotor flux angle dynamics, facilitate the construction of a standard Lyapunov stability argument. The construction of a standard Lyapunov exponential stability argument allows one to easily design adaptive controllers to compensate for parametric uncertainty associated with the mechanical load. Simulation results are included to illustrate the improvement in performance over the standard IFOC scheme.