Stability analysis of nonlinear multi-agent relay tracking systems over a finite time interval

The problem of optimal control over a finite time interval for a mathematical model of a three-sector economic cluster is posed. The economic system is reduced by means of transformations to the optimal control problem for one class of nonlinear systems with coefficients depending on the state of the control object. Two optimal control problems for one class of nonlinear systems with and without control constraints are considered. The nonlinear objective functional in these problems depends on the control and state of the object. Then, using the results of solving optimal control problems on a finite interval, an algorithm for solving the problem for a nonlinear system of a three-sector economic cluster is developed. A nonlinear control based on the feedback principle using Lagrange multipliers of a special kind is found. The results obtained for nonlinear systems are used to construct the control parameters of a mathematical model of a three-sector economic cluster at a finite time interval with a given functional and various initial conditions. The results of the system state calculation are shown in the figures, the optimal controls satisfy the given constraints. The optimal distribution of labor and investment resources for a three-sector economic cluster is determined. They ensure that the system is brought into an equilibrium state and satisfy balance ratios. These results are useful for practice and are important because there are a number of optimal control problems when it is necessary to transfer a system from an initial state to a desired final state for a given time interval. Such problems often arise for an economic system when a certain level of development is required.

Analysis of Nonlinear Systems with Stochastic Input and Stochastic Parameters—II

H∞ Tracking with Preview for Linear Systems with Impulsive Effects -State Feedback and Full Information Cases-

This paper investigates the finite-time stability problem for a class of discrete-time switched linear systems with impulse effects. Based on the average dwell time approach, a sufficient condition is established which ensures that the state trajectory of the system remains in a bounded region of the state space over a pre-specified finite time interval. Different from the traditional condition for asymptotic stability of switched systems, it is shown that the total activation time of unstable subsystems can be greater than that of stable subsystems. Moreover, the finite-time stability degree can also be greater than one. Two examples are given to illustrate the merit of the proposed method.

Enhanced robust stability analysis of large hydraulic control systems via a bifurcation-based procedure

This paper considers the consensus problem of two class of multi-agent systems with communication disturbance by using iterative learning control(ILC) method and both of them has a fixed information topology with a spanning tree. Firstly, a distributed iterative learning-based control protocol is designed for a time-varying linear multi-agent system, a sufficient condition is obtained such that the consensus problem is solved. By the same way, a sufficient condition is also given for a class of nonlinear time-varying multi-agent systems to solve consensus problem. The main contribution of the proposed results is that they can restrain any type of repetitive disturbance. The validity of them is verified by the simulation results.

In this paper, the problem of consensus tracking control for a class of second-order leader-following nonparametric uncertain multi-agent systems, which perform a given repetitive task over a finite interval with arbitrary initial error. By means of learning control and initial shift rectifying, a first-order attractor control algorithm is presented.In the tracking process, the proposed algorithm simultaneously rectifies all the initial state shifts, and after enough iterations, the all following multi-agents’ states perfectly track the leader’s state in the preset time interval. Finally, simulation results demonstrate the effectiveness of the learning control algorithm.

Practical stability analysis and synthesis for nonlinear singular systems .- 3 Strongly absolute stability analysis for Lur'e singular .- 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems. 4 Input-to-state stability analysis and design for Lur'e singular systems .- 5 Observer design for nonlinear singular systems .- 6 Absolute stability of Lur'e singularly perturbed systems .- 7 Multi-objective control for T-S fuzzy singularly perturbed systems.

This paper proposes robust formation control laws for uncertain multiagent systems subjected to an unknown control direction and disturbances under the assumption that information about the reference trajectory is only available to some of the agents. Different from the existing results, the proposed control algorithms can enable the agents to converge to the specified points utilizing only local relative measurements, in which no control direction information and upper bounds of external uncertainties are required. To simplify and facilitate the analysis, external disturbances are roughly divided into structured and unstructured uncertainties. To attenuate the errors caused by the structured uncertainties, an adaptive control technique is applied to obtain the estimates of the unknown constant coefficients, and compensating functions with learning ability are developed to eliminate the errors caused by the unstructured uncertainties. A Nussbaum-type function is employed to settle the formation control problem in the presence of unknown signs of the control direction. Formation stability analysis for uncertain nonlinear multiagent systems is performed according to the Lyapunov stability theory. It is proved that the formation errors are bounded within a small desired accuracy by implementing the proposed robust control laws, and the desired formation is then achieved. Finally, two illustrative examples are presented to support the obtained theoretical results.

We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by either compound Poisson shot noise or finite‐measure Lévy noise. For each noise type, we compare trajectories of the perturbed system with distinct noise sample paths against trajectories of the nominal, unperturbed system. We show that for a finite number of jumps arising from the noise process, the mean‐squared error between the trajectories exponentially converge toward a bounded error ball across a finite interval of time under practical boundedness assumptions. The convergence rate for shot noise systems is the same as the exponentially stable nominal system, but with a tradeoff between the parameters of the shot noise process and the size of the error ball. The convergence rate and the error ball for the Lévy noise system are shown to be nearly direct sums of the respective quantities for the shot and white noise systems separately, a result which is analogous to the Lévy–Khintchine theorem. We demonstrate both empirical and analytical computation of the error ball using several numerical examples, and illustrate how varying the parameters of the system affect the tightness of the bound.

Theory of nonlinear systems

Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems.

This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are defined, stabilization of the system is straight-forward. The sum of squares (SOS) decomposition and semidefinite programming has also provided an efficient methodology for analysis of nonlinear systems. The computational method used in this paper relies on the SOS decomposition of multivariate polynomials. By using SOS, we construct a (some) Lyapunov function(s) for the hybrid system. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be practically unsolvable. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Some examples are given to demonstrate the capabilities of the proposed approach.

Analysis of fast-sampled non-linear systems: generalised frequency response functions for δ-operator models