This paper deals with stability analysis of pin-jointed beams that are affected to random pulsating load. The stability conditions of a pin-jointed beam are analysed using a mathematical model of the beam characterised by longitudinal force with Poisson characteristics and applying the stochastic modification of the second Lyapunov method.
In this paper, a continuous-time distributed algorithm is presented to solve a class of decomposable quadratic programming problems. In the quadratic programming, even if the objective function is nonconvex, the algorithm can still perform well under an extra condition combining with the objective, constraint and coupling matrices. Inspired by recent advances in distributed optimization, the proposed continuous-time algorithm described by multi-agent network with consensus is designed and analyzed. In the network, each agent only accesses the local information of its own and from its neighbors, then all the agents in a connected network cooperatively find the optimal solution with consensus.
In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant sets of the steering and braking control systems at various velocities and road conditions. Illustration examples show that, depending on the environments, different vehicle dynamic regions can be reached and stabilized by these controllers. The results can be applied to the theoretical basis of their interventions into the vehicle control system.
The algorithm for estimating the stability domain of zero equilibrium to the system of nonlinear differential equations with a quadratic part and a fractional part is proposed in the article. The second Lyapunov method with quadratic Lyapunov functions is used as a method for studying such systems.
The paper presents two different approaches to estimating the region of stability of differential equation. Estimation of the region of stability is an essential practice in relation to control of the dynamical system. In this paper the objects of examination are differential equations with quasi-derivation. The equations have features that do not allow the application of classical methods for establishing stability. The goal is to compare the results of an analytic approach using Lyapunov method and computer simulation using a numerical method. The brief description of both methods are introduced and graphical results are presented and compared
Simple environment for developing methods of controlling chaos in spatially distributed systems
The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure the symmetry of the system state trajectory. In addition, a real system, which can be modeled by the CML, is presented. In general, this article describes basic elements of environment, which can be used for creating and examining methods of chaos controlling in systems with spatiotemporal dynamics.
Using the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.
The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.
The issue of controlling a swarm of autonomous unmanned surface vehicles (USVs) in a practical maritime environment is studied in this paper. A hierarchical control framework associated with control algorithms for the USV swarm is proposed. In order to implement the distributed control of the autonomous swarm, the control framework is divided into three task layers. The first layer is the tele-operated task layer, which delivers the human operator’s command to the remote USV swarm. The second layer deals with autonomous tasks (i.e. swarm dispersion, or avoidance of obstacles and/or inner-USV collisions), which are defined by specific mathematical functions. The third layer is the control allocation layer, in which the control inputs are designed by applying the sliding mode control method. The motion controller is proved asymptotically stable by using the Lyapunov method. Numerical simulation of USV swarm motion is used to verify the effectiveness of the control framework.