A methodology for estimating the region of attraction for autonomous nonlinear systems is developed. The methodology is based on a proof that the region of attraction can be estimated accurately by the zero sublevel set of an implicit function which is the viscosity solution of a time-dependent Hamilton–Jacobi equation. The methodology starts with a given initial domain and yields a sequence of region of attraction estimates by tracking the evolution of the implicit function. The resulting sequence is contained in and converges to the exact region of attraction. While alternative iterative methods for estimating the region of attraction have been proposed, the methodology proposed in this paper can compute the region of attraction to achieve any desired accuracy in a dimensionally independent and efficient way. An implementation of the proposed methodology has been developed in the Matlab environment. The correctness and efficiency of the methodology are verified through a few examples.

No abstract

The flight envelope plays an important role in flight safety. The concept of posing the flight envelope as a region of attraction is explored further, and it is investigated whether the stable manifold for the region of attraction computation is an efficient method for determining envelope. The stable manifold describes the flight dynamic envelope of an aircraft in an explicit representation, which means that the computation needs to be done only on the envelope, not the entire state space. In this paper, the stable manifold is computed by using a fast method which reduces the computation to solving a system of partial differential equation. Then, the stable manifold grows in the way of advancing front mesh generation framework. The stable manifold is then applied to the envelope determination of a nonlinear F-16 model. The result is compared to the results obtained with the level set method, demonstrating that the stable manifold provides a feasible and accurate result to the dynamic envelope. The proposed method is then used to investigate the effect of actuator failure on the flight safety. The proposed method can also be used as a safety assessing tool during the design phase of an aircraft.

No abstract

This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation

In this paper, the research contents are mainly focused on the technology of the underwater wheeled vehicle speed control. For providing a passive towed underwater wheeled vehicle with accelerating, uniform motion and decelerating capability which can simulate an underwater navigation environment for the carried unit, we devised a novel open-type hydraulic flexible towing system. Combining the hydrodynamic model of the vehicle and the hydraulic mechanism model, the dynamic characteristics of the novel towing system are studied by computing simulation. Aiming at the force coupling character of double driving hydraulic winches, a master-slave synchronization control strategy is proposed. Then, in view of the flexible towing system features, i.e., strong coupling, nonlinear, time-varying load, and environmental constraints, a real speed controller based on fast terminal sliding mode control theory is designed and manufactured. To verify the effectiveness of the controller, a hardware-in-the-loop simulation test is carried out on the strength of a semiphysical simulation platform based on Matlab/Simulink and VxWorks real-time system. The experiment results show that the speed controller based on fast terminal sliding mode control has excellent effect on rapidity, stability, and anti-interference characteristics.

No abstract

No abstract