Optimal Design for Anti-Skid Control of Electric Vehicles by Fuzzy Approach

In this paper, a new fuzzy approach is applied to optimal design of the anti-skid control for electric vehicles. The anti-skid control is used to maintain the wheel speed when there are uncertainties. The control is able to provide an appropriate torque for wheels when the vehicle is about to skid. The friction coefficient and the moments of inertia of wheels and motor are considered as uncertain parameters. These nonlinear, bounded and time-varying uncertainties are described by fuzzy set theory. The control is deterministic and is not based on IF-THEN fuzzy rules. Then, the optimal design for this fuzzy system and control cost is proposed by fuzzy information. In this way, the uniform boundedness and uniform ultimate boundedness are guaranteed and the average fuzzy performance is minimized. Numerical simulations show that the control can prevent vehicle skidding with the minimum control cost under uncertainties.

STABILITY AND BOUNDEDNESS BEHAVIOUR OF SOLUTIONS OF A CERTAIN SECOND ORDER NON-AUTONOMOUS DIFFERENTIAL EQUATIONS

In this paper, we give sufficient conditions for the stability and ultimate boundedness of solutions to a certain second order non-autonomous differential equations with damped and forced functions. Our results improve and extend some of the stability and boundedness results in the literature which themselves are extensions of some results cited therein. We give example to illustrate the result obtained.

Ultimate Boundedness of Discrete-Time Uncertain Neural Networks with Leakage and Time-Varying Delays

In this paper, by using the general discrete Halanay inequalities, the techniques of inequalities and some other properties, we study the ultimate boundedness of a class of the discrete-time uncertain neural network systems and obtain several sufficient conditions to ensure the ultimate boundedness of discrete-time uncertain neural networks with leakage and time-varying delays. Finally numerical examples are given to verify the correctness of the conclusion.

Dynamics of a stochastic Holling II predator-prey model with Lévy jumps and habitat complexity

This paper investigates a stochastic Holling II predator-prey model with Lévy jumps and habit complexity. It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique, and the stochastic ultimate boundedness of this positive solution is also obtained. Sufficient conditions are established for the extinction and persistence of this solution. Moreover, some numerical simulations are carried out to support the obtained results.

Nonlinear Attitude Control Of Underactuated Spacecraft

This dissertation investigates the nonlinear control of the attitude for an underactuated rigid-body spacecraft system in the body-orbital and inertial frames. The problem involving the stabilization of the body-orbital attitude of an underactuated output-feedback system is examined. Using sliding mode control in conjunction with finite-time nonlinear observer, a novel observer-based control law is rigorously analyzed and proven to achieve attitude convergence. Under time-varying disturbances, inertia matrix uncertainties, and high initial errors, the proposed novel law achieves attitude convergence for three-axis stability and ultimate boundedness within 5 degrees and 0.01 deg/s, for attitude error norm and angular velocity norm, respectively. Next, the attitude control problem is rigorously analyzed in the inertial frame, where the underactuated rigid-body spacecraft system equations of motion are highly nonlinear, and the linearized equations of motion are not controllable. To this end, a generalized velocity-free time-varying state feedback controller is developed to achieve globally exponential stability with respect to the homogenous norm and proven to provide ultimate boundedness of all signals with 5 degrees attitude error norm and 0.5 rad/s angular velocity error norm. Finally, the inertial frame attitude stabilization problem is treated as an optimal control problem. For this case, the Legendre pseudospectral method is used to discretized the spacecraft dynamics into Legendre-Gauss-Lobatto (LGL) node points, where the Lagrange polynomial interpolation is applied to obtain a suitable candidate optimal control sequence. Model predictive control is used to implement the optimal control in predefined control windows sequentially to achieve three-axis stability for a rest-to-rest maneuver within 0.3 orbit.

Nonlinear Attitude Control Of Underactuated Spacecraft

This dissertation investigates the nonlinear control of the attitude for an underactuated rigid-body spacecraft system in the body-orbital and inertial frames. The problem involving the stabilization of the body-orbital attitude of an underactuated output-feedback system is examined. Using sliding mode control in conjunction with finite-time nonlinear observer, a novel observer-based control law is rigorously analyzed and proven to achieve attitude convergence. Under time-varying disturbances, inertia matrix uncertainties, and high initial errors, the proposed novel law achieves attitude convergence for three-axis stability and ultimate boundedness within 5 degrees and 0.01 deg/s, for attitude error norm and angular velocity norm, respectively. Next, the attitude control problem is rigorously analyzed in the inertial frame, where the underactuated rigid-body spacecraft system equations of motion are highly nonlinear, and the linearized equations of motion are not controllable. To this end, a generalized velocity-free time-varying state feedback controller is developed to achieve globally exponential stability with respect to the homogenous norm and proven to provide ultimate boundedness of all signals with 5 degrees attitude error norm and 0.5 rad/s angular velocity error norm. Finally, the inertial frame attitude stabilization problem is treated as an optimal control problem. For this case, the Legendre pseudospectral method is used to discretized the spacecraft dynamics into Legendre-Gauss-Lobatto (LGL) node points, where the Lagrange polynomial interpolation is applied to obtain a suitable candidate optimal control sequence. Model predictive control is used to implement the optimal control in predefined control windows sequentially to achieve three-axis stability for a rest-to-rest maneuver within 0.3 orbit.