Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.

Time-Varying Asymmetrical BLFs Based Adaptive Finite-Time Neural Control of Nonlinear Systems With Full State Constraints

This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state constraints.During the process of backstepping recursion,the approximation properties of NNs are exploited to address the problem of unknown internal dynamics.The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied.According to the Lyapunov stability and finitetime stability theory,it is proven that all the signals in the closedloop systems are uniformly ultimately bounded(UUB)and the system output is driven to track the desired signal as quickly as possible near the origin.In the meantime,in the scope of finitetime,all states are guaranteed to stay in the pre-given range.Finally,a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.

Approach and landing guidance design for reusable launch vehicle using multiple sliding surfaces technique

An autonomous approach and landing（A＆L） guidance law is presented in this paper for landing an unpowered reusable launch vehicle（RLV） at the designated runway touchdown. Considering the full nonlinear point-mass dynamics, a guidance scheme is developed in threedimensional space. In order to guarantee a successful A＆L movement, the multiple sliding surfaces guidance（MSSG） technique is applied to derive the closed-loop guidance law, which stems from higher order sliding mode control theory and has advantage in the finite time reaching property.The global stability of the proposed guidance approach is proved by the Lyapunov-based method.The designed guidance law can generate new trajectories on-line without any specific requirement on off-line analysis except for the information on the boundary conditions of the A＆L phase and instantaneous states of the RLV. Therefore, the designed guidance law is flexible enough to target different touchdown points on the runway and is capable of dealing with large initial condition errors resulted from the previous flight phase. Finally, simulation results show the effectiveness of the proposed guidance law in different scenarios.