The finite-time control design problem of half-vehicle active suspension systems with uncertain dynamics and external disturbances is investigated in this work. The unknown functions, which caused by uncertain parameters and unknown dynamics, are approximated with help of neural networks (NNs). An extended Lyapunov condition of finite-time stability is employed to achieve the control of the vertical and pitch motions more quickly. Then, assisted by the practical finite-time theory, the finite-time controller is proposed. It can ensure that half-vehicle active suspension systems achieve the stability in a finite time and the ride comfort can be enhanced. In addition, the developed adaptive finite-time control approach is performed to half-vehicle active suspension systems. By comparing analysis of simulation results, the validity of the established scheme is demonstrated and the performance of half-vehicle active suspension systems is exhibited.

The finite-time control problem of the generalized discrete-time systems is a major challenging problem to be solved. In this work, the discrete-time adaptive fuzzy finite-time control scheme is presented for nonlinear systems with discrete form and uncertain dynamics. The fuzzy logic systems (FLSs) are employed to approach uncertain dynamics of systems. Then, the sufficient condition of semiglobal finite-time stability of discrete-time nonlinear systems (DTNSs) is constructed. The discrete-time filters are used to overcome the noncausal problem from the traditional backstepping controller design processes of DTNSs. With the help of the discrete finite-time theorem, discrete-time filters, backstepping techniques, and FLSs, an adaptive fuzzy discrete finite-time control scheme is proposed in a unified framework. The stability analysis can ensure the boundedness of all signals of the closed-loop systems and the achieving the desired tracking control performance in the finite-time. Finally, two examples are adopted to verify abovementioned claims.

This letter addresses the state safety constraint problems for a class of discrete-time nonlinear systems based on discrete time barrier Lyapunov functions (BLFs). Unlike traditional log and tan BLFs, a discrete-time BLF is developed for guaranteeing that all system states do not violate their constraint boundaries. In order to estimate uncertain parameters, a multiple model set consisting of $q+1$ identification models is constructed. Then, a convex hull makes better use of the information of all identification models. One of the main advantages of this convex hull scheme is that it not only solves the convergence problem of the estimation algorithm of parameters, but also improves the cooperativity of the multiple model control method. At the same time, discrete-time BLFs and discrete-time filter techniques are employed to construct the actual controller in a unified framework. It has been demonstrated conclusively that all signals are bounded and all states can be limited in a prescribed region. Finally, one simulation example is provided to validate the theoretical findings mentioned above.