In this work, a novel discrete-time fractional-order sliding mode control (SMC) scheme is proposed, which guarantees the desired tracking performance of a linear motor control system. By using Euler’s discretization method, a discrete-time model is firstly established for the linear motor, which includes the nonlinear friction and the uncertainties. Considering the practicability of the engineering application, a new discrete-time fractional-order sliding surface is constructed by taking the Grünwald–Letnikov definition based fractional-order difference of the tracking error into account. Compared to the classical integer-order sliding surface, by the proposed fractional-order sliding surface in this work, a better performance can be achieved due to the memory effect of the fractional calculus. To drive the system trajectories to the predefined sliding surface in finite sampling steps, a novel equivalent control is then designed, which can adjust the switching control input adaptively. Meanwhile, the theoretical analysis for the tracking error of the linear motor system is presented, and the practical reachability of the sliding surface is validated by numerical simulations. Finally, the effectiveness of the proposed control strategy is verified by a group of tracking experiments on a linear motor platform.

In this research article, the finite-time asynchronous sliding mode control (SMC) scheme for Markovian jump systems (MJSs) subject to sensor and actuator faulty signals, is investigated based on the average dwell time approach. Firstly, an asynchronous stochastic hybrid model is proposed in the light of the existing non-synchronization phenomenon of unmeasurable state and indirect access to jump information of original systems. The average dwell time technique, which has the ability to compensate the effects of arbitrary switching by generating a sequence of signals to regulate/choose an appropriate feedback Markov switching signal among the Markov chains, is developed during the reaching phase and sliding motion phase of the sliding mode dynamics. Secondly, based on the asynchronous stochastic hybrid model, a mode-dependent sliding mode surface function is designed. Moreover, the SMC law is synthesized such that the system state trajectories can be driven onto the specified sliding surface in a prescribed limited time. Thirdly, the finite-time analysis method combining with a mode-dependent Lyapunov function, which can reduce drastically the design conservatism, is adopted to guarantee the finite-time boundedness of the sliding mode dynamics both in the reaching phase and sliding motion phase. Fourthly, sufficient conditions are interpreted for the solutions of asynchronous controller gain matrices and an algorithm is provided to assist computing the SMC gain as an auxiliary tool. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design techniques.

In this paper, a practical state estimation strategy against joint sensor and actuator attacks is proposed for cyber-physical systems (CPSs). The CPSs are formulated based on delta operator for the requirement of real control systems with high-sampling or variable-sampling periods. The attacks fulfilling sparse observation condition are supposed to be randomly injected into both sensor and actuator units. Various numbers of attacks on sensors and actuators can be properly handled. Based on multiple observations of the attacked measurements, a new estimator in delta-domain is proposed to estimate the states of the attacked CPS. The convergence of the corresponding estimation error is analyzed based on pole assignment analysis and some matrix equality constraints. Further, by utilization of a dissipativity approach, estimator-based time-driven controller and self-triggered controller are designed for the enhancement of the estimations and the resource saving. Simulations for the joint attack scenario are provided to testify the applicability and effectiveness of the proposed estimation methods.

This paper is concerned with the state estimation and sliding-mode control problems for continuous-time Markovian jump singular systems with unmeasured states. Firstly, a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic admissibility of the unforced Markovian jump singular system. Then, the sliding-mode control problem is considered by designing an integral sliding surface function. An observer is designed to estimate the system states, and a sliding-mode control scheme is synthesized for the reaching motion based on the state estimates. It is shown that the sliding mode in the estimation space can be attained in a finite time. Some conditions for the stochastic admissibility of the overall closed-loop system are derived. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

This technical brief is concerned with dissipativity analysis and dissipativity-based sliding mode control (SMC) of continuous-time switched stochastic systems. Firstly, a sufficient condition is proposed to guarantee the mean-square exponential stability and strict dissipativity for the switched stochastic system. Then, an integral-type sliding surface function is designed for establishing a sliding mode dynamics, which can be formulated by a switched stochastic system with an external disturbance/uncertainty. Dissipativity analysis and synthesis are both investigated for the sliding mode dynamics, and consequently sufficient conditions are derived, which pave the way for solving the dissipativity analysis and control problems. Moreover, a SMC law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time. Finally, the efficiency of the theoretical findings is demonstrated by an illustrative example.