Stabilization of two kinds of nonhomogeneous Markovian jump systems via sliding mode control

Abstract

In this article, the stabilization is addressed for the continuous‐time nonhomogeneous nonlinear Markovian jump system (MJS) with parameter uncertainty and stochastic disturbance via sliding mode control (SMC) technique. By using a piecewise homogeneous Markov chain to describe its time‐varying characteristics, the considered nonhomogeneous MJS is established by two kinds of piecewise homogeneous MJSs. After that, an integral sliding mode function is constructed. Then, by applying the SMC theory, two control schemes are proposed to force the states of the piecewise homogeneous MJSs onto the designed sliding surface. Sufficient conditions are given to assure the stochastic stability of the sliding mode dynamics. In addition, the reachability of the system states under the developed SMC law is discussed via Lyapunov stability theory. Lastly, some simulation results are provided to show the effectiveness of the presented SMC methods.

High-Precision Volume Measurement of Potholes in Pavement Maintenance

“…Volume Error 3DAS [17] 0.000353517 0.000031437 TIN [18,19] 0.000315592 0.000006488 CPF [30,31] 0.000106487 0.000215593 QPF [30,31] 0.…”

“…To give convincing results, four methods are included in our comparative studies such as 3DAS [17], TIN [18,19], cubic polynomial tting (CPF) [30,31], and quartic polynomial tting (QPF) [30,31]. 3DAS nds the contour of the point set, and then, the volume of the contour is regarded as the volume of the point set.…”

“…Method Volume Error 3DAS [17] 2.1963 0.1019 TIN [18,19] 2.0807 0.0137 CPF [30,31] 2.0795 0.0149 QPF [30,31] 1.9631 0.1313 Proposed 2.0867 0.0077…”

“…Method Volume Error 3DAS [17] 2.216799 0.1224037 TIN [18,19] 2.094320 7.5505e-05 CPF [30,31] 2.106128 0.0117329 QPF [30,31] 2.015663 0.0787321 Proposed 2.094404 9.0607e-06 intersection of the road and the hemisphere, the secondorder estimator has obvious uctuations. is is because SEK re ects the curvature change of the points and surrounding points.…”

Dynamic output feedback model predictive control for asynchronous Markovian jump systems under try‐once‐discard protocol

“…When it comes to the networked control problem for MJSs, it needs to be mentioned that the network communication might make negative impacts on the timely receiving of system modes by the controller, resulting in the asynchronous phenomenon between the system modes and the controller modes 47‐49 . To this end, a special class of MJSs, namely hidden Markov models (HMMs), have been used to describe such MJSs with asynchronous modes.…”