Mohammad Reza Zarrabi

Assistant Professor of Applied Mathematics

Selected Publications

Zarrabi, M.R., Farahi, M.H., Effati, S., Koshkouei, A.J. Measure theory approach in sliding mode control for nonlinear systems with disturbances (2015) International Journal of Modelling, Identification and Control, 24 (2), pp. 120-126.

DOI: 10.1504/IJMIC.2015.071888

A new sliding mode control (SMC) design approach using measure theory and Lyapunov functional candidate is presented for nonlinear control problems with disturbances. Lyapunov function is supposed for designing a sliding surface (SS). In fact, the problem that is considered is as follows. A state trajectory from a given initial point reaches a given point on a sliding surface in a short time, and then tends to the origin (equilibrium point) along the sliding surface. Measure theory approach with embedding process is used to solve such a problem in two phases. In the first phase, after designing an appropriate SS by a suggested Lyapunov function, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, then in the second phase, using SS, a control is designed such that the system trajectory tends to the origin along the SS. Copyright © 2015 Inderscience Enterprises Ltd.

AUTHOR KEYWORDS: Lyapunov function; Measure theory; Sliding mode control; Sliding surface design; SMC; Time optimal control
INDEX KEYWORDS: Discrete time control systems; Lyapunov functions; Optimal control systems; Problem solving; Trajectories, Lyapunov functionals; Measure theory; Nonlinear control problems; Sliding surface; SMC; System trajectory; Time optimal control; Time-optimal control problems, Sliding mode control
PUBLISHER: Inderscience Enterprises Ltd.