Nalin Kumar Sharma

Continuity and order of continuity in discrete-time higher order sliding mode

Discrete-time sliding mode is inherently discontinuous in nature. But a relaxed version of continuity can be provided with the help of continuity in discrete sets. In this paper, a definition of higher order sliding mode in discrete-time systems using the concept of relaxed version of continuity in discrete-sets, (p,q)-continuity, is proposed. Moreover, a generalized relationship between sliding order and (p,q)-continuity is defined as the order of the continuity. These definitions facilitates to define ideal sliding and real sliding in arbitrary order discrete-time sliding mode based on (p,q)-continuity concept. Finally, for validation of definitions introduced in this paper, some existing first-order and second-order discrete-time sliding mode control algorithms are used.

Stochastic discrete higher order sliding mode control

This paper defines the stochastic discrete higherorder sliding mode. A control input is designed for an uncertain stochastic system with partial state information such that stochastic discrete higher-order sliding mode takes place. The proposed definition and control scheme is validated through the simulation of a rectilinear plant.

Stochastic Discrete-Time Higher Order Sliding Mode

To accommodate the systems with probabilistic uncertainties, the concept of discrete-time higher order sliding mode is extended to stochastic systems and a definition of stochastic discrete higher order sliding mode (SDHOSM), in probabilistic sense, is introduced. An appropriate control law which steers uncertain stochastic system to the defined SDHOSM takes place in a band, is also explored.

Discrete-Time Higher Order Sliding Mode Control of Unmatched Uncertain Systems

The disturbances affecting a system need not necessarily affect the system through the input channel, hence, discrete-time higher order sliding mode control for an LTI system in the presence of the unmatched uncertainties is studied. A disturbance forecasting technique is used to forecast the disturbance to design DHOSM control.

Optimal Discrete-Time Higher Order Sliding Mode

An idea of an optimal discrete-time higher order sliding mode is explored. A surface is designed for an LTI system such that when the system’s state trajectory confined to it, a specified linear quadratic function is minimized and DHOSM is ensured in spite of disturbance in the system.

Discrete-Time Higher Order Sliding Mode

A definition of discrete-time higher order sliding mode (DHOSM) for a discrete time system is proposed. Based on the definition of DHOSM, a second order sliding mode control is designed for a discrete-time linear time invariant (LTI) system. Subsequently, the behavior and stability of the resulting second-order sliding mode are analyzed.