Abhisek K. Behera

Event-triggered sliding mode control for a class of nonlinear systems

ABSTRACT Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.

Event based robust stabilization of linear systems

This paper discusses the robust stabilization of a linear time-invariant system based on event triggering strategy. In most practical system, it is not possible to update control in continuous manner, so it is given to plant at some periodic discrete instants only. Recently, the event based control technique for control law update has become popular as it uses the resources efficiently while guaranteeing closed loop system stability. We address here the event based sliding mode control for a linear system in the presence of disturbances and it is shown that the closed loop system achieves stability with respect to measurement errors. The expression for minimum control execution time, where the control law gets updated only after this time interval is also derived. Simulation results are given to verify the theoretical analysis.

Robust Sliding Mode Control: An Event-Triggering Approach

Event-triggered sliding mode control (SMC) achieves robust performance in the presence of external disturbances. However, this triggering scheme for SMC does not have a global property even for linear time-invariant systems. Here, “global” means that the triggering scheme ensures the stability of the system globally in the state space. Therefore, in this brief, a global event-triggering realization of SMC is proposed. In this proposed scheme, it is established that the system trajectory is attracted toward the sliding manifold and remains within a band thereafter in the presence of uncertainties. The simulation result is given to show the effectiveness of the result.

Steady-state behaviour of discretized terminal sliding mode

In this paper, the steady-state behaviour of discretized terminal sliding mode control is studied. A discrete terminal sliding mode control is designed by discretizing the continuous-time system and then the steady-state behaviour is analysed in terms of periodic orbits. We have shown that by this discrete terminal sliding mode control the discretized second order system exhibits only period- 2 motion in steady-state. To ensure this, existence and stability conditions of all possible periodic orbits are found out analytically and shown that only period- 2 conditions are satisfied by the state evolution of the discretized system in steady-state. Next, a higher order single-input-single-output system is considered and we also establish that only period- 2 motion exists in steady-state.

Event based sliding mode control with quantized measurement

In this paper, an event based implementation of sliding mode control with quantized state measurements only is analysed. In many practical applications, the state information are available up to some finite precision. This indeed induces some quantization error into the system. However, in this work we consider the sampled state information are quantized measurements and the systems is subjected to both sampling (measurement) induced error and quantization error. The sample measurements are used in event condition. We also ensure that, there is no accumulation of triggering instants occur. Numerical simulations are provided to show effective of the above analysis.

Event-Triggered Sliding Mode Control for Robust Stabilization of Linear Multivariable Systems

Event-triggered sliding mode control for robust stabilization of linear systems is presented here. In event-triggered control strategy the control law is not updated in periodic manner but a specific condition is used to generate the possible triggering instant for the control update. It is seen that with the sliding mode control the sequence of triggering instants generated by event condition does not exhibit accumulation of triggering instants in the presence of disturbances. We propose the sufficient event condition for the sliding mode control that guarantees that in the finite time sliding mode occurs in the system in the vicinity of sliding surface and remains within a predesigned region. An analysis for event triggered stabilization of fractional order systems is briefly given. The same triggering condition developed for integer order systems also guarantees stability of fractional order systems. A numerical example is given to show the effectiveness of the above result.

Discrete event-triggered sliding mode control with fast output sampling feedback

This paper deals with event-triggering based design of discrete-time sliding mode (DTSM) control for linear systems. Multirate output feedback based DTSM is designed with event-triggering strategy such that the system trajectories remain bounded in the vicinity of sliding manifold. An event-triggering rule is developed for DTSM which is evaluated only at periodic time intervals. The control is updated whenever the triggering instant is generated at these discrete time instants. It is shown that with this technique the system trajectories remain bounded. Also, in this triggering scheme there is always guaranteed Zeno free execution of triggering sequences as it is inherently discrete. Simulation results are shown to demonstrate the theoretical treatments of this paper.

Decentralized event-triggered sliding mode control

In this paper, we discuss event-triggering scheme with sliding mode control where sensors are distributed over network. Here, a decentralized event-triggering mechanism is proposed where event is observed at each sensor nodes with local information for possible triggering and control update is done whenever a centralized event is triggered. In order to achieve this, the states are sampled at any one of the local triggering instant and then a centralized triggering condition is evaluated for possible control update. The utility of the scheme is analysed through a numerical simulation.

A new geometric proof of super-twisting control with actuator saturation

Abstract In this note, the stability of an uncertain system with actuator saturation using super-twisting controller (STC) is analysed. First, a new proof of STC ensuring finite-time stability of the system is proposed using geometric method which gives a new gain conditions. Then, using the proposed proof the domain of attraction (DOA) is explicitly calculated for the system with bounded control.

Periodic event-triggered sliding mode control

In this paper, we propose the periodic event-triggering based design of sliding mode control (SMC) for the linear time-invariant (LTI) systems. In this technique, the triggering instants are generated by a triggering mechanism which is evaluated periodically at those time instants when the state measurements are available. So, the continuous state measurement, as it is usually needed in the continuous event-triggering strategy, is no longer required in this proposed triggering strategy. The main advantages of this triggering mechanism are: (1) a uniform positive lower bound for the inter event time is guaranteed and (2) this technique is more economical and realistic than its continuous counterpart due to the relaxation of continuous measurements. In this work, we use SMC to design the periodic event-triggering condition where SMC is designed in such a way that it allows periodic evaluation of triggering rule while guaranteeing the robust performance of the system. Moreover, an upper bound of the sampling period for the periodic measurements is also obtained in this design. Finally, the simulation results are given to demonstrate the design methodology and performance of the system with the proposed event-triggering strategy.