Decentralised sliding mode control for nonlinear interconnected systems in the regular form

In this paper, a decentralised control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems in regular form. All the isolated subsystems and interconnections are fully nonlinear. It is not required that the nominal isolated subsystems are either linearizable or partially linearizable. The uncertainties are nonlinear and bounded by nonlinear functions. Specifically, uncertainties in the input distribution and interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed by only employing local information. Sufficient conditions are developed under which information on the interconnections is employed for decentralised controller design to reduce conservatism. The bounds on the uncertainties have more general forms compared with previous work. A simulation example is used to demonstrate the effectiveness of the proposed method

Stabilisation of Time Delay Systems with Nonlinear Disturbances Using Sliding Mode Control

This paper focuses on a class of control systems with delayed states and nonlinear disturbances using sliding mode techniques. Both matched and mismatched uncertainties are considered which are assumed to be bounded by known nonlinear functions. The bounds are used in the control design and analysis to reduce conservatism. A sliding function is designed and a set of sufficient conditions is derived to guarantee the asymptotic stability of the corresponding sliding motion by using the Lyapunov-Razumikhin approach which allows large time varying delay with fast changing rate. A delay dependent sliding mode control is synthesised to drive the system to the sliding surface in finite time and maintain a sliding motion thereafter. Effectiveness of the proposed method is demonstrated via a case study on a continuous stirred tank reactor system

Stabilization of hybrid systems by intermittent feedback controls based on discrete-time observations with a time delay

This paper mainly investigates stabilization of hybrid stochastic differential equations (SDEs) via periodically intermittent feedback controls based on discrete-time state observations with a time delay. First, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for the stability of hybrid SDEs. Then, we prove the intermittent stabilization for a given unstable nonlinear hybrid SDE by comparison theorem. Two numerical examples are discussed to support our results of theoretical analysis

Stabilisation in distribution by delay feedback control for hybrid stochastic differential equations

This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection

Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations

Recently, Mao [1] proposed a kind of feedback control based on discrete time state observations to stabilize continuous-time hybrid stochastic systems in mean-square sense. We find that the feedback control there still depends on the continuous-time observations of the mode. However, it usually costs to identify the current mode of the system in practice. So we can further improve the control to reduce the control cost by identifying the mode at discrete times when we make observations for the state. In this paper, we aim to design such a type of feedback controls based on the discrete-time observations of both state and mode to stabilize the given unstable hybrid stochastic differential equations (SDEs) in the sense of mean-square exponential stability. Moreover, a numerical example is given to illustrate our results

Stabilization of nonlinear hybrid stochastic delay systems by feedback control based on discrete-time state and mode observations

This paper is concerned with the stabilization problem for nonlinear stochastic delay systems with Markovian switching by feedback control based on discrete-time state and mode observations. By constructing an efficient Lyapunov functionals, we establish the sufficient stabilization criteria not only in the sense of exponential stability (both the mean-square stability and the almost sure stability) but also in other sense – that of H∞ stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is obtained. Numerical examples are provided to demonstrate the effectiveness of our theoretical results

Generalised regular form based SMC for nonlinear systems with application to a WMR

In this paper, a generalised regular form is proposed to facilitate sliding mode control (SMC) design for a class of nonlinear systems. A novel nonlinear sliding surface is designed using implicit function theory such that the resulting sliding motion is globally asymptotically stable. Sliding mode controllers are proposed to drive the system to the sliding surface and maintain a sliding mo-tion thereafter. Tracking control of a two-wheeled mobile robot is considered to underpin the developed theoretical results. Model-based tracking control of a wheeled mobile robot (WMR) is first transferred to a stabilisation problem for the corresponding tracking error system, and then the developed theoretical results are applied to show that the tracking error system is globally asymptotically stable even in the presence of matched and mismatched uncertainties. Both experimental and simulation results demonstrate that the developed results are practicable and effective

Generalised regular form based SMC for nonlinear systems with application to a WMR

In this paper, a generalised regular form is proposed to facilitate sliding mode control (SMC) design for a class of nonlinear systems. A novel nonlinear sliding surface is designed using implicit function theory such that the resulting sliding motion is globally asymptotically stable. Sliding mode controllers are proposed to drive the system to the sliding surface and maintain a sliding mo-tion thereafter. Tracking control of a two-wheeled mobile robot is considered to underpin the developed theoretical results. Model-based tracking control of a wheeled mobile robot (WMR) is first transferred to a stabilisation problem for the corresponding tracking error system, and then the developed theoretical results are applied to show that the tracking error system is globally asymptotically stable even in the presence of matched and mismatched uncertainties. Both experimental and simulation results demonstrate that the developed results are practicable and effective

Application of Emotional Design to the Form Redesign of a Midwifery Training Aid

This paper focuses on the form redesign of a midwifery training aid. The training aid needed to represent a pregnant woman as well as having an appearance suitable for a medical device. The redesign was informed by Donald Norman’s Emotional Design Theory in order to explore the design form to combine functionality and technology, as well to gain attention and elicit positive emotional responses from the user. The redesigned prototype was realised using 3D printing and other rapid prototyping technologies. The prototype was exhibited at an international exhibition and feedback from medical simulation experts indicated that the design form was appropriate for the intended purpose

Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique

This paper deals with the robust stabilization of continuous-time hybrid stochastic systems with timevarying delay by feedback controls based on discrete-time state observations. By employing the Razumikhin technique, delay-independent criteria to determine controllers and time lags are established just under a weaker condition that the time-varying delay should be a bounded function. Meanwhile, for the nondelay system, we obtain a better bound on the duration τ between two consecutive state observations. The new theory developed in this paper improves the existing results. Numerical examples are provided to demonstrate the effectiveness of our results