138 research outputs found
A new result on observer-based sliding mode control design for a class of uncertain Ito^ stochastic delay systems
© 2017 The Franklin Institute This paper develops a new observer-based sliding mode control (SMC) scheme for a general class of Ito^ stochastic delay systems (SDS). The key merit of the presented scheme lies in its simplicity and integrity in design process of the traditional sliding mode observer (SMO) strategy, i.e., the state observer and sliding surface design as well as the associated sliding mode controller synthesis. For guaranteeing to use the scheme, a new LMIs-based criterion is established to ensure the exponential stability of the underlying sliding mode dynamics (SMDs) in mean-square sense with H∞ performance. A bench test example is provided to numerically demonstrate the efficacy of the scheme and illustrate the application procedure for potential readers/users with interest in their ad hoc applications and methodology expansion
Almost sure H∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays
This paperinvestigatesthealmostsure H1 sliding mode control (SMC) problem for non linear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the topping time method combined with martingale in equalities, sufficient conditions are established to ensure the almost surely exponential stability and the H 1 performance of the system dynamics in the specified sliding surface. ASMC law is designed to guarantee the reach ability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix in equalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme
Sliding mode control for singular stochastic Markovian jump systems with uncertainties
This paper considers sliding mode control design for singular stochastic Markovian jump systems with uncertainties. A suitable integral sliding function is proposed and the resulting sliding mode dynamics is an uncertain singular stochastic Markovian jump system. A set of new sufficient conditions is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics, but is also constructive and determines all the parameter matrices in the integral sliding function. A set of new sufficient conditions is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics, but also determines all the parameter matrices in the integral sliding function. Then, a sliding mode control law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, three examples are given to demonstrate the effectiveness of the results
H
This paper addresses the problem of H∞ control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method
Robust Stabilisation of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes
This paper addresses the robust stabilisation problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a non-parallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for T-S fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analysed and the sliding mode controller is parameterised in terms of the solutions of a set of linear matrix inequalities (LMIs) which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented
Design of sliding-mode observer for a class of uncertain neutral stochastic systems
© 2016 Informa UK Limited, trading as Taylor & Francis Group. The problem of robust H∞ control for a class of uncertain neutral stochastic systems (NSS) is investigated by utilising the sliding-mode observer (SMO) technique. This paper presents a novel observer and integral-type sliding-surface design, based on which a new sufficient condition guaranteeing the resultant sliding-mode dynamics (SMDs) to be mean-square exponentially stable with a prescribed level of H∞ performance is derived. Then, an adaptive reaching motion controller is synthesised to lead the system to the predesigned sliding surface in finite-time almost surely. Finally, two illustrative examples are exhibited to verify the validity and superiority of the developed scheme
Nonlinear Systems
Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems
Qualitative Properties of Hybrid Singular Systems
A singular system model is mathematically formulated as a set of coupled differential
and algebraic equations. Singular systems, also referred to as descriptor or differential
algebraic systems, have extensive applications in power, economic, and biological systems.
The main purpose of this thesis is to address the problems of stability and stabilization for
singular hybrid systems with or without time delay.
First, some su cient conditions on the exponential stability property of both continuous
and discrete impulsive switched singular systems with time delay (ISSSD) are proposed.
We address this problem for the continuous system in three cases: all subsystems are
stable, the system consists of both stable and unstable subsystems, and all subsystems are
unstable. For the discrete system, we focus on when all subsystems are stable, and the
system consists of both stable and unstable subsystems. The stability results for both the
continuous and the discrete system are investigated by first using the multiple Lyapunov
functions along with the average-dwell time (ADT) switching signal to organize the jumps
among the system modes and then resorting the Halanay Lemma.
Second, an optimal feedback control only for continuous ISSSD is designed to guarantee
the exponential stability of the closed-loop system. Moreover, a Luenberger-type observer
is designed to estimate the system states such that the corresponding closed-loop error
system is exponentially stable. Similarly, we have used the multiple Lyapunov functions
approach with the ADT switching signal and the Halanay Lemma.
Third, the problem of designing a sliding mode control (SMC) for singular systems
subject to impulsive effects is addressed in continuous and discrete contexts. The main
objective is to design an SMC law such that the closed-loop system achieves stability.
Designing a sliding surface, analyzing a reaching condition and designing an SMC law are investigated throughly. In addition, the discrete SMC law is slightly modi ed to eliminate
chattering.
Last, mean square admissibility for singular switched systems with stochastic noise in
continuous and discrete cases is investigated. Sufficient conditions that guarantee mean
square admissibility are developed by using linear matrix inequalities (LMIs)
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