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Proceedings ArticleDOI

Stochastic discrete higher order sliding mode control

TL;DR: The proposed definition and control scheme is validated through the simulation of a rectilinear plant and it is shown that a control input is designed for an uncertain stochastic system with partial state information such that stoChastic discrete higher-order sliding mode takes place.
Abstract: 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.
Citations
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22 citations


Cites background from "Stochastic discrete higher order sl..."

  • ...2 Switching control design To compensate the uncertainty in the system, the switching control part us(k) is designed to be us(k) = −αsgn[s̄(k)], (31) where α is a design parameter....

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  • ...30 On considering the equivalent control (30), the switching control (31), and disturbance estimation technique given in the work of Sharma and Janardhanan,30 the combined control law is obtained to be u(k) = − ( c̄B̄2 )−1c̄Ā21x̄(k) − (c̄B̄2)−1c̄Ā22ξ(k) − αsgn(s̄(k)) − (c̄B̄2)−1c̄ ̂̄ d2(k), (32) where ̂̄ d2 is the estimate of d̄2....

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Journal ArticleDOI
TL;DR: A new approach to design a SMC-based functional observer for discrete-time stochastic systems based on the Kronecker product approach is presented, which leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter.
Abstract: Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.

20 citations

Journal ArticleDOI
TL;DR: This brief addresses the problem of sliding mode control (SMC) design using functional observer (FO) for discrete-time stochastic systems with norm-bounded parametric uncertainty in the system matrix by using FO-based approach for estimating SMC design.
Abstract: This brief addresses the problem of sliding mode control (SMC) design using functional observer (FO) for discrete-time stochastic systems with norm-bounded parametric uncertainty in the system matrix. SMC is a most powerful, robust control technique to stabilize discrete-time systems. However, the application of SMC becomes difficult when the system states are not accessible for feedback. Hence the proposed method uses FO-based approach for estimating SMC design. To mitigate the side effect of the parameter uncertainty on the estimation error, a sufficient condition of stability is provided based on Gershgorin disc theorem. The feasibility and effectiveness of our derived results are illustrated through a simulation example.

9 citations

Proceedings ArticleDOI
01 Dec 2017
TL;DR: This paper presents a new method to design functional observers for linear discrete-time stochastic systems, based on the Kronecker product approach, with existence conditions and stability analysis of the functional observers.
Abstract: This paper presents a new method to design functional observers for linear discrete-time stochastic systems, based on the Kronecker product approach. Existence conditions and stability analysis of the functional observers are provided. Further, covariance condition is provided for minimizing the effect of measurement and process noise in the functional observer. A simulation example is provided to demonstrate the usefulness of the proposed design method.

9 citations

Journal ArticleDOI
TL;DR: A technique to design a DHOSM control with adaptive switching gains where the bound on the disturbance is considered to be unknown is presented.
Abstract: The concept of discrete-time higher order sliding mode (DHOSM) has received increased attention. However, because of the dearth of knowledge on bound of the external disturbance in the system, an adaptive control law is desirable. This brief presents a technique to design a DHOSM control with adaptive switching gains where the bound on the disturbance is considered to be unknown.

7 citations


Cites background from "Stochastic discrete higher order sl..."

  • ...DHOSM control for stochastic systems in the presence of noise is designed in [29]....

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References
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Journal ArticleDOI
Arie Levant1
TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

2,954 citations


"Stochastic discrete higher order sl..." refers background in this paper

  • ...The continuous higher order sliding mode can successfully remove the chattering in the control input [9]–[12]....

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Journal ArticleDOI
TL;DR: It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay and a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced.
Abstract: The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.

2,714 citations


"Stochastic discrete higher order sl..." refers background in this paper

  • ...Here, r is known as sliding order [25] and Bd is a constant....

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Book
01 Jan 2001
TL;DR: This edition of A Course in Probability Theory includes an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.
Abstract: Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

2,647 citations

Journal ArticleDOI
TL;DR: This paper presents a treatment of discrete variable structure control systems, and a recently introduced "reaching law approach" is conveniently used to develop the control law for robust control.
Abstract: This paper presents a treatment of discrete variable structure control systems. The purpose is to lay a foundation upon which design of such type of systems can be made properly. Phenomena of switching, reaching, and quasi-sliding mode are investigated thoroughly. Terms pertaining to discrete variable structure control are defined. A method of quasi-sliding mode design is given. The inherently existing quasi-sliding mode band is analyzed. A recently introduced "reaching law approach" is conveniently used to develop the control law for robust control. Comments are given regarding chattering. The design technique is illustrated by a simulated system. >

1,428 citations


"Stochastic discrete higher order sl..." refers background in this paper

  • ...But, because of finite switching frequency, discrete sliding function can not move on the sliding manifold and exhibits the chattering [7], [8]....

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Journal ArticleDOI
TL;DR: It is shown that the newly proposed non-smooth control-based DSMC can guarantee the same level of accuracy for the sliding mode motion as that of an equivalent control- based DSMC.

250 citations


"Stochastic discrete higher order sl..." refers background in this paper

  • ...Therefore, discrete-time sliding mode (DSM) controller has received increased attention [1]–[5]....

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