716 research outputs found
Recommended from our members
On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper
H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays
This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the H∞ filtering problem for a general class of nonlinear discrete-time stochastic systems with randomly varying sensor delays, where the delayed sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law. In terms of the Hamilton–Jacobi–Isaacs inequalities, preliminary results are first obtained that ensure the addressed system to possess an l2-gain less than a given positive scalar γ. Next, a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation. Furthermore, it is shown that our main results can be readily specialized to the case of linear stochastic systems. Finally, a numerical simulation example is used to demonstrate the effectiveness of the results derived.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor James Lam under the direction of Editor Ian R. Petersen. This work was supported by the Shanghai Natural Science Foundation under Grant 07ZR14002, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany
Optimal control of partially observable linear quadratic systems with asymmetric observation errors
This paper deals with the optimal quadratic control problem for non-Gaussian discrete-time stochastic systems. Our main result gives explicit solutions for the optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. For this purpose an asymmetric version of the Kalman filter based on asymmetric least squares estimation is used. We illustrate the applicability of our approach with numerical results
Event-based security control for discrete-time stochastic systems
This study is concerned with the event-based security control problem for a class of discrete-time stochastic systems with multiplicative noises subject to both randomly occurring denial-of-service (DoS) attacks and randomly occurring deception attacks. An event-triggered mechanism is adopted with hope to reduce the communication burden, where the measurement signal is transmitted only when a certain triggering condition is violated. A novel attack model is proposed to reflect the randomly occurring behaviours of the DoS attacks as well as the deception attacks within a unified framework via two sets of Bernoulli distributed white sequences with known conditional probabilities. A new concept of mean-square security domain is put forward to quantify the security degree. The authors aim to design an output feedback controller such that the closed-loop system achieves the desired security. By using the stochastic analysis techniques, some sufficient conditions are established to guarantee the desired security requirement and the control gain is obtained by solving some linear matrix inequalities with nonlinear constraints. A simulation example is utilised to illustrate the usefulness of the proposed controller design scheme.This work was supported in part by Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61573246 and 61374039, the Shanghai Rising-Star Programme of China under Grant 16QA1403000, the Program for Capability Construction of Shanghai Provincial Universities under Grant 15550502500 and the Alexander von Humboldt Foundation of Germany
A Unified Filter for Simultaneous Input and State Estimation of Linear Discrete-time Stochastic Systems
In this paper, we present a unified optimal and exponentially stable filter
for linear discrete-time stochastic systems that simultaneously estimates the
states and unknown inputs in an unbiased minimum-variance sense, without making
any assumptions on the direct feedthrough matrix. We also derive input and
state observability/detectability conditions, and analyze their connection to
the convergence and stability of the estimator. We discuss two variations of
the filter and their optimality and stability properties, and show that filters
in the literature, including the Kalman filter, are special cases of the filter
derived in this paper. Finally, illustrative examples are given to demonstrate
the performance of the unified unbiased minimum-variance filter.Comment: Preprint for Automatic
OPTIMAL CONTROL OF PARTIALLY OBSERVABLE LINEAR QUADRATIC SYSTEMS WITH ASYMMETRIC OBSERVATION ERRORS
This paper deals with the optimal quadratic control problem for non-Gaussian discrete-time stochastic systems. Our main result gives explicit solutions for the optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. For this purpose an asymmetric version of the Kalman filter based on asymmetric least squares estimation is used. We illustrate the applicability of our approach with numerical results.
Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems
We consider the problem of learning control policies in discrete-time
stochastic systems which guarantee that the system stabilizes within some
specified stabilization region with probability~. Our approach is based on
the novel notion of stabilizing ranking supermartingales (sRSMs) that we
introduce in this work. Our sRSMs overcome the limitation of methods proposed
in previous works whose applicability is restricted to systems in which the
stabilizing region cannot be left once entered under any control policy. We
present a learning procedure that learns a control policy together with an sRSM
that formally certifies probability~ stability, both learned as neural
networks. We show that this procedure can also be adapted to formally verifying
that, under a given Lipschitz continuous control policy, the stochastic system
stabilizes within some stabilizing region with probability~. Our
experimental evaluation shows that our learning procedure can successfully
learn provably stabilizing policies in practice.Comment: Accepted at ATVA 2023. Follow-up work of arXiv:2112.0949
Rumour Processes on N
We study four discrete time stochastic systems on \bbN modeling processes
of rumour spreading. The involved individuals can either have an active or a
passive role, speaking up or asking for the rumour. The appetite in spreading
or hearing the rumour is represented by a set of random variables whose
distributions may depend on the individuals. Our goal is to understand - based
on those random variables distribution - whether the probability of having an
infinite set of individuals knowing the rumour is positive or not
- …