398 research outputs found
Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays
The stabilization of uncertain LTI/LPV time delay systems with time varying
delays by state-feedback controllers is addressed. At the difference of other
works in the literature, the proposed approach allows for the synthesis of
resilient controllers with respect to uncertainties on the implemented delay.
It is emphasized that such controllers unify memoryless and exact-memory
controllers usually considered in the literature. The solutions to the
stability and stabilization problems are expressed in terms of LMIs which allow
to check the stability of the closed-loop system for a given bound on the
knowledge error and even optimize the uncertainty radius under some performance
constraints; in this paper, the performance measure is
considered. The interest of the approach is finally illustrated through several
examples
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Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities
Copyright [2001] 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.This paper investigates the robust reliable control problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, state time-delay, parameter uncertainties, possible actuator failures and unknown nonlinear disturbances, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback memoryless controllers such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains stochastically exponentially stable in mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the desired robust reliable exponential stability despite possible actuator failures, which are in terms of the solutions to algebraic Riccati inequalities. An illustrative example is exploited to demonstrate the applicability of the proposed design approac
Adaptive Backstepping Controller Design for Stochastic Jump Systems
In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques
Control of distributed delay systems with uncertainties: a generalized Popov theory approach
summary:The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for -attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples. Dedicated to Acad. Vlad Ionescu, in memoriam
Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections
In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach
Robust Performance Guarantees for System Level Synthesis
We generalize the system level synthesis framework to systems defined by bounded causal linear operators, and use this parameterization to make connections between robust system level synthesis and the robust control literature. In particular, by leveraging results from ℒ₁ robust control, we show that necessary and sufficient conditions for robust performance with respect to causal bounded linear uncertainty in the system dynamics can be translated into convex constraints on the system responses. We exploit this connection to show that these conditions naturally allow for the incorporation of delay, sparsity, and locality constraints on the system responses and resulting controller implementation, allowing these methods to be applied to large-scale distributed control problems - to the best of our knowledge, these are the first such robust performance guarantees for distributed control systems
Robust Performance Guarantees for System Level Synthesis
We generalize the system level synthesis framework to systems defined by
bounded causal linear operators, and use this parameterization to make
connections between robust system level synthesis and classical results from
the robust control literature. In particular, by leveraging results from L1
robust control, we show that necessary and sufficient conditions for robust
performance with respect to causal bounded linear uncertainty in the system
dynamics can be translated into convex constraints on the system responses. We
exploit this connection to show that these conditions naturally allow for the
incorporation of delay, sparsity, and locality constraints on the system
responses and resulting controller implementation, allowing these methods to be
applied to large-scale distributed control problems -- to the best of our
knowledge, these are the first such robust performance guarantees for
distributed control systems.Comment: To appear at IEEE ACC 2020; added numerical exampl
Robust H∞ control of networked control systems with access constraints and packet dropouts
We consider a class of networked control systems (NCSs) where the plant has time-varying norm-bounded parameter uncertainties, the network only provides a limited number of simultaneous accesses for the sensors and actuators, and the packet dropouts occur randomly in the network. For this class of NCSs with uncertainties and access constraints as well as packet dropouts, we derive sufficient conditions in the form of linear matrix inequalities that guarantee robust stochastic stabilisation and synthesis of H∞ controller. An example is provided to illustrate our proposed method
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Robust filtering for uncertain linear systems with delayed states and outputs
Copyright [2002] 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.Deals with the robust filtering problem for uncertain linear systems with delayed states and outputs. Both time-invariant and time-varying cases are considered. For the time-invariant case, an algebraic Riccati matrix inequality approach is proposed to design a robust H∞ filter such that the filtering process remains asymptotically stable for all admissible uncertainties, and the transfer function from the disturbance inputs to error state outputs satisfies the prespecified H∞ norm upper bound constraint. We establish the conditions under which the desired robust H ∞ filters exist, and derive the explicit expression of these filters. For the time-varying case, we develop a differential Riccati inequality method to design the robust filters. A numerical example is provided to demonstrate the validity of the proposed design approac
Non-fragile Dynamic Output Feedback H∞ Control for a Class of Uncertain Switched Systems with Time-varying Delay
The problem of non-fragile dynamic output feedback H∞ control for a class of uncertain switched systems with time-varying delay is discussed. Firstly, the form of non-fragile dynamic output feedback H∞ controller is given. Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously, Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique; Secondly, we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the inequality, and then introduce the J-function to obtain a nonlinear matrix inequality that satisfies the H∞ performance index γ, we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities, a sufficient condition for the existence of a non-fragile dynamic output feedback H∞ controller and satisfying the H∞ performance index γ is concluded for a class of uncertain switching systems with variable time delay; Finally, a switched system composed of two subsystems is considered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox.
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