共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper uses a frequency domain approach to the analysis of H2 performance of continuous time periodically time varying controllers. For control of linear time invariant plants, it is shown that the time varying dynamics of the periodic controller deteriorates the closed-loop system H2 performance and a linear time invariant controller can be found to provide strictly better H2 control of the system. 相似文献
2.
Robust output-feedback control of linear discrete-time systems 总被引:1,自引:0,他引:1
The problem of designing H∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope. 相似文献
3.
This study proposes a fault-tolerant control method for stochastic systems with multiple intermittent faults (IFs) and nonlinear disturbances, and both sensor and actuator faults are considered. The occurrence and disappearance of IFs are governed by Markov chain, and its transition probabilities are partly known. Hence, the faulty system can be described by a Markovian jump system (MJS). In order to ensure that the MJS is stochastically stable and satisfies H∞ performance index, mode-dependent output feedback controllers are modelled using linear matrix inequalities. Numerous sufficient conditions for stochastic stability are obtained on the basis of Lyapunov stability theory. Finally, the effectiveness of the developed method is evaluated on the three-tank system. 相似文献
4.
The problem of H∞ filtering of stationary discrete-time linear systems with stochastic uncertainties in the state space matrices is addressed, where the uncertainties are modeled as white noise. The relevant cost function is the expected value, with respect to the uncertain parameters, of the standard H∞ performance. A previously developed stochastic bounded real lemma is applied that results in a modified Riccati inequality. This inequality is expressed in a linear matrix inequality form whose solution provides the filter parameters. The method proposed is applied also to the case where, in addition to the stochastic uncertainty, other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope. The problem of mixed H2/H∞ filtering for the above system is also treated. The theory developed is demonstrated by a simple tracking example. 相似文献
5.
This paper deals with the problem of H∞ output feedback control for uncertain stochastic systems with time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is the design of a full-order dynamic output feedback controller ensuring robust exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system, irrespective of the uncertainties. A sufficient condition for the existence of such an output feedback controller is obtained and the expression of desired controllers is given. 相似文献
6.
This article is concerned with the mixed ?2/?∞ control problem over a finite horizon for a class of nonlinear Markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures. The stochastic nonlinearities described by statistical means could cover several types of well-studied nonlinearities, and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval. The purpose of the addressed problem is to design state feedback controllers such that the closed-loop system achieves the expected ?2 performance requirement with a guaranteed ?∞ disturbance attenuation level. The solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations. The controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations. A numerical example is given to illustrate the effectiveness and applicability of the proposed algorithm. 相似文献
7.
This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H2/H∞ specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem. 相似文献
8.
In this paper, we clarify a new relationship between invariant zeros of a generalized plant and the order reduction of H∞ controllers by using linear matrix inequalities in both continuous-time and discrete-time cases. In contrast with our recent paper, where a relationship between an unstable transmission-zero structure and the H∞ controller order reduction is initiated in a fundamental manner, results obtained in this paper are more flexible in two senses: assumptions that are made for the generalized plant are relaxed, and stable as well as unstable invariant zeros are characterized to obtain a reduced-order H∞ controller. 相似文献
9.
The algorithm being developed here is based on the generating function approach for finite-time H ∞ control and application of canonical transformation of linear Hamiltonian system. First, an equivalent finite-time H ∞ control law in terms of the third-type generating function is derived. Then, by using symplectic structure of the Hamiltonian system's state transition matrix, a group of matrix recursive formulae are deduced for the evaluation of the finite-time H ∞ control law. Combining with a matrix singularity testing procedure, this recursive algorithm verifies the existence condition of sub-optimal H ∞ controllers and gives the minimum H ∞ norm of finite-time control systems. Inherited from the canonical transformation, the matrix recursive formulae have a standard symplectic form; this structure-preserving property helps facilitate reliable and effective computation. Numerical results show the effectiveness of the proposed algorithm. 相似文献
10.
Mark M. Kogan 《International journal of control》2016,89(4):691-700
New stochastic γ0 and mixed H∞/γ0 filtering and control problems for discrete-time systems under completely unknown covariances are introduced and solved. The performance measure γ0 is the worst-case steady-state averaged variance of the error signal in response to the stationary Gaussian white zero-mean disturbance with unknown covariance and identity variance. The performance measure H∞/γ0 is the worst-case power norm of the error signal in response to two input disturbances in different channels, one of which is the deterministic signal with a bounded energy and the other is the stationary Gaussian white zero-mean signal with a bounded variance provided the weighting sum of disturbance powers equals one. In this framework, it is possible to consider at the same time both deterministic and stochastic disturbances highlighting their mutual effects. Our main results provide the complete characterisations of the above performance measures in terms of linear matrix inequalities and therefore both the γ0 and H∞/γ0 optimal filters and controllers can be computed by convex programming. H∞/γ0 optimal solution is shown to be actually a trade-off between optimal solutions to the H∞ and γ0 problems for the corresponding channels. 相似文献
11.
This paper investigates the problem of robust H∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H∞ control and robust pole assignment of uncertain systems. 相似文献
12.
Jinrong Liu James Lam Mouquan Shen Zhan Shu 《International journal of systems science》2017,48(10):2168-2181
In this paper, the issue of designing non-fragile H∞ multivariable proportional-integral-derivative (PID) controllers with derivative filters is investigated. In order to obtain the controller gains, the original system is associated with an extended system such that the PID controller design can be formulated as a static output-feedback control problem. By taking the system augmentation approach, the conditions with slack matrices for solving the non-fragile H∞ multivariable PID controller gains are established. Based on the results, linear matrix inequality -based iterative algorithms are provided to compute the controller gains. Simulations are conducted to verify the effectiveness of the proposed approaches. 相似文献
13.
For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H∞ optimal control. Another measure of the gain of a system is the H2 norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H2 norm is bounded by the H∞ norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H∞ norm as a function of the H2 norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H2 norm can be bounded by a function of the H∞ norm and the bandwidth of the system. 相似文献
14.
This paper discusses the problem of robust H∞ control for linear discrete time two-dimensional (2-D) singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainties. The purpose is the design of static output feedback controllers such that the resulting closed-loop system is acceptable, jump modes free, stable and satisfies a prescribed H∞ performance level for all admissible uncertainties. A version of bounded realness of 2-D SRM is established in terms of linear matrix inequalities. Based on this, a sufficient condition for the solvability of the robust H∞ control problem is solved, and a desired output feedback controller can be constructed by solving a set of matrix inequalities. A numerical example is provided to demonstrate the applicability of the proposed approach. 相似文献
15.
In this paper, we make a foray in the role played by a set of four operators on the study of robust H2 and mixed H2/H∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H2 performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H2 controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H2/H∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm. 相似文献
16.
M.-G.Myung-Gon Yoon Valery A. Ugrinovskii Ian R. Petersen 《Systems & Control Letters》2004,52(2):99-112
We study a finite-horizon robust minimax filtering problem for time-varying discrete-time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which the stochastic noises, driving the system, are defined. The optimal minimax filter has been found by applying techniques of risk-sensitive LQG control. The structure and properties of resulting filter are analyzed and compared to H∞ and Kalman filters. 相似文献
17.
In this paper, we deal with the problem of stochastic Nash differential games of Markov jump linear systems governed by Itô-type equation. Combining the stochastic stabilizability with the stochastic systems, a necessary and sufficient condition for the existence of the Nash strategy is presented by means of a set of cross-coupled stochastic algebraic Riccati equations. Moreover, the stochastic H2/H∞ control for stochastic Markov jump linear systems is discussed as an immediate application and an illustrative example is presented. 相似文献
18.
Fadel Lashhab Kevin Moore Tyrone Vincent Deyuan Meng Khalid Kuwairi 《International journal of control》2018,91(8):1906-1919
This paper studies an H∞ suboptimal control problems of consensus networks whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. We apply model, orthogonal and diagonal transformations to a dynamic consensus network in order to reduce the overall system into N ? 1 independent subsystems. We then establish a generalised methodology for designing a controller for a dynamic consensus network in the presence of external disturbances, focusing especially on using decentralised controllers that achieve consensus in the absence of disturbances and attenuation of disturbances to a prescribed H∞ performance level. A design example is given to illustrate our results. 相似文献
19.
20.
Junlin Xiong 《International journal of systems science》2013,44(3):255-265
This article deals with the robust H 2 control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H 2 performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H 2 performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory. 相似文献