共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It transforms the initial feasibility problem to an equivalent convex optimization problem, which is subsequently solved by means of an iterative algorithm. While this algorithm always converges to a feasible solution in a finite number of iterations, it requires that the radius of a non-empty ball contained into the solution set is known a priori. This rather restrictive assumption is released in this paper, while retaining the convergence property. Given an initial ellipsoid that contains the solution set, the approach proposed here iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. At each iteration a random uncertainty sample is generated with a specified probability density, which parameterizes an LMI. For this LMI the next minimum-volume ellipsoid that contains the solution set is computed. An upper bound on the maximum number of possible correction steps, that can be performed by the algorithm before finding a feasible solution, is derived. A method for finding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real-life diesel actuator benchmark model with real parametric uncertainty, for which a
robust state-feedback controller is designed. 相似文献
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A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs 总被引:1,自引:0,他引:1
Many robust control problems can be formulated in abstract form as convex feasibility programs, where one seeks a solution x that satisfies a set of inequalities of the form . This set typically contains an infinite and uncountable number of inequalities, and it has been proved that the related robust feasibility problem is numerically hard to solve in general.
In this paper, we discuss a family of cutting plane methods that solve efficiently a probabilistically relaxed version of the problem. Specifically, under suitable hypotheses, we show that an Analytic Center Cutting Plane scheme based on a probabilistic oracle returns in a finite and pre-specified number of iterations a solution x which is feasible for most of the members of , except possibly for a subset having arbitrarily small probability measure. 相似文献
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Yasuaki Oishi Author Vitae 《Automatica》2007,43(3):538-545
A randomized approach is considered for a feasibility problem on a parameter-dependent linear matrix inequality (LMI). In particular, a gradient-based and an ellipsoid-based randomized algorithms are improved by introduction of a stopping rule. The improved algorithms stop after a bounded number of iterations and this bound is of polynomial order in the problem size. When the algorithms stop, either of the following two events occurs: (i) they find with high confidence a probabilistic solution, which satisfies the given LMI for most of the parameter values; (ii) they detect in an approximate sense the non-existence of a deterministic solution, which satisfies the given LMI for all the parameter values. These results are important because the original randomized algorithms have issues to be settled on detection of convergence, on the speed of convergence, and on the assumption of feasibility. The improved algorithms can be adapted for an optimization problem constrained by a parameter-dependent LMI. A numerical example shows the efficacy of the proposed algorithms. 相似文献
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Marco C. Campi Author Vitae Simone Garatti Author Vitae 《Annual Reviews in Control》2009,33(2):149-157
The ‘scenario approach’ is an innovative technology that has been introduced to solve convex optimization problems with an infinite number of constraints, a class of problems which often occurs when dealing with uncertainty. This technology relies on random sampling of constraints, and provides a powerful means for solving a variety of design problems in systems and control. The objective of this paper is to illustrate the scenario approach at a tutorial level, focusing mainly on algorithmic aspects. Its versatility and virtues will be pointed out through a number of examples in model reduction, robust and optimal control. 相似文献
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An improved robust model predictive control for linear parameter‐varying input‐output models 下载免费PDF全文
This paper describes a new robust model predictive control (MPC) scheme to control the discrete‐time linear parameter‐varying input‐output models subject to input and output constraints. Closed‐loop asymptotic stability is guaranteed by including a quadratic terminal cost and an ellipsoidal terminal set, which are solved offline, for the underlying online MPC optimization problem. The main attractive feature of the proposed scheme in comparison with previously published results is that all offline computations are now based on the convex optimization problem, which significantly reduces conservatism and computational complexity. Moreover, the proposed scheme can handle a wider class of linear parameter‐varying input‐output models than those considered by previous schemes without increasing the complexity. For an illustration, the predictive control of a continuously stirred tank reactor is provided with the proposed method. 相似文献
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We study the behaviour of stochastic discrete-time models controlled by an output linear feedback during a tracking process. The controlled system is assumed to be nonlinear satisfying the global ‘quasi-Lipschitz’ condition and subjected to stochastic input and output disturbances. Two gain matrices (in a feedback and in an observer) define an ‘averaged’ ellipsoid in the tracking-error space where all system's trajectories arrive ‘with probability one’. The selection of the ‘best’ gain matrices is realised numerically by application of the robust attractive ellipsoid method with the linear matrix inequality technique application. The suggested approach is illustrated by designing of a robust tracking controller for a benchmark example in the presence of stochastic noises both in the state dynamics and in the output observations. 相似文献
8.
Randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak and Tempo [(Syst. Control Lett. 43(5) (2001) 343)] and Calafiore and Polyak [(IEEE Trans. Autom. Control 46 (11) (2001) 1755)] for the present problem. It is possible however to show that the expected number of iterations necessary to have a deterministic solution is infinite. In order to make this number finite, the improved algorithm is proposed. The number of iterations necessary to have a probabilistic solution is also considered and is shown to be independent of the parameter dimension. A numerical example is provided. 相似文献
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Karina A. Barbosa Carlos E. de Souza Alexandre Trofino 《Systems & Control Letters》2005,54(3):251-262
This paper addresses the design of robust filters for linear continuous-time systems subject to parameter uncertainty in the state-space model. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Two methods based on parameter-dependent Lyapunov functions are proposed for designing linear stationary asymptotically stable filters that assure asymptotic stability and a guaranteed performance, irrespective of the uncertain parameters. The proposed filter designs are given in terms of linear matrix inequalities which depend on a scalar parameter that should be searched for in order to optimize the filter performance. 相似文献
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Shu-Xiang Guo 《International journal of systems science》2018,49(7):1491-1506
Interval models are frequently used for dealing with uncertainties of control systems. However, it is well known that direct analysis and synthesis of a controlled dynamic system with interval matrix uncertainties may be a NP-hard problem. In this work, an efficient methodology for robustness analysis and robust control design of dynamic systems with interval matrix uncertainties is presented systematically, in which the uncertainties appearing in the controlled plant and controller realisation are taken into account simultaneously in an integrated framework. The fundamental problems, such as quadratic stability, guaranteed cost control and H∞ control of uncertain systems are taken as examples to show the methodology. Necessary and sufficient conditions for linear dynamic systems with interval matrices are derived by transforming all the interval matrices into some more tractable forms. The whole reasoning process is logical and rigorous, and NP-hard problem is successfully avoided. The presented formulations are within the framework of linear matrix inequality and can be implemented conveniently. In contrast to existing vertex-set methods, in which the vertices of interval matrices need to be constructed and checked, the presented methods are more efficient. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method. 相似文献
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In this paper the observation process of stochastic discrete‐time nonlinear system is analyzed. The system to be observed is assumed to be uncertain, but fulfilling the global "quasi‐Lipschitz" condition and is subjected to stochastic input and output disturbances of a white noise type. The combination of a traditional Luenberger residual term with a discontinuous one is considered. The designing of the best observer gain matrices is realized by using the Robust Attractive Ellipsoid Method for the analysis of the averaged observation error. The construction of this attractive ellipsoid is based on the numerical solution of some matrix optimization problem under specific constraints of Bilinear and Linear Matrix Inequalities (BMI's and LMI's) type applied to improve the attractiveness zone estimation. Two numerical xamples illustrate the effectiveness of the suggested approach. 相似文献
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Eugenio Cinquemani Mayank Agarwal Debasish Chatterjee John LygerosAuthor vitae 《Automatica》2011,47(9):2082-2087
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost subject to probabilistic constraints. We study the convexity of a finite-horizon optimization problem in the case where the control policies are affine functions of the disturbance input. We propose an expectation-based method for the convex approximation of probabilistic constraints with polytopic constraint function, and a Linear Matrix Inequality (LMI) method for the convex approximation of probabilistic constraints with ellipsoidal constraint function. Finally, we introduce a class of convex expectation-type constraints that provide tractable approximations of the so-called integrated chance constraints. Performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example. 相似文献
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Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach 总被引:1,自引:0,他引:1
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme. 相似文献
18.
A team algorithm based on piecewise quadratic simultaneous Lyapunov functions for robust stability analysis and control design of uncertain time‐varying linear systems is introduced. The objective is to use robust stability criteria that are less conservative than the usual quadratic stability criterion. The use of piecewise quadratic Lyapunov functions leads to a non‐convex optimization problem, which is decomposed into a convex subproblem in a selected subset of decision variables, and a lower‐dimensional non‐convex subproblem in the remaining decision variables. A team algorithm that combines genetic algorithms (GA) for the non‐convex subproblem and interior‐point methods for the solution of linear matrix inequalities (LMI), which form the convex subproblem, is proposed. Numerical examples are given, showing the advantages of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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This paper addresses robust constrained model predictive control (MPC) for a class of nonlinear systems with structured time‐varying uncertainties. First, the Takagi‐Sugeno (T‐S) fuzzy model is employed to represent a nonlinear system. Then, we develop some techniques for designing fuzzy control which guarantees the system stabilization subject to input and output constraints. Both parallel and nonparallel distributed compensation control laws (PDC and non‐PDC) are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. A simulation example is presented to illustrate the design procedures and performances of the proposed methods. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society 相似文献
20.
Li Li Author Vitae Valery A. Ugrinovskii Author Vitae Robert Orsi Author Vitae 《Automatica》2007,43(11):1932-1944
This paper addresses the problem of decentralized robust stabilization and control for a class of uncertain Markov jump parameter systems. Control is via output feedback and knowledge of the discrete Markov state. It is shown that the existence of a solution to a collection of mode-dependent coupled algebraic Riccati equations and inequalities, which depend on certain additional parameters, is both necessary and sufficient for the existence of a robust decentralized switching controller. A guaranteed upper bound on robust performance is also given. To obtain a controller which satisfies this bound, an optimization problem involving rank constrained linear matrix inequalities is introduced, and a numerical approach for solving this problem is presented. To demonstrate the efficacy of the proposed approach, an example stabilization problem for a power system comprising three generators and one on-load tap changing transformer is considered. 相似文献