共查询到20条相似文献，搜索用时 15 毫秒
1.
In this paper, we consider the mixed ??2/??∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled Hamilton–Jacobi–Isaacs equations (HJIEs). For linear systems, it is shown that these conditions reduce to a pair of coupled Riccati equations similar to the ones for the control case. Both the finite‐horizon and the infinite‐horizon problems are discussed. Simulation results are presented to show the usefulness of the scheme, and the results are generalized to include other classes of nonlinear systems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
In this paper, we study the problem of disturbance attenuation by output feedback for linear systems subject to actuator saturation. A nonlinear output feedback, expressed in the form of a quasi‐linear parameter‐varying system with state‐dependent scheduling parameter, is constructed that leads to the attenuation of the effect of the disturbance on the output of the system. The level of disturbance attenuation is measured in terms of the restricted ℒ︁2 gain and the restricted ℒ︁2–ℒ︁∞ gain over a class of bounded disturbances. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
3.
In this paper, we consider the ??∞‐filtering problem for singularly perturbed (two time‐scale) nonlinear systems. Two types of filters are discussed, namely, (i) decomposition and (ii) aggregate, and sufficient conditions for the solvability of the problem in terms of Hamilton–Jacobi–Isaac's equations (HJIEs) are presented. Reduced‐order filters are also derived in each case, and the results are specialized to linear systems, in which case the HJIEs reduce to a system of linear‐matrix‐inequalities (LMIs). Based on the linearization of the nonlinear models, upper bounds ε* of the singular parameter ε that guarantee the asymptotic stability of the nonlinear filters can also be obtained. The mixed ??2/??∞‐filtering problem is also discussed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
A novel delay‐dependent filtering design approach is developed for a class of linear piecewise discrete‐time systems with convex‐bounded parametric uncertainties and time‐varying delays. The time‐delays appear in the state as well as the output and measurement channels. The filter has a linear full‐order structure and guarantees the desired estimation accuracy over the entire uncertainty polytope. The desired accuracy is assessed in terms of either ??∞‐performance or ??2–??∞ criteria. A new parametrization procedure based on a combined Finsler's Lemma and piecewise Lyapunov–Krasovskii functional is established to yield sufficient conditions for delay‐dependent filter feasibility. The filter gains are determined by solving a convex optimization problem over linear matrix inequalities. In comparison to the existing design methods, the developed methodology yields the least conservative measures since all previous overdesign limitations are almost eliminated. By means of simulation examples, the advantages of the developed technique are readily demonstrated. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
5.
W. H. T. M. Aangenent G. Witvoet W. P. M. H. Heemels M. J. G. van de Molengraft M. Steinbuch 《国际强度与非线性控制杂志
》2010,20(11):1213-1233
》2010,20(11):1213-1233
In this paper we present a general linear matrix inequality‐based analysis method to determine the performance of a SISO reset control system in both the ??2 gain and ??2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ??2 gain performance and the ??2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear‐based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ??2 gain and ??2 norm calculations and show that, for an input constrained ??2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
6.
J. De Caigny J. F. Camino R. C. L. F. Oliveira P. L. D. Peres J. Swevers 《国际强度与非线性控制杂志
》2012,22(5):535-558
》2012,22(5):535-558
This paper presents synthesis conditions for the design of gain‐scheduled dynamic output feedback controllers for discrete‐time linear parameter‐varying systems. The state‐space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective ??∞ and ??2 gain‐scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real‐time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter‐dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
7.
In this paper we give an optimal state–space solution to the ???/??∞ fault‐detection (FD) problem for linear time invariant dynamic systems. An optimal ???/??∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. We provide a state–space realization of the optimal filter in an observer form using the solution of a linear matrix inequalities optimization problem. We also show that, through the use of weighting filters, the detection performance can be enhanced and some assumptions can be removed. Two numerical examples are given to illustrate the algorithm. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
Repetitive processes propagate information in two independent directions where the duration of one is finite. They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops controller design algorithms for differential linear processes, where information in one direction is governed by a matrix differential equation and in the other by a matrix discrete equation, in an ??2/??∞ setting. The objectives are stabilization and disturbance attenuation, and the controller used is actuated by the process output and hence the use of a state observer is avoided. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
9.
Keith G. Woodgate 《国际强度与非线性控制杂志
》1997,7(1):29-42
》1997,7(1):29-42
The paper presents a complete solution for the multivariable, continuous-time Generalized ℋ︁∞ (𝒢ℋ︁∞) sensitivity minimization problem. In contrast with existing solutions, derived via polynomial methods, the state-space solution given here is essentially non-iterative. Closed formulae for the minimum and a particular optimal controller are derived in terms of a real Schur decomposition, the solution of two Lyapunov equations and a single, well-conditioned eigenvalue problem. © 1997 by John Wiley & Sons, Ltd. 相似文献
10.
In this paper, a new theory of two‐degrees‐of‐freedom (2‐DOF)‐??∞ and certainty‐equivalent filters is presented. Exact and approximate solutions to the nonlinear ??∞ filtering problem using this class of filters are derived in terms of discrete‐time Hamilton–Jacobi–Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree‐of‐freedom, these filters are a substantial improvement over the earlier 1‐DOF case. The theory presented is also generalized to n‐DOF filters, which bore strong connections to linear infinite‐impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
11.
This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time‐delays are mode dependent. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process and the uncertainties are norm‐bounded. We construct an appropriate Lyapunov–Krasovskii functional and design a simultaneous ℋ︁2/ℋ︁∞ controller which minimizes a quadratic ℋ︁2 performance measure while satisfying a prescribed ℋ︁∞‐norm bound on the closed‐loop system. It is established that sufficient conditions for the existence of the simultaneous ℋ︁2/ℋ︁∞ controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, we will first derive a general synthesis condition for the output‐feedback ??∞ control of smooth nonlinear systems. Computationally efficient ??∞ control design procedure for a subclass of smooth nonlinear systems with polynomial vector field is then proposed by converting the resulting Hamilton‐Jacobi‐Isaacs inequalities from rational forms to their equivalent polynomial forms. Using quadratic Lyapunov functions, both the state‐feedback and output‐feedback problems will be reformulated as semi‐definite optimization conditions and locally tractable solutions can be obtained through sum‐of‐squares (SOS) programming. The proposed nonlinear ??∞ design approach achieves significant relaxations on the plant structure compared with existing results in the literature. Moreover, the SOS‐based solution algorithm provides an effective computational scheme to break the bottleneck in solving nonlinear ??∞ and optimal control problems. The proposed nonlinear ??∞ control approach has been applied to several examples to demonstrate its advantages over existing nonlinear control techniques and its usefulness to engineering problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, the ??∞ and l2–l∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ??∞ and l2–l∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ??∞ and l2–l∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
14.
The exponential output tracking problem for a class of single‐input, single‐output uncertain nonlinear systems, including systems with extended matching unstructured uncertainties and without a well‐defined global relative degree, is addressed. Conditions on the uncertain system dynamics are derived, which allow us to design a state‐feedback learning control achieving semi‐global exponential output tracking of sufficiently smooth and periodic reference signals of known period, while guaranteeing ??2 and ??∞ transient performances during the learning phase. The application of the proposed learning approach to the position tracking control problem for uncertain permanent magnet step motors with non‐sinusoidal flux distribution and uncertain position‐dependent load torque allows us to provide a solution to a yet unsolved problem. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
Hiroshi Ito 《国际强度与非线性控制杂志
》2004,14(18):1433-1467
》2004,14(18):1433-1467
This paper proposes a novel approach to the problem of ??2 disturbance attenuation with global stability for nonlinear uncertain systems by placing great emphasis on seamless integration of linear and nonlinear controllers. This paper develops a new concept of state‐dependent scaling adapted to dynamic uncertainties and nonlinear‐gain bounded uncertainties that do not necessarily have finite linear‐gain, which is a key advance from previous scaling techniques. The proposed formulation of designing global nonlinear controllers is not only a natural extension of linear robust control, but also the approach renders the nonlinear controller identical with the linear control at the equilibrium. This paper particularly focuses on scaled ??∞ control which is widely accepted as a powerful methodology in linear robust control, and extends it nonlinearly. If the nonlinear system belongs to a generalized class of triangular systems allowing for unmodelled dynamics, the effect of the disturbance can be attenuated to an arbitrarily small level with global asymptotic stability by partial‐state feedback control. A procedure of designing such controllers is described in the form of recursive selection of state‐dependent scaling factors. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
16.
In this paper, we address the ??∞ model reduction problem for linear time‐invariant discrete‐time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well‐known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the ??∞ optimal reduced‐order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous‐time system setting. 相似文献
17.
In this paper, we study the design problem of PID controllers for networked control systems (NCSs) with polyhedral uncertainties. The load disturbance and measurement noise are both taken into account in the modeling to better reflect the practical scenario. By using a novel technique, the design problem of PID controllers is converted into a design problem of output feedback controllers. Our goal of this paper is two‐fold: (1) To design the robust PID tracking controllers for practical models; (2) To develop the robust ??∞ PID control such that load and reference disturbances can be attenuated with a prescribed level. Sufficient conditions are derived by employing advanced techniques for achieving delay dependence. The proposed controller can be readily designed based on iterative suboptimal algorithms. Finally, four examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
This paper investigates the problem of ??∞ filtering for a class of uncertain Markovian jump linear systems. The uncertainty is assumed to be norm‐bounded and appears in all the matrices of the system state‐space model, including the coefficient matrices of the noise signals. It is also assumed that the jumping parameter is available. We develop a methodology for designing a Markovian jump linear filter that ensures a prescribed bound on the ??2‐induced gain from the noise signals to the estimation error, irrespective of the uncertainty. The proposed design is given in terms of linear matrix inequalities. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
In this paper, the problem of ‘system identification in ??∞’ is investigated in the case when the given frequency response data are not necessarily on a uniformly spaced grid of frequencies. A large class of robustly convergent identification algorithms is derived. A particular algorithm is further examined and explicit worst case error bounds (in the ??∞ norm) are derived for both discrete-time and continuous-time systems. An example is provided to illustrate the application of the algorithms. 相似文献
20.
This paper proposes a convex approach to regional stability and ℒ︁2‐gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input‐to‐output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential‐algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ︁2‐gain of the input‐to‐output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full‐order) output feedback controller with a guaranteed bound on the ℒ︁2‐gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献