Stochastic H/sub 2//H/sub /spl infin// control with state-dependent noise

This paper discusses the stochastic H/sub 2//H/sub /spl infin// control problem with state-dependent noise. By means of the stabilization, exact observability and stochastic detectability of stochastic systems, the infinite horizon stochastic H/sub 2//H/sub /spl infin// control design is developed. For the finite horizon H/sub 2//H/sub /spl infin// control problem, our results generalize the corresponding deterministic ones to the stochastic models. Finally, the observer-based suboptimal stochastic H/sub 2//H/sub /spl infin// control is discussed in which the state variables cannot be measured directly, and a feasible design algorithm is proposed.     

H/sub /spl infin// design with first-order controllers

The problem of determining all first order controllers (C(s)=(x/sub 1/s+x/sub 2//s+x/sub 3/)) which stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) plant of arbitrary order has been recently solved. In this note, these results are extended to determine the subset of controllers which also satisfy various robustness and performance specifications which can be formulated as specific H/sub /spl infin// norm constraints. The problem is solved by converting the H/sub /spl infin// problem into the simultaneous stabilization of the closed-loop characteristic polynomial and a family of related complex polynomials. The stability boundary of each of these polynomials can be computed explicitly for fixed x/sub 3/ by solving linear equations. The union of the resulting stability regions yields the set of all x/sub 1/ and x/sub 2/ which simultaneously satisfy the H/sub /spl infin// condition and closed-loop stability for a fixed x/sub 3/. The entire three-dimensional set meeting specifications is obtained by sweeping x/sub 3/ over the stabilizing range.     

Robust H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization designs of nonlinear communication systems: fuzzy interpolation approach

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H/sub /spl infin// equalizer is proposed to treat the state estimation problem from the worst case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the mixed H/sub 2//H/sub /spl infin// equalizer is employed to take the advantage of both H/sub 2/ optimal performance with nominal statistics of noises and the H/sub /spl infin// robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H/sub 2//H/sub /spl infin// equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.     

H/sub /spl infin// filtering for singular systems

This note considers the H/sub /spl infin// filtering problem for linear continuous singular systems. The purpose is the design of a linear filter such that the resulting error system is regular, impulse-free and stable while the closed-loop transfer function from the disturbance to the filtering error output satisfies a prescribed H/sub /spl infin//-norm bound constraint. Without decomposing the original system matrices, a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. Finally, an illustrative example is presented to demonstrate the applicability of the proposed approach.     

Fault detection in a mixed H/sub 2//H/sub /spl infin// setting

In this note, we study the problem of fault detection in linear time-invariant (LTI) systems which are simultaneously effected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. This problem is formulated as a mixed H/sub 2//H/sub /spl infin// filtering problem. Necessary and sufficient conditions for local optimality are presented. Moreover, it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality (LMI) constrains. A numerical example is given to illustrate the advantage of the mixed H/sub 2//H/sub /spl infin// approach as compared to existing techniques which are based on optimization of H/sub 2/ and H/sub /spl infin// criteria.     

On H/sub /spl infin// model reduction using LMIs

In this note, we deal with the problem of approximating a given nth-order linear time-invariant system G by an rth-order system G/sub r/ where r相似文献   

An H/sub /spl infin// approach to networked control

In this paper, we study the effect of a network in the feedback loop of a control system. We use a stochastic packet-loss model for the network and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. We measure performance using an H/sub /spl infin// norm and compute this norm via a necessary and sufficient matrix inequality condition. We also derive necessary and sufficient linear matrix inequality (LMI) conditions for the synthesis of the H/sub /spl infin// optimal controller for a discrete-time jump system. Finally, we apply these results to study the effect of communication losses on vehicle control.     

An exact solution to continuous-time mixed H/sub 2//H/sub /spl infin// control problems

Multiobjective control problems have been the object of much attention in the past few years, since they allow for handling multiple, perhaps conflicting, performance specifications and model uncertainty. One of the earliest multiobjective problems is the mixed H/sub 2//H/sub /spl infin// control problem, which can be motivated as a nominal LQG optimal control problem subject to robust stability constraints. This problem has proven to be surprisingly difficult to solve, and at this time no closed-form solutions are available. Moreover, it has been shown that except in some trivial cases, the optimal controller is infinite-dimensional. In this paper, we propose a solution to general continuous-time mixed H/sub 2//H/sub /spl infin// problems, based upon constructing a family of approximating problems, obtained by solving an equivalent discrete-time problem. Each of these approximations can be solved efficiently, and the resulting controllers converge strongly in the H/sub 2/ topology to the optimal solution.     

/spl Lscr//sub /spl infin//-multipliers for robust performance analysis

Linear systems subject to nonlinear time-varying sector-bounded uncertainties are considered. Robust performance is measured in terms of the worst-case ratio between the /spl Lscr//sub /spl infin//-norms of the output and input signals. A new class of multipliers is introduced and characterized. The characterization can be used to compute an upper bound for robust performance, which tightens the bound obtained by the scaled small gain theorem. While the standard Popov multipliers and their extensions have been developed within the /spl Lscr//sub 2/ framework, our multipliers are adapted to /spl Lscr//sub /spl infin//.     

Nonlinear H/sub /spl infin// controllers for electromagnetic suspension systems

This note presents a unified framework to derive nonlinear H/sub /spl infin// state and output feedback controllers for magnetically levitated (Maglev) vehicles with controlled dc electromagnets, referred to as electromagnetic suspension systems. The theoretical exposition, based on the Taylor series expansion solution to the Hamilton-Jacobi-Isaacs inequality, is followed by an assessment of some of the practical issues in realizing the nonlinear controllers with a digital signal processor and embedded hardware. A select set of experimental results from a single-degree-of-freedom suspension system is included to highlight the effectiveness of the proposed nonlinear stateand output-feedback H/sub /spl infin// controllers to suppress guideway-induced disturbances.     

H/sub /spl infin// observer design for lipschitz nonlinear systems

The problem of observer design for Lipschitz nonlinear systems is considered. A new dynamic framework which is a generalization of previously used Lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented. The equivalence between this condition and an H/sub /spl infin// optimal control problem which satisfies the standard regularity assumptions in H/sub /spl infin// optimization theory is shown and a parameterization of all possible observers is also presented. A design procedure which is less restrictive than the existing design approaches is proposed, and a simulation example is given to illustrate the observer design.     

Delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering for a class of uncertain nonlinear time-delay systems

This note presents delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filter designs for a class of nonlinear systems with multiple time-varying delays in the state and parameter uncertainties residing in a polytope. The nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H/sub /spl infin// or L/sub 2/-L/sub /spl infin// sense. The admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms.     

H/sub /spl infin// control for discrete-time nonlinear stochastic systems

In this note, we develop an H/sub /spl infin//-type theory for a large class of discrete-time nonlinear stochastic systems. In particular, we establish a bounded real lemma (BRL) for this case. We introduce the notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems, and utilize it in the derivation of the BRL. In particular, this BRL establishes a necessary and sufficient condition, in terms of a certain Hamilton Jacobi inequality (HJI), for a discrete-time nonlinear stochastic system to have l/sub 2/-gain/spl les//spl gamma/. The time-invariant case is also considered as a special case. In this case, the BRL guarantees necessary and sufficient conditions for the system to have l/sub 2/-gain/spl les//spl gamma/, by means of a solution to a certain algebraic HJI. An application of this theory to a special class of systems which is a characteristic of numerous physical systems, yields a more tractable HJI which serves as a sufficient condition for the underlying system to possess l/sub 2/-gain/spl les//spl gamma/. Stability in both the mean square sense and in probability, is also discussed. Systems that possess a special structure (norm-bounded) of uncertainties in their model are considered. Application of the BRL to this class of systems yields a linear state-feedback stabilizing controller which achieves l/sub 2/-gain/spl les//spl gamma/, by means of certain linear matrix inequalities (LMIs).     

H/sub /spl infin// model reduction with application to flexible systems

In this note, H/sub /spl infin// model reduction of continuous time linear systems is revisited. The main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem. The quality of the proposed suboptimal solution is assessed through comparisons, performed via simulation, with the already classical balanced truncation method, leading to the conclusion that the proposed method performs significantly better. Finally, the proposed method is applied to the determination of a reduced order model of a flexible bar.     

Stochastic H/sub /spl infin// tracking with preview for state-multiplicative systems

The problem of finite-horizon H/sub /spl infin// tracking for linear time-varying systems with stochastic parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal, i.e., whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. For each of the above three cases a game theory approach is applied for the state-feedback case where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbance. The problems are solved using an expected value of the standard performance index over the stochastic parameters, where necessary and sufficient conditions are found for the existence of a saddle-point equilibrium. The infinite-horizon time-invariant tracking problem is also solved. The theory developed is demonstrated by a simple tracking example.     

Robust H/sub 2/ and H/sub /spl infin// filters for uncertain LFT systems

In this note, robust H/sub 2/ and H/sub /spl infin// filter design problems are considered. The uncertainties, unstructured or structured, are norm bounded and represented by linear fractional transformation (LFT). The main result is that after upper-bounding the objectives, the problems of minimizing the upper bounds are converted to finite dimensional convex optimization problems involving linear matrix inequalities (LMIs). These are extensions of well-known results for systems with polytopic uncertainty. It is shown that for the unstructured, norm bounded uncertainty case, the upper bounds are directly minimized (without further overbounding), yielding less conservative results than previously available. An elementary numerical example is given to illustrate the results.     

H/sub /spl infin//-optimal preview controller and its performance limit

In this note, H/sub /spl infin//-optimal preview control problem is discussed. The problem is reduced to finite-dimensional H/sub /spl infin// problem, whose solution algorithm is well known. Also, the performance limit by the optimal controller is clearly explained.     

Global H/sub /spl infin// controllers for a class of nonlinear systems

In this note, the problem of state feedback H/sub /spl infin// control for a class of nonlinear systems is considered. The class under study is a generalization of the well-known Lur'e systems. The H/sub /spl infin// problem is addressed via a class of storage functions of the Lur'e-Postnikov type whose integral term is parameterized by a nonlinear scalar function. The related H/sub /spl infin// controllers consist of a linear term, which is designed for the underlying linearized system, plus a nonlinear term which depends on the nonlinear function. A simple geometrical criterion is provided for the characterization of the set of controllers which ensure a given level of L/sub 2/-performance globally. Some guidelines for an effective design of the controller within this set are discussed via two examples.