H/sub /spl infin// control for networked systems with random communication delays

This note is concerned with a new controller design problem for networked systems with random communication delays. Two kinds of random delays are simultaneously considered: i) from the controller to the plant, and ii) from the sensor to the controller, via a limited bandwidth communication channel. The random delays are modeled as a linear function of the stochastic variable satisfying Bernoulli random binary distribution. The observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and also achieve the prescribed H/sub /spl infin// disturbance attenuation level. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality (LMI) approach. An illustrative example is provided to show the applicability of the proposed method.     

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.     

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.     

Nonsmooth H/sub /spl infin// synthesis

We develop nonsmooth optimization techniques to solve H/sub /spl infin// synthesis problems under additional structural constraints on the controller. Our approach avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems. The proposed framework is versatile and can accommodate a number of challenging design problems including static, fixed-order, fixed-structure, decentralized control, design of PID controllers and simultaneous design and stabilization problems. Our algorithmic strategy uses generalized gradients and bundling techniques suited for the H/sub /spl infin// norm and other nonsmooth performance criteria. We compute descent directions by solving quadratic programs and generate steps via line search. Convergence to a critical point from an arbitrary starting point is proved and numerical tests are included to validate our methods. The proposed approach proves to be efficient even for systems with several hundreds of states.     

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.     

An LPD approach to robust H/sub 2/ and H/sub /spl infin// static output-feedback design

A linear parameter dependent approach for designing a constant output feedback controller for a linear time-invariant system with uncertain parameters that achieves a minimum bound on either the H/sub 2/ or H/sub /spl infin// performance level is introduced. Assuming that the uncertain parameters reside in a given polytope, a parameter dependent Lyapunov function is described which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope.     

An innovation approach to H/sub /spl infin// fixed-lag smoothing for continuous time-varying systems

This note studies the finite horizon H/sub /spl infin// fixed-lag smoothing problem for linear continuous time-varying systems. A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H/sub /spl infin// fixed-lag smoother. The condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two Riccati differential equations (RDEs), one standard H/sub /spl infin// filtering RDE and one H/sub 2/ type of RDE. Examples demonstrate the proposed H/sub /spl infin// fixed-lag smoother design and the fact that the existence of an H/sub /spl infin// smoother does not depend on the solvability of H/sub /spl infin// filtering.     

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// 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.     

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.     

H/sub /spl infin// output tracking control for nonlinear systems via T-S fuzzy model approach

This paper studies the problem of H/sub /spl infin// output tracking control for nonlinear time-delay systems using Takagi-Sugeno (T-S) fuzzy model approach. An LMI-based design method is proposed for achieving the output tracking purpose. Illustrative examples are given to show the effectiveness of the present results.     

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   

Robust nonlinear control associating robust feedback linearization and H/sub /spl infin// control

In this note, a robust nonlinear controller for a nonlinear system subject to model uncertainties is proposed. Such a controller associates a "robust feedback linearization" with a robust linear H/sub /spl infin// controller. The robust feedback linearization exactly transforms the nonlinear system into a linear system equal to the linear approximation of the original nonlinear system around a nominal operating point. The robustness of the resulting overall nonlinear controller is proved by theoretical arguments and illustrated through an application example, the control of a magnetic bearing system.     

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.     

Constantly scaled H/sub /spl infin// control problems for pseudofull information problems

This paper proposes a class of the constantly scaled H/sub /spl infin// control problem, where the class is characterized by an assumption also proposed in this paper. In general, the scaled H/sub /spl infin// control problem leads to nonconvex solvability conditions. On the other hand, for the problems in the proposed class, we show that a convex but sufficient solvability condition can be given. Moreover, the convexity of the state feedback and the full information problems can be regarded as the extreme cases of the sufficient condition. This fact motivates us to call the assumption the pseudofull information condition.     

Robust sampled-data H/sub /spl infin// control of linear singularly perturbed systems

State-feedback H/sub /spl infin// control problem for linear singularly perturbed systems with norm-bounded uncertainties is studied. The fast variables are sampled with fast rates, while for the slow variables both cases of slow and of fast sampling are considered. The recent "input delay" approach to sampled-data control is applied, where the closed-loop system is represented as a continuous one with time-varying input delay. Linear matrix inequalities (LMIs) for solution of H/sub /spl infin// control problem are derived via input-output approach to stability and L/sub 2/-gain analysis of time-delay systems. A numerical example illustrates the efficiency of the method.