Multiobjective H2/H∞ control

For a linear time-invariant system with several disturbance inputs and controlled outputs, we show how to minimize the nominal H₂-norm performance in one channel while keeping bounds on the H₂-norm or H_∞-norm performance (implying robust stability) in the other channels. This multiobjective H₂ /H_∞-problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems. We show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller. If it exists, we reveal how the novel trick of optimizing the trace norm of the Youla parameter over certain convex constraints allows one to design a nearly optimal controller whose Youla parameter is of the same order as the optimal one     

Dissipative H2/H∞ controller synthesis

In certain applications, such as the colocated control of flexible structures, the plant is known to be positive real. Hence, closed-loop stability is unconditionally guaranteed as long as the controller is also positive real. One approach to designing positive real controllers is the LQG-based positive real synthesis technique of Lozano-Leal and Joshi. The contribution of this paper is the extension of this positive real synthesis technique to include an H_∞-norm constraint on closed-loop performance     

H2 and H∞ control forinfinite-dimensional systems with jumps

We consider a semigroup model with jumps in the state that covers distributed parameter systems with impulse control or sampled-data distributed parameter systems with control realized through zero-order or first-order hold. We then introduce the H₂ and H_∞ problems for this system and give the solutions in terms of the solutions of Riccati equations with jumps     

H2 and H∞ robust filtering for convexbounded uncertain systems

Investigates robust filtering design problems in H₂ and H_∞ spaces for continuous-time systems subjected to parameter uncertainty belonging to a convex bounded-polyhedral domain. It is shown that, by a suitable change of variables, both designs can be converted into convex programming problems written in terms of linear matrix inequalities. The results generalize the ones available in the literature to date in several directions. First, all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured. Then, assuming the order of the uncertain system is known, the optimal guaranteed performance H₂ and H_∞ filters are proven to be of the same order as the order of the system. A numerical example illustrate the theoretical results     

Relating H2 and H∞-norm bounds forsampled-data systems

We relate the H_∞ and H₂ norms for multi-input/multi-output sampled-data feedback control systems, where a continuous-time plant is controlled by a digital compensator with hold and sampler. Upper bounds on both H₂ and H_∞ norms are obtained based on fundamental relations derived by two different approaches, namely the hybrid state-space approach and the fast sampling and lifting approach     

Bandwidth vs. gains design of H∞ tracking controllers for current-fed induction motors

This paper describes a systematic procedure for designing speed and rotor flux norm tracking H_∞ controllers with unknown load torque disturbances for current-fed induction motors. A new effective design tool is developed to allow selection of the control gains so as to adjust the disturbances’ rejection capability of the controllers in the face of the bandwidth requirements of the closed-loop system. Application of the proposed design procedure is demonstrated in a case study, and the results of numerical simulations illustrate the satisfactory performance achievable even in presence of rotor resistance uncertainty.     

Robust H2/H∞-state estimation fordiscrete-time systems with error variance constraints

This paper studies the problem of an H_∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H_∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results     

Nonlinear H∞ control and its application to rigidspacecraft

The problem of H_∞ control of a rigid spacecraft with three control torques and disturbances is addressed. The Hamilton-Jacobi-Isaacs inequality for H_∞ feedback design is solved. An H_∞ suboptimal feedback is given, and the stability properties of the closed-loop system are studied     

Mixed H2/H∞ fuzzy output feedbackcontrol design for nonlinear dynamic systems: an LMI approach

This study introduces a mixed H₂/H_∞ fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H₂/H_∞ controller is developed to achieve the suboptimal H₂ control performance with a desired H_∞ disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H₂/H_∞ control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method     

H∞ strong stabilization

This note presents a technique for designing stable H_∞ controllers. Similar to some methods in the existing literature, the proposed method also uses the parameterization of all suboptimal H _∞ controllers so that the stable H_∞ design problem can be (conservatively) converted into another 2-block standard H_∞ problem. However, a weighting function is introduced in this method to alleviate the conservativeness of the previous formulations. It is further shown that the resulting high-order controller can be significantly reduced by a two-step reduction algorithm. Numerical examples are presented to demonstrate the effectiveness of the proposed method     

Time-domain H∞ identification

The problem of parameter identification, for single-input, single-output ARX systems, is considered. Recent results in H_∞-nonlinear filtering are used to formulate a nonlinear H_∞ time-domain prediction-error-modeling (PEM) identification method. The performance of the new method is guaranteed by a preassigned bound on the ratio between the energy of the prediction error of the obtained model and the energy of the exogenous disturbances. The potential usefulness of the H_∞ time-domain identification method is illustrated by a numerical example     

Robust H2/H∞-state estimation forsystems with error variance constraints: the continuous-time case

The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H_∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H_∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approach     

Hierarchical optimization in H∞

This paper considers a hierarchical optimal control problem which involves an optimal H_∞-norm cost in the primary problem and an H_∞-norm type or a quadratic secondary objective. Using allpass dilation techniques and results from superoptimal interpolation theory, it is shown that the problem can be reduced to a multidisk minimization in terms of a free parameter of reduced dimensions. Convex programming techniques may then be employed to obtain a numerical solution to the problem     

不确定离散时间系统的H2/ H∞最优保性能控制

针对具有两个不同被调输出的一类不确定离散时间系统,研究其H2/H∞状态反馈保性能控制问题,基于线性矩阵不等式处理方法。推导出存在H2/H∞保性能控制律的充分必要条件,并用一个线性矩阵不等式的可行解给出了所有保性能控制律的参数化表示,进而通过建立和求解一个凸优化问题,给出了H2/H∞最优保性能控制律设计方法,最后通过一个例子说明了所提出方法的有效性。     

H∞ optimization with time-domain constraints

Standard H_∞ optimization cannot handle specifications or constraints on the time response of a closed-loop system exactly. In this paper, the problem of H_∞ optimization subject to time-domain constraints over a finite horizon is considered. More specifically, given a set of fixed inputs wⁱ, it is required to find a controller such that a closed-loop transfer matrix has an H_∞-norm less than one, and the time responses yⁱ to the signals wⁱ belong to some prespecified sets Ωⁱ. First, the one-block constrained H_∞ optimal control problem is reduced to a finite dimensional, convex minimization problem and a standard H_∞ optimization problem. Then, the general four-block H_∞ optimal control problem is solved by reduction to the one-block case. The objective function is constructed via state-space methods, and some properties of H_∞ optimal constrained controllers are given. It is shown how satisfaction of the constraints over a finite horizon can imply good behavior overall. An efficient computational procedure based on the ellipsoid algorithm is also discussed     

Discrete Fourier transform and H∞ approximation

It is shown that uniform rational approximation of nonrational transfer functions can always be obtained by means of the discrete Fourier transform (DFT) as long as such approximants exist. Based on this fact, it is permissible to apply the fast Fourier transform (FFT) algorithm in carrying out rational approximations without being apprehensive of convergence. The DFT is used to obtain traditional approximations for transfer functions of infinite-dimensional systems. Justification is provided for using the DFT in such approximations. It is established that whenever a stable transfer function can be approximated uniformly on the right half-plane by a rational function, its approximants can always be recognized by means of a DFT     

Robust H∞ stabilization via parametrized Lyapunovbounds

The parametrized Lyapunov bounding technique of Haddad and Bernstein (1991, 1993, 1995) is extended to include an H_∞ -disturbance attenuation constraint. The results presented in this paper provide a framework for designing fixed-order (i.e., full- and reduced-order) controllers that guarantee robust H₂ and H_∞ performance in the presence of structured constant real parameter variations in the state space model     

A note on H2 optimal control problems with passivityconstraints

Considers the problem of determining the closest function that has a positive real part on the unit disk to a given function in H₂ . An explicit characterization of the projection is given, remarks on potential applications using this projection result to control synthesis and system identification problems are made     

Optimal solution and approximation to thel1/H∞ control problem

This paper addresses the l₁/H_∞ optimal control problem for a system described by linear time-invariant finite dimensional discrete-time equations. It is shown that a solution to this problem exists and can be approximated arbitrarily by real-rational transfer matrices. Perhaps more interesting from a computational point of view, a bound on the order of a δ-suboptimal solution is also given     

Robust H∞ output feedback control for nonlinearsystems

In this paper we present a new approach to the solution of the output feedback robust H_∞ control problem. We employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state. The resulting controller is an information state feedback controller and is intrinsically infinite dimensional. Stability results are obtained using the theory of dissipative systems, and our results are expressed in terms of dissipation inequalities