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     

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     

Nonlinear H2 and H∞ optimal controllersfor current-fed induction motors

This paper presents a nonlinear control design for both the H₂ and H_∞ optimal control for current-fed induction motor drives. These controllers are derived using analytical stationary solutions that minimize a generalized convex energy cost function including the stored magnetic energy and the coil losses, while satisfying torque regulation control objectives. Explicit control expressions for both the H₂ and H_∞ optimal design are given. Furthermore, the optimal attenuation factor, i.e., the optimal H_∞ norm and the corresponding worst case disturbance, are both computed explicitly     

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     

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     

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     

H∞ state feedback control for discrete singularsystems

Deals with the problem of state feedback H_∞ control for discrete singular systems. It is not assumed that the singular system under consideration is necessarily regular. The problem we address is the design of a state feedback controller, such that the resulting closed-loop system is not only regular, causal, and stable, but also satisfies a prescribed H_∞-norm-bound condition. In terms of certain matrix inequalities, a necessary and sufficient condition for the solution to this problem is obtained, and a suitable state feedback-control law is also given     

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     

On control relevant criteria in H∞ identification

This paper proposes a technique for using control relevant criteria in H_∞ identification. The work reported here has its background in a desire to understand the closed-loop versus open-loop issue in control relevant identification. The proposed technique has some features in common with the iterative closed-loop Schrama scheme, but is constructed so as to be able to obtain control relevant reduced complexity models also directly from open-loop data (for stable systems). It is demonstrated that the proposed technique solves, with the initial open-loop data only, the examples treated earlier in the literature using the iterative closed-loop Schrama scheme     

Reliable H∞ control for affine nonlinear systems

This paper addresses the reliable H_∞-control problems for affine nonlinear systems. Based on the Hamilton-Jacobi inequality approach developed in the H∞-control problems for affine nonlinear systems, a method for the design of reliable nonlinear control systems is presented. The resulting nonlinear control systems are reliable in that they provide guaranteed local asymptotic stability and H_∞ performance not only when all control components are operational, but also in the case of some component outages within a prespecified subset of control components. A numerical example is also given     

On nonlinear H∞ control under sampled measurements

This paper deals with the nonlinear H_∞ control problem with sampled measurement feedback. This problem has already been studied in Suzuki et al. (1995), where, using a certainty equivalence principle, a control solution involving a state estimator with a linear injection gain is proposed. Using the same general framework, we propose a more refined estimator with a nonlinear injection gain. This gain is shown to be connected to a periodic solution of a Hamilton-Jacobi inequality with jumps     

H∞ control of uncertain dynamical fuzzydiscrete-time systems

A new kind of dynamical fuzzy model is proposed to represent discrete-time complex systems which include both linguistic information and system uncertainties. A new stability analysis and control system design approach is then developed for this kind of dynamical fuzzy model. Furthermore, a constructive algorithm is developed to obtain the H(infinity) feedback control law. An example is given to illustrate the application of the 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     

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 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     

Global optimization for H∞ control with constantdiagonal scaling

This paper considers the H_∞-control problem with constant diagonal scaling related to the robust control synthesis for systems with structured time-varying uncertainties. The problem is not convex in general, and hence it is difficult to find a global solution. The purpose of this paper is to provide an algorithm to find a suboptimal solution with any specified small tolerance from the globally optimal solution for the optimization problem. The algorithm based on the triangle covering method is proposed. The computational complexity analysis shows that its worst case order is polynomial in the inverse of the tolerance and the size of an a priori given interval of scaling with a fixed number of uncertainty blocks     

Mixed l1/H∞ control of MIMO systems viaconvex optimization

We present a methodology for designing mixed l₁/H_∞ controllers for MIMO systems. These controllers allow for minimizing the worst case peak output due to persistent disturbances, while at the same time satisfying an H_∞-norm constraint upon a given closed loop transfer function. Therefore, they are of particular interest for applications dealing with multiple performance specifications given in terms of the worst case peak values, both in the time and frequency domains. The main results of the paper show that: 1) contrary to the H₂/H_∞ case, the l₁/H_∞ problem admits a solution in l₁; and 2) rational suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a four-block H_∞ problem. Moreover, this sequence of controllers converges in the l₁ topology to an optimum     

H∞ control via measurement feedback for generalnonlinear systems

This paper shows how the problem of (local) disturbance attenuation via measurement feedback, with internal stability, can be solved for a nonlinear system of rather general structure. The solution of the problem is shown to be related to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, which are associated with state-feedback and, respectively, output-injection design