Robust nonlinear H∞-output feedback control

This paper investigates the problem of robust H_∞-output feedback control for nonlinear systems with time-varying parameter uncertainty satisfying some integral functional constraints. We address the problem of designing a compensator such that the L₂-gain of the mapping from the exogenous input noise to the penalty output is minimized or guaranteed to be less than or equal to a prescribed value. We establish the interconnection between the robust nonlinear H_∞-control problem and the nonlinear H _∞-control problem, Based on this connection, a sufficient condition for the existence of a solution to the robust nonlinear H_∞-output feedback control problem is derived in terms of a “scaled” Hamilton-Jacobi inequality     

Robust H∞ control of uncertain nonlinear systemvia state feedback

This technical note presents a solution of robust H_∞ control problem for an affine nonlinear system with gain bounded uncertainty. It is shown that the L₂-induced norm of a closed-loop system with the uncertainty is less than one if an extended nonlinear system with no uncertainty is dissipative with respect to a supply rate. In consequence of this result, a state feedback law such that the closed-loop system has H_∞ robust performance is derived based on the Hamilton-Jacobi inequality. It is also shown that the existing results for linear systems are special cases of the presented results     

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     

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     

Decentralized H∞-controller design for nonlinearsystems

Considers the decentralized H_∞-controller design problem for nonlinear systems. Sufficient conditions for the solution of the problem are presented in terms of solutions of Hamilton-Jacobi inequalities. The resulting design guarantees local asymptotic stability and ensures a predetermined L₂-gain bound on the closed-loop system     

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     

H∞ tuning for task-space feedback control of robotwith uncertain Jacobian matrix

The H_∞ tuning problem for task-space feedback control of a robot with uncertain kinematics and Jacobian matrix from joint space to task space is formulated and solved. H_∞ tuning methods are presented for two task-space feedback controllers when the systems are subject to external disturbance. It is shown that the conditions for the establishment of H_∞ tuning can be obtained in simple forms without solving the Hamilton-Jacobi inequalities even in the presence of kinematics uncertainty     

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     

Robust H∞ performance for lineardelay-differential systems with time-varying uncertainties

The present paper concerns robust H∞ performance for linear delay-differential systems which involve an uncertain time delay and time-varying norm-bounded parameter uncertainties. Based on the Lyapunov functional, a simple criterion is proposed which assures the pseudo-quadratic stability as a well as an H_∞-norm bound. The criterion is given in the form of a linear matrix inequality which is affine or convex in additional scalar parameters. A simple criterion is presented to evaluate the extent of the performance robustness     

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     

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     

H∞ and positive-real control for linear neutraldelay systems

This note is concerned with the H_∞ and positive-real control problems for linear neutral delay systems. The purpose of H_∞ control is the design of a memoryless state feedback controller which stabilizes the neutral delay system and reduces the H_∞ norm of the closed-loop transfer function from the disturbance to the controlled output to a prescribed level, while the purpose of positive-real control is to design a memoryless state feedback controller such that the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expected memoryless state feedback controllers can be easily constructed via convex optimization     

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     

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.     

On robust H∞ control for nonlinear discrete andsampled-data systems

The linearization technique for H_∞ control for nonlinear discrete and sampled-data systems is developed in a unified framework under minimal assumptions. It is shown directly, without using any Riccati or Hamilton-Jacobi-Isaacs equation, that H_∞ control for a linearized system is also H_∞ control for a nonlinear original one     

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     

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     

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