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     

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     

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     

H∞ multiple objective robust controllers forinfinite-horizon single measurement single control input problems

A graphical method is introduced that solves the robust infinite horizon H_∞ multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H_∞ control problem. The new method links between the theories of H_∞ and quantitative feedback theory (QFT). It can be used to design robust H_∞ controllers with almost no overdesign, and it provides a convenient solution of H_∞ multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input, or the measurement output     

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     

Output feedback control of Markov jump linear systems incontinuous-time

This paper addresses the dynamic output feedback control problem of continuous-time Markovian jump linear systems. The fundamental point in the analysis is an LMI characterization, comprising all dynamical compensators that stabilize the closed-loop system in the mean square sense. The H₂ and H_∞-norm control problems are studied, and the H₂ and H_∞ filtering problems are solved as a by product     

Fundamental limits in sensitivity minimization:multiple-input-multiple-output (MIMO) plants

This paper provides a bridge between the H_∞ literature and that of fundamental limits. By applying operator theoretic tools developed for the standard frequency domain, model-matching approach to sensitivity minimization, explicit closed form expressions are given for tight bounds on the H_∞ norm of weighted sensitivity functions for output feedback control of linear multivariable systems     

基于约束H∞输出反馈的四轮转向模型跟踪控制

以跟踪参考模型为控制策略,提出一种基于约束H_∞输出反馈控制的四轮转向（4WS）控制新方法．将前馈控制和反馈控制相结合,同时控制前、后轮转角,以实现实际车辆模型对参考模型的期望性能跟踪．兼顾抗干扰能力与执行机构输出饱和,将约束H_∞输出反馈控制应用于反馈控制器的设计．仿真实验表明所设计的4WS车辆系统可以很好地跟踪参考车辆模型,提高了车辆的操纵稳定性．     

H∞ decentralized fuzzy model reference tracking controldesign for nonlinear interconnected systems

In general, due to the interactions among subsystems, it is difficult to design an H_∞ decentralized controller for nonlinear interconnected systems. The model reference tracking control problem of nonlinear interconnected systems is studied via H_∞ decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H∞ model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H_∞ tracking control design problem for nonlinear interconnected systems. The problem of H _∞ decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods     

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     

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     

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∞ 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∞ 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     

Nonlinear H∞-control of time-varying systems: aunified distribution-based formalism for continuous and sampled-datameasurement feedback design

Nonlinear H_∞-controller synthesis is presented for time-varying systems via sampled-data measurement feedback. The H _∞-control problem for a nonlinear system with a sampled-data measurement output is shown to be equivalent to the H_∞-control problem for a certain nonlinear system with a time-continuous measurement output. Special mathematical tools are developed to straightforwardly derive a local solution of the sampled-data measurement feedback (SMF) H_∞-control problem from that of the time-continuous measurement feedback (CMF) H _∞-control problem     

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     

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     

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     

Continuous-time tracking problems in an H∞setting: a game theory approach

This paper investigates the problem of finite-horizon H_∞ tracking for linear time-varying systems. Three tracking problems are considered, depending on whether the reference signal is perfectly known in advance, measured on-line, or previewed in fixed interval of time ahead. No a priori knowledge of a dynamic model for the reference signal is assumed. A game theory approach to the latter tracking problems is presented where, given a specific reference signal, the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise. Necessary and sufficient conditions for the existence of a saddle-point equilibrium are determined, and H_∞ tracking controllers for both the cases of state and output feedback are derived. Tracking problems for time-invariant systems on infinite-horizon are also analyzed, and time invariant tracking controllers are obtained for zero initial conditions