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     

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     

Approximated solutions to nonlinear discrete-time H∞-control

It is shown that there exists an analytic solution to the discrete Hamilton-Jacobi equation arising in the nonlinear discrete-time H_∞-control problem if and only if the H_∞ -control problem associated to the linear approximated system is solvable. Starting from the solution of the Riccati equation associated to this linear problem, we show that the nonlinear solution can be computed at any desired degree of approximation. On this basis the control solution can be computed iteratively     

H∞-control of discrete-time nonlinear systems

This paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback, state feedback, and dynamic output feedback, respectively, for discrete-time nonlinear systems. The H_∞-control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality, differential game, and LaSalle's invariance principle in discrete time. A substantial difficulty that V(A(x)+B(x)u+E(x)w) [respectively, V(f(x,u,w))] is no longer quadratic in [_w^u] arising in the case of discrete-time nonlinear systems has been surmounted in the paper. In the case of a linear system, we show how the results reduce to the well-known ones recently proposed in the literature     

Relationship between availability of states and pole/zerocancellations in H∞-control

This note compares servo systems designed with three methods of H _∞-control, that is, output feedback control, state feedback control and partial state feedback control. The three kinds of control use different information of the plant to generate the control input. We show that if more states are used, then the number of the pole/zero cancellations can be reduced     

J-inner-outer factorization, J-spectral factorization, and robustcontrol for nonlinear systems

The problem of expressing a given nonlinear state-space system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor is obtained as the solution of an associated nonlinear spectral factorization problem. As an application, one can arrive at the solution of the nonlinear H_∞-control problem for the disturbance feedforward case     

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     

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     

All fixed-order H∞ controllers: observer-basedstructure and covariance bounds

This note obtains a parameterization of the set of all stabilizing controllers of order less than or equal to the plant, which yields for the closed-loop transfer matrix a specified H_∞ norm bound. The algebraic results of covariance control are applied to the H _∞ control problem to yield a parameterization in terms of the Lyapunov matrix, which carries many system properties (such as H ₂ performance, covariance bounds, system entropy at infinity, etc.). All low-order H_∞ controllers are shown to have observer-based structure for “reduced-order models” of the plant and are characterized by two Riccati equations with a coupling condition     

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     

LMI approach to an H∞-control problem withtime-domain constraints over a finite horizon

The discrete time H_∞-control problem is considered with time-domain constraints over a finite horizon. It is shown that a solution of this problem can be obtained from a system of linear matrix inequalities     

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     

Characterization of the strict bounded real condition of nonlinearsystems

This paper is concerned with the strict bounded real condition of nonlinear systems, which plays an important role in the nonlinear H_∞-control theory. Namely, a necessary and sufficient condition for nonlinear systems to be internally asymptotically stable and to have the L₂ gain <γ is given via the Hamilton-Jacobi equation with a stabilizing solution, although some assumptions are required     

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     

State feedback ℋ∞-suboptimal control of arigid spacecraft

A state feedback ℋ_∞-suboptimal control problem on TSO(3) for a rigid spacecraft with three control torques and disturbances is addressed, the Hamilton-Jacobi inequality associated with a corresponding state feedback ℋ_∞-suboptimal control problem on TS³ is solved globally. The ℋ_∞-suboptimal state feedback on TS³ involves the Euler parameters and solves the original problem on TSO(3) when the initial values of the Euler parameters are appropriately chosen     

Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

The problem of output feedback stabilization of nonlinear sampled-data control systems is considered under the low measurement rate constraint. A dual-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the missing output values between measured output samples. It is shown that if an observer-based output feedback controller that semiglobally practically asymptotically (SPA) stabilizes the single-rate sampled-data plant model is given, then the SPA stability property will be preserved for the closed-loop dual-rate sampled-data system, on the basis of the proposed dual-rate control scheme under standard assumptions. A numerical example is given to illustrate the design method.     

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 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∞ type problem for sampled-data control systems-asolution via minimum energy characterization

This paper aims at deriving a solution for H_∞ type problem for sampled-data control systems. The solution is given in terms of an equivalent discrete-time H_∞ problem. The reduction procedure is viewed and characterized from the viewpoint of minimum energy principle and J-unitary transformations     

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