Dynamic input-output decoupling of nonlinear control systems

The problem of dynamic input-output decoupling of nonlinear control systems is studied. Based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem. The solution of the problem is constructed by applying a series of simple precompensations and linking maps. Some interesting connections with other approaches in nonlinear control theory are discussed. The authors also give a few (simple) examples to illustrate the methods used     

Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model

Most of existing results on robust output regulation problem of singular nonlinear systems are limited to local solutions. In this paper, the semi-global robust output regulation problem for a class of singular nonlinear systems is investigated by using a nonlinear internal model. Attaching a nonlinear internal model to the singular nonlinear system yields an augmented singular nonlinear system whose semi-global robust stabilisation solution leads to the solution of the semi-global robust output regulation problem of the original singular nonlinear system. The solvability conditions of the semi-global output regulation problem are established by addressing the solvability of the robust stabilisation problem of augmented singular nonlinear system. Finally, a numerical simulation example is used to illustrate the design of the semi-global regulator for the singular nonlinear systems.     

Dynamic output feedback robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of uncertain switched nonlinear systems

The problem of robust H _∞ control problem for a class of switched nonlinear systems with parameter uncertainty is studied by using single Lyapunov function method. The problem under switch-dependent and switch-independent dynamic output feedbacks is solved respectively. Sufficient conditions for solvability of the problem are obtained. The Lyapunov function and the corresponding switching law are explicitly constructed. A numerical example is given to demonstrate the validity of the proposed approach.     

Regulation of relaxed static stability aircraft

The authors formulate and solve a regulator problem for nonlinear parameter-dependent dynamics. It is shown that the problem is solvable except at parameter values associated with bifurcation of the equilibrium equations and that such bifurcations are inherently linked to the system zero dynamics. These results are applied to the study of the regulation of the longitudinal dynamics of aircraft. It is shown how bifurcation points arise in these problems and why they affect solvability of the regulator problem. The relationships between bifurcation, system zeros, and dynamic and static stability are illustrated     

一类非线性控制系统的输出调节

对一类非线性控制系统的输出调节问题,首先通过推广的精确线性化方法,将其转化为一类特殊的受扰线性控制系统对非线性系统的跟踪问题,然后利用可解性的概念解决了该问题,得到了非线性系统输出调节问题的局部和全局的结果。     

Explicit constructions of global stabilization and nonlinear H∞ control laws for a class of nonminimum phase nonlinear multivariable systems

This paper investigates a global stabilization problem and a nonlinear H_∞ control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, an asymptotic time‐scale and eigenstructure assignment method is adopted to construct the control laws for the stabilization problem and the nonlinear H_∞ control problem. A sufficient solvability condition is established onthe unstable zero dynamics of the system for global stabilization problem and nonlinear H_∞ control problem, respectively. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L₂‐gain is estimated for the nonlinear H_∞ control problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator

This paper investigates the cooperative output regulation problem of linear multi-agent systems with a linear exogenous system (exo-system). The network topology is described by a directed graph which contains a directed spanning tree with the exo-system as the root. Aiming at improving the transient performance of the multi-agent systems, a dynamic control law is developed by the composite nonlinear feedback (CNF) control technique. In particular, a distributed dynamic compensator independent of the interaction on the compensator states of agents among the network, is adopted. The solvability condition for the cooperative output regulation problem is obtained using the small-gain theory, which will not be destroyed by adding the nonlinear feedback part of the CNF control law. It is also shown that in the case with the exo-system not diverging exponentially, the small-gain condition can be guaranteed using the low-gain design. Finally, simulation results illustrate that the proposed CNF control law improves the transient performance for the cooperative output regulation of linear multi-agent systems.     

Disturbance Decoupling of Time Delay Systems

A necessary and sufficient condition is derived for the solvability of the disturbance decoupling problem by a pure shift dynamic compensator. It corrects previously obtained results for multi‐input multi‐output (MIMO) systems. Also, necessary and sufficient conditions are given for the solvability of the problem by a dynamic compensator for single input single output (SISO) systems.     

Global robust servomechanism problem of lower triangular systems in the general case

The global robust servomechanism problem (alternatively, global robust output regulation problem) for lower triangular systems has been studied for two special cases. The first case assumes that the systems only contain polynomial nonlinearities, and the second case limits the exogenous signals and the unknown parameters to be within a known bounded set. This paper presents the solvability conditions of the global robust servomechanism problem for the lower triangular systems for the most general case where neither of the above two assumptions is needed. Our approach consists of two steps. In the first step, we convert the problem into a global adaptive regulation problem for lower triangular systems subject to both dynamic and static uncertainties. In the second step, we derive the solvability conditions of the problem by appealing to the recent result on the solvability of the global adaptive regulation problem for lower triangular systems with both dynamic and static uncertainties.     

On the solvability of the regulator equations for a class of nonlinear systems

Regulator equations arise in studying the output regulation problem for nonlinear systems. The solvability of the regulator equations is the necessary condition for that of the output regulation problem. It has been shown under various assumptions that the solvability of the regulator equations can be reduced to that of a center manifold equation defined by the zero dynamics of a composite system consisting of the plant and exosystem. In this paper we further show that, for a quite general class of nonlinear systems, the solvability of the regulator equations can be reduced to that of a center manifold equation if the relative degree of the composite system at the origin exists.     

Global robust output regulation of lower triangular systems with nonlinear exosystems and its application

This paper studies the global robust output regulation problem for lower triangular systems subject to nonlinear exosystems. By employing the internal model approach, this problem can be boiled down to a global robust stabilization problem of a time-varying nonlinear system in the cascade-connected form. Then, a set of sufficient conditions for the solvability of the problem is derived, and thus, leading to the solution to the global robust output regulation problem. An application of the main result of this paper is also proposed.     

Computer-aided solution of some problems relating to control of the complicated mechanical systems

Consideration was given to control of a complex object whose motion obeys a multivariable nonlinear nonstationary mathematical model. Rigid constraints were imposed on the object’s dynamic precision. The paper considered computer-aided generation of the current equations of object motion with regard for the actuators which differ from subsystem to subsystem. The object is controlled adaptively with regard for the computer-based realization. The algorithms of control system operation that maintain the guaranteed precision of object motion were constructed. Conditions for problem solvability were formulated. The freeflying space robot was discussed by way of example.     

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

In this paper, the adaptive control problem for a class of switched nontriangular nonlinear systems is investigated, which allows the control gains to vanish at some points. Neither the triangular structure nor the solvability of the adaptive control problem is required for each subsystem. A key point of this work is to solve the adaptive control problem of switched nontriangular nonlinear systems with vanishing control gains by the dual design of the controllers and switching signals. To this end, firstly, a hysteresis‐type control gains‐dependent switching law is designed, which makes the control gain of the active subsystem not vanish and thus the associated designed control input can enter into the active subsystem. Moreover, the designed switching law guarantees a dwell time between any adjacent switching instants, which rules out the Zeno behavior. Secondly, when the adaptive control problem of each subsystem is unsolvable, a sufficient condition ensuring the solvability of the adaptive control problem of switched nontriangular nonlinear systems is developed even if no control input can enter into subsystems at some points. Finally, the effectiveness of the proposed result is illustrated by two examples.     

Zeros at infinity for affine nonlinear control systems

A definition of zeros at infinity for affine nonlinear control systems is proposed. The definition is local, which means that we exclude certain singularities. We argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling. In particular, we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity.     

一类非线性奇异控制系统的块解耦

讨论了在正则状态下反馈作用下，一类非线性奇异控制系统的输入输出块解耦问题，首先给一种算法，然后利用该算法导出系统输入块解耦问题可解的充分必要条件。     

Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

The approach to robust stabilization of linear systems using normalized left coprime factorizations with _∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward _∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation.     

Relaxed fault detection and isolation: An application to a nonlinear case study

Given a number of possibly concurrent faults (and disturbances) that may affect a nonlinear dynamic system, it may not be possible to solve the standard fault detection and isolation (FDI) problem, i.e., to detect and isolate each single fault from all other, possibly concurrent faults and disturbances, due to the violation of the available necessary conditions of geometric nature. Motivated by a robotic application where this negative situation structurally occurs, we propose some relaxed formulations of the FDI problem and show how necessary and sufficient conditions for their solution can be derived from those available for standard FDI. The design of a hybrid residual generator follows directly from the fulfillment of the corresponding solvability conditions. In the considered nonlinear case study, a robotic system affected by possible actuator and/or force sensor faults, we detail the application of these results and present experimental tests for validation.     

A nonlinear observer design for an activated sludge wastewater treatment process

This paper treats the problem of estimating simultaneously the state and the unknown inputs of a class of nonlinear discrete-time systems. An observer design method for nonlinear Lipschitz discrete-time systems is proposed. By assuming that the linear part of this class of systems is time-varying, the state estimation problem of nonlinear system is transformed into a state estimation problem for LPV system. The stability analysis is performed using a Lyapunov function that leads to the solvability of linear matrix inequalities (LMIs). Performances of the proposed observer are shown through the application to an activated sludge process model.     

The matching of a prescribed linear input-output behavior in a nonlinear system

In this paper we deal with the problem of finding a feedback under which the input-output behavior of a nonlinear system becomes exactly the same as that of a specified linear model. The solvability of this problem is shown to depend on a formal infinite zero structure associated with the system.     

Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This work investigates the problem of robust output feedback H/sub /spl infin// control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi-Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H/sub /spl infin// norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H/sub /spl infin// control for a class of uncertain nonlinear discrete delay systems.