On input-output linearization of discrete-time nonlinear systems

We consider a nonlinear discrete-time system of the form Σ: x(t+1)=f(x(t), u(t)), y(t) =h(x(t)), where x ε R^N, u ε R^m, y ε R^q and f and h are analytic. Necessary and sufficient conditions for local input-output linearizability are given. We show that these conditions are also sufficient for a formal solution to the global input-output linearization problem. Finally, we show that zeros at infinity of ε can be obtained by the structure algorithm for locally input-output linearizable systems.     

A new adaptive scheme for a class of discrete-time nonlinear systems

A new adaptive control scheme for discrete-time systems is proposed. The objective is the tracking of the trajectory. Global boundedness convergence and boundedness are obtained for a certain subclass of nonlinear systems.     

On H∞-control of discrete-time nonlinear systems

Following recent works on continuous-time nonlinear H_∞-control, where connections with game theory and passivity conditions have been set, the present paper studies the corresponding problem for discrete-time systems. The paper describes sufficient conditions for the existence and the construction of a feedback law which imposes a prescribed level of disturbance attenuation with internal stability. Both cases of state feedback and measurement feedback are considered.     

Volterra filter modeling of a nonlinear discrete-time system based on a ranked differential evolution algorithm

This paper presents a ranked differential evolution （RDE） algorithm for solving the identification problem of non- linear discrete-time systems based on a Volterra filter model. In the improved method, a scale factor, generated by combining a sine function and randomness, effectively keeps a balance between the global seareh and the local search. Also, the mutation operation is modified after ranking all candidate solutions of the population to help avoid the occurrence of premature convergence. Finally, two examples including a highly nonlinear discrete-time rational system and a real heat exchanger are used to evaluate the per- formance of the RDE algorithm and five other approaches. Numerical experiments and comparisons demonstrate that the RDE algorithm performs better than the other approaches in most cases.     

On the realization problem for stationary,homogeneous, discrete-time systems

For degree 2, stationary, homogeneous systems, we consider realizations in the form of state-affine difference equations, and in the form of feedback-free interconnections of stationary linear systems, adders, and multipliers. Realizability conditions are presented in terms of the symmetric transfer function (or kernel), and in terms of a new representation called the regular transfer function (or kernel). A procedure is given for constructing a minimal dimension state-affine realization, and the corresponding interconnection.     

Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems

We consider the problem of stabilizing a discrete-time nonlinear system using a feedback which is not necessarily smooth. A sufficient condition for global dynamical stabilizability of single-input triangular systems is given. We obtain conditions expressed in terms of distributions for the nonsmooth feedback triangularization and linearization of discrete-time systems. Relations between stabilization and linearization of discrete-time systems are given.     

On finite dimensional realization theory of discrete time nonlinear systems

We characterize finite dimensional realizability of discrete time nonlinear systems which have a Volterra series development with separable structure of the Volterra kernels.     

A new symbolic calculus for the response of nonlinear systems

We present a new operational calculus for computing the response of nonlinear systems to various deterministic excitations. The use of a new tool: noncommutative generating power series, allows us to derive, by simple algebraic manipulations, the Volterra functional series of the solution of a large class of nonlinear forced differential equations. The symbolic calculus introduced appears as a natural generalization to the nonlinear domain, of the well known Heaviside operational calculus. Moreover, this method has the advantage of allowing the use of a computer.     

Multiple model-based event-triggered adaptive control of a class of discrete-time nonlinear systems

In this study, the problem of event-triggered-based adaptive control (ETAC) for a class of discrete-time nonlinear systems with unknown parameters and nonlinear uncertainties is considered. Both neural network (NN) based and linear identifiers are used to approximate the unknown system dynamics. The feedback output signals are transmitted, and the parameters and the NN weights of the identifiers are tuned in an aperiodic manner at the event sample instants. A switching mechanism is provided to evaluate the approximate performance of each identifier and decide which estimated output is utilised for the event-triggered controller design, during any two events. The linear identifier with an auxiliary output and an improved adaptive law is introduced so that the nonlinear uncertainties are no longer assumed to be Lipschitz. The number of transmission times are significantly reduced by incorporating multiple model schemes into ETAC. The boundedness of both the parameters of identifiers and the system outputs is demonstrated though the Lyapunov approach. Simulation results demonstrate the effectiveness of the proposed method.     

Invariant codistributions and the feedforward form for discrete-time nonlinear systems

The goal of this paper is two-fold. First, given an arbitrary n-dimensional discrete-time nonlinear dynamical system, necessary and sufficient conditions for the existence of a one-dimensional invariant codistribution are obtained. Second, it is shown that the previous conditions can be used iteratively to obtain a nested sequence of n invariant codistributions with the properties that each codistribution contains the previous one and the last one coincides with the cotangent bundle of the state manifold. As a byproduct, necessary and sufficient conditions are obtained for a discrete-time nonlinear dynamical system to be equivalent to the so-called feedforward form.     

On the immersion of a discrete-time polynomial analytic system into a polynomial affine one

The concept of immersion, just recently introduced by Fliess and Kupka, is related to the capability of reproducing the input-output maps of a given system by means of another one. In this paper we give necessary and sufficient conditions under which a polynomial analytic system, i.e. a system whose dynamics are polynomial with respect to the input and nonlinear analytic with respect to the state, is immersed into a polynomial affine system, i.e. a system whose dynamics are polynomial in the input and linear in the state. An application to the problem of the reproducibility of a linear analytic state feedback acting on a given system by means of a preprocessor suitably initialized is also performed.     

Adaptive control of a class of discrete-time MIMO nonlinear systems with uncertain couplings

In this article, adaptive control is investigated for a class of discrete-time multi-input-multi-output nonlinear systems in block-triangular form with uncertain couplings of delayed states among subsystems. Future states prediction is carried out to facilitate adaptive control design and auxiliary outputs are introduced to develop a novel compensation mechanism for the uncertain nonlinear couplings. By using Lyapunov method and ordering signals growth rate, it is rigorously proved that all the signals in the whole closed-loop systems are globally bounded and the output tracking errors asymptotically converge to zeros. The effectiveness of the proposed control is demonstrated in the simulation study.     

On the induced norms of discrete-time and hybrid time-varying systems

Characterizations for the induced norms of two types of systems are considered. It is first shown that the induced l₂ norm of a discrete-time linear time-varying system may be characterized by the existence requirement on solutions to operator algebraic Riccati equations. A similar result is derived for systems that arise in sampled-data systems involving a mixture of continuous and discrete-time signals. © 1997 by John Wiley & Sons, Ltd.     

Robust output regulation for containment control of heterogeneous discrete-time nonlinear multi-agent systems

ABSTRACT

In existing researches on containment control of heterogeneous multi-agent systems (MASs), the solution is usually dependent on the solvability of regulator equations. However, the closed-form solution of many nonlinear regulator equations of systems is rarely obtained. Towards this end, in this paper the containment control problem of heterogeneous discrete-time nonlinear MASs subject to parameter uncertainties is considered, and the power series approach is adopted to solve complex regulator equations by decomposing them into a series of solvable linear equations. Then, a distributed robust control law based on internal model principle is presented by utilising the solution of the linear equations. Theoretical analysis shows that under certain assumptions asymptotic containment control is achieved for the heterogeneous discrete-time nonlinear MASs with sufficiently small parameter perturbations. Finally, a numerical simulation is implemented to verify the proposed control law.     

纯反馈非线性离散系统的自适应神经网络控制

针对一类未知的纯反馈非线性离散系统,提出了基于反步法设计的自适应神经网络控制方法.为避免反步法设计中可能出现的因果矛盾问题,首先将系统进行等价变换,然后利用隐函数定理证实了理想虚拟控制输入和实际控制输入的存在性.利用高阶神经网络估计这些控制量,并基于反步法设计自适应神经网络控制系统,证明了闭环系统半全局一致最终有界.仿真结果验证了所提出方法的有效性.     

Feedback passivity of nonlinear discrete-time systems with direct input-output link

This paper is devoted to the study of the feedback passivity property in nonlinear discrete-time systems. The relative degree and zero dynamics of the non-passive system are related to the feedback passivity of the system. Two main results are presented. First, some relative degree-related properties of passive systems in general form are stated. Second, sufficient conditions in order to render a multiple-input multiple-output (MIMO) system passive by means of a static state feedback control law are obtained.