Dynamic output linearization of nonlinear discrete-time control systems

In the paper we give more general then previous ([l],[7],[8]) definition of dynamic feedback output (state) equivalence of two nonlinear discrete-time input-output control system. Feedback transformations that are presented depend both on past and future values of outputs and controls (or states and controls).

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

Output stabilizability conditions for some classes of discrete-time linear and nonlinear control systems are formulated by using dynamic controllers. Methods for constructing static and dynamic controllers that provide a specified evaluation of the weighted damping level of external and initial disturbances are proposed for systems with controllable and observable outputs. The implementation of these methods with the use of static state feedback or complete order dynamic controllers is based on the solution of systems of linear matrix inequalities. The example of a controller synthesis for a two-mass mechanical system is given.

This paper analyzes the amplitude dependent behavior of discrete-time and discrete-value (discretized/quantized) nonlinear control systems in a frequency domain. First, the robust stability condition which was derived in our previous papers is applied to a discrete-time control system with a stepwise nonlinear element. Then, an instability condition for that type of nonlinear feedback system is given. By considering restricted areas (two sectors) in the stepwise nonlinear characteristic, the amplitude of sustained oscillations for the feedback system will be estimated.

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC:15A09, 52A10, 74M05, 93D05.

Robust Failure Detection and Isolation in Non-Linear Control Systems

In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic nonlinear control systems with possibly degenerate distributed disturbances. The notions are inspired by the analogue notions that exist for probabilistic chains and for behavioral systems, respectively. Connections between the two notions and also with stochastic reachability are discussed. For the subclass of discrete-time stochastic linear control systems with multivariate possibly degenerate normal distributed disturbances, geometric necessary and sufficient conditions for checking stochastic bisimulation equivalence and stochastic external behavior equivalence are derived. The proposed results nicely extend the theory of bisimulation equivalence and equivalence of external behavior known for non-deterministic control systems to a stochastic setting.

We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s. asymptotic stability, and (b) we present a method for learning neural network RSMs. We prove that our approach guarantees a.s. asymptotic stability of the system and provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not. Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies.

This paper is concerned with the event-triggered $H_{\infty }$ control problem for discrete-time nonlinear networked control systems with unreliable communication links. First, an event-triggered scheme is proposed to determine whether the sampled data should be released into the network or not. Second, when the released data is transmitted in the network, a Bernoulli process is employed to model the phenomenon of data losses. Third, considering the instants at which the sampled data is not released or data losses occur, a new random process is first developed to model the input data sequence of the controller under the effect of the buffer. Consequently, a novel method is presented to address the stability analysis and control synthesis problems based on the polynomial fuzzy model approach. Finally, some simulation results are given to illustrate the effectiveness of the proposed method.

The control problem for the networked suspension control system of maglev train with random induced time delay and packet dropouts is investigated. First, Takagi-Sugeno (T-S) fuzzy models are utilized to represent the discrete-time nonlinear networked suspension control system, and the parameters uncertainties of the nonlinear model have also been taken into account. The controllers take the form of parallel distributed compensation. Then, a sufficient condition for the stability of the networked suspension control system is derived. Based on the criteria, the state feedback fuzzy controllers are obtained, and the controller gains can be computed by using MATLAB LMI Toolbox directly. Finally, both the numerical simulations and physical experiments on the full-scale single bogie of CMS-04 maglev train have been accomplished to demonstrate the effectiveness of this proposed method.

In this article, a novel hybrid event-triggered (ET) control framework is constructed based on the adaptive critic technique, aiming to address the optimal tracking issue of discrete-time nonlinear networked control systems. First, an augmented plant is created by combining the system state with the reference trajectory, transforming the optimal tracking control design into the optimal regulation problem of the reconstructed nonlinear error system. Subsequently, to conserve communication network resources and ensure the stability of the error system, a hybrid ET mechanism is developed to determine a constant interval for event silence. This approach not only alleviates the limited network bandwidth but also eliminates the need for continuous evaluation of triggering conditions, as seen in traditional event-based methods. Regarding algorithm implementation, the model, critic, and action networks are established to execute the online adaptive critic algorithm, which allows the tracking control policy to be adjusted in real-time to reach the optimal level. Finally, an experimental plant with nonlinear characteristics is presented to illustrate the overall performance of the proposed online tracking control method with the hybrid ET mechanism.

The paper focuses on unification of the study of continuous- and discrete-time nonlinear control systems using the mathematical tools of pseudo-linear algebra. The realization problem is studied through the language of differential forms. Necessary and sufficient conditions are given for the existence of the state space realization of the nonlinear input-output equation defined in terms of the pseudo-linear operator. The sufficiency part of the proof gives a constructive procedure (up to integration of the one-forms) for obtaining the observable state equations. The special cases for continuous- and discrete-time systems, described either in terms of the shift or difference operator, follow from the general result as the special cases. Moreover, the result accommodates also the systems described via q-shift or q-difference operators.

The package NLControl, developed in the Institute of Cybernetics at Tallinn University of Technology within the Mathematica environment, has been made partially available over the internet using webMathematica tools. The package consists of functions that assist the solution of different modelling, analysis, and synthesis problems for nonlinear control systems, described either by state or by input-output equations. This paper focuses on describing the webMathematica-based tools for discrete-time nonlinear control systems.

This paper describes discretized PID control and robust stabilization for continuous plants on a grid pattern that is composed of integers. Although all control systems are currently realized using discretized signals, the analysis and design of discrete-time and discrete-value (digital) control systems has not been elucidated. In this paper, a designing problem of such nonlinear discrete-time control systems based on the PID algorithm is presented in a frequency domain. In the design procedure, the concept of a modified Nyquist and Hall diagram (off-axis M-circles) for nonlinear control systems is applied. Numerical examples for continuous plants with time delay are provided to verify the design method.

Surprisingly, computer algebra systems have not been used for the analysis of discrete-time nonlinear control systems. The only exceptions seem to be papers based on Reduce and on Maple. This paper presents certain modelling problems of discrete-time nonlinear system as an example of what can be done with symbolic computation in nonlinear discrete-time control with Mathematica.