Nonlinear Sampled-data Control Systems Research Articles

Secure Nonlinear Sampled-Data Control System Against Stealthy Attack: Multirate Approach

In this paper, we provide a novel defence strategy for a nonlinear sampled-data control system under zero-dynamics attacks. In a sampled data structure, sampling zeros induced by discretization make a system vulnerable to deception attacks. we analyze the dissipativity in the zero-dynamics part of the system equipped with a multi-rate setup and find conditions on sampling rates to neutralize the attacker's target plan. We show that, under some mild conditions, using multi-rate sampling in the nonlinear sampled-data system not only preserves the dissipativity property of the intrinsic zero-dynamics but also stabilizes the extrinsic zero-dynamics induced by the sample and hold process, and as a result attenuate the effects of attacks on the system stability. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

Continuous-time synthesizing robust sampled-data dynamic output-feedback controllers for uncertain nonlinear systems in Takagi–Sugeno form: A descriptor representation approach

This paper discusses controller design techniques for robust sampled-data dynamic output-feedback (DOF) for nonlinear systems in the Takagi–Sugeno (T–S) fuzzy form with parametric uncertainties and L2/L∞ disturbances. We perform the sampled-data syntheses in a continuous-time domain based on an augmented sampled-data closed-loop model in descriptor form. Hence, the investigation does not require any (approximate) discrete-time model of a T–S fuzzy system, which is a significant obstacle in nonlinear sampled-data control system designs. Moreover, various cross-product terms among system matrices, to-be-designed DOF controller matrices, and other decision variables are reduced, yielding single-stage linear matrix inequality-based design conditions.

Regional stabilization of nonlinear sampled-data control systems: A quasi-LPV approach

This paper addresses the asymptotic stabilization of a class of continuous-time nonlinear systems under a sampled-data control. The proposed approach is based on a quasi linear parameter varying (quasi-LPV) model for the nonlinear system and the use of a parameter dependent looped-functional to deal with the aperiodic sampling effects. Explicitly taking into account that the model parameters are functions of the state and therefore are bounded only in a given region of the state space, quasi-LMI conditions are proposed to compute a regional stabilizing nonlinear state feedback control law under aperiodic sampling. These conditions are then incorporated in convex optimization problems to compute the control law aiming at the maximization of an estimate of the region of attraction of the origin or the maximization of an upper bound on the intersampling time, with a guaranteed region of stability.

Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems

This paper investigates the global asymptotical stabilization using sampled-data output feedback (i.e., not all state information is available at the output) for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin. A homogeneous version of Gronwall–Bellman inequality is introduced as the essential tool to estimate trajectory of nonlinear sampled-data control systems between two successive sampling instants. With the help of this new tool as well as the homogeneous domination approach, a sampled-data observer-based controller is constructed to globally asymptotically stabilize the origin of the nonlinear system under a homogeneous growth condition.

Symbolic Models for Nonlinear Control Systems Without Stability Assumptions

Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any nonlinear sampled-data control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle.

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.

Data Preprocessing Circuit Designs and Analyses for Subsonic Cruise Missile Infrared Image Seeker

In this literature, a data pre-processing circuit designs and analyses for an infrared image seeker of a subsonic cruise missile are proposed. The flight speed of the missile is 250m/s. Therefore, automatic contrast control and automatic brightness control are usually needed to keep wanted contrast and brightness for best image properties in target recogni- tion and tracking; especially for the missile at the terminal approaching phase to prevent signal saturation. Signal satura- tion implies target lost. The major parameters of imaging systems for contrast and brightness controls include average, maximum and minimum of gray level of the whole picture in the sampling interval. Therefore, the overall system is a compli- cated nonlinear sampled-data control system. It is difficult to describe, analyze and design the system. In this literature, the over- all system is first decomposed into two linearized sampled-data control systems to get needed loop compensations, and verified by a special range-dependent testing signal to the overall system secondly. The controlled system is further verified by a thermal plate and real flight testing. Testing results give the proposed method can provide effective way to analyze and design the consid- ered system. INTRODUCTIONS Multiple sensors for ECCM are generally expected for missile homing systems. The first dual seeker application of the world for subsonic antiship missile is the HF-2 devel- oped in Taiwan. It includes a Radar seeker and an IR image seeker with data fusing algorithm. This application prompts the capability for ECCM from chaff jamming to RF seeker and thermal jamming to IR Image seeker. The problem for IR image seeker for the missile application is the thermal energy to the charge-coupled device (CCD) (1-3) is the fourth power of the reciprocal the distance between image seeker and thermal source; i.e.; missile and target. It needs faster automatic gain control (AGC) for contrast and auto- matic pedestal control (APC) for brightness (4-7) to keep best imaging properties for target recognition and tracking; especially for the missile at terminal approaching phase. Slower response for coping with thermal energy increasing will make the signal output be saturated; i.e., all white of full frame and will lost tracking centre point for missile guidance. It this literature, models for contrast, brightness and dy- namic signals are proposed to analyses and designs of the AGC and APC circuit loops. The AGC and APC are the pre- processing systems of the video signal. The block diagram considered is shown in Fig. (1). It includes thermal sensors, analog circuits, and microprocessor. The output of the proc- essed signal satisfies RS-170 video standard. The sensor elements for thermal imaging is 256�256 focal plane CCD(1-3), the gray level of each element is digitalized to be 256 states with 8bit A/D converter. Fig. (2) shows typical minimal and maximal gray level of a thermal picture. Analog circuit gives faster signal amplification in forward-loop. It needs 256� 256� 60�10Hz at least for 60Hz picture

ADAPTIVE CONTROL REDESIGN FOR NONLINEAR SAMPLED-DATA SYSTEMS

Semi-global practical stabilization of a general class of nonlinear sampled-data feedback control systems with unknown parameter is addressed. Due to the appearance of powers series of the unknown parameter in the analytic development of the exact discretized systems, an overparameterization is realized for the adaptive law. Then, sufficient conditions for the design of a high order controller are given, based on the Lyapunov analysis, that guarantees the desired stability properties.

On the stabilization of sampled-data non-linear systems by using backstepping on the higher order approximate models

In this paper, we study the stabilization of non-linear sampled-data feedback control systems. Our controller design is based on a backstepping procedure applied on the higher order approximations of the exact discretized associated systems.

Stability Theory of Hybrid Dynamical Systems With Time Delay

By defining the bounded time lag space and other related concepts, this note formulates the notion of hybrid dynamical systems with time delay, which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis. It also investigates stability properties of invariant sets by the method of Lyapunov functions and the Razumihin techniques. Criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with time delay. Those criteria are then applied to conduct stability analysis for impulsive delay differential systems and nonlinear sampled-data feedback control systems with time delay.

AMPLITUDE DEPENDENT ANALYSIS AND STABILIZATION FOR NONLINEAR SAMPLED-DATA CONTROL SYSTEMS

The robust stability condition for sampled-data control systems with a sector nonlinearity was presented in our previous paper. Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system can belong to this type of class. This paper analyzes the amplitude dependent behavior of nonlinear sampled-data (i.e., discrete-time) control systems in a frequency domain. First, the robust stability condition which was derived in our previous papers is applied to a sampled-data system containing a single time-invariant nonlinear element. Then, an instability condition for that type of nonlinear feedback system is derived. By considering restricted areas (two sectors) in the nonlinear characterisitic, the existence of a sustained oscillation is estimated (whether it is periodic or not), and the relationship between the stable (unstable) conditions and the result which is derived from the classic describing function is compared. Based on these considerations, the stabilization of nonlinear discrete-time control systems is examined in the frequency domain.

Amplitude Dependent Stability Analysis for Non-Linear Sampled-Data Control Systems in a Frequency Domain

This paper analyzes the amplitude dependent behavior of nonlinear sampled-data control systems in a frequency domain. First, a robust stability condition for nonlinear discrete-time feedback systems (which was derived in our previous papers) is applied to a sampled-data control system containing a single time-invariant nonlinear element in the forward path. Then, an instability condition for that type of nonlinear feedback system is derived. By considering restricted areas (sectors) in the nonlinear characteristic, the existence of a sustained oscillation (whether it is periodic or not) can be predicted and estimated accurately. Numerical examples will be presented to illustrate the theory. The concept described herein can be expanded to multi-loop nonlinear sampled-data control systems. A robust stability condition for the multi-loop system will be given at the end of this paper.

Robust Stability Evaluation of Sampled-Data Control Systems with a Sector Nonlinearity

This paper describes a robust stability evaluation of sampled-data control systems containing a sector nonlinearity in the forward path. The result of this paper is derived from the norm condition in the frequency domain by extending the Popov's criterion theory. Some lemmas are presented, a theorem for l2-stability is proved, and the stability margin (allowable sector) of a nonlinear element is explicitly exhibited. This theorem is valid only for classes of nonlinear sampled-data control systems that satisfy some of assumptions. A theorem for the validity of extended Aizerman's conjecture is also presented. Some numerical examples are given to illustrate these results.

061 Hausdorff dimension of fractal basin boundaries of a class of one-dimensional nonlinear sampled-data control systems

061 Hausdorff dimension of fractal basin boundaries of a class of one-dimensional nonlinear sampled-data control systems

Existing Conditions of Fractal Boundaries of Invariant Sets of a Class of One-Dimensional Nonlinear Discrete-Time Systems

In this paper, fractal basin boundaries are investigated in connection with a class of one-dimensional nonlinear discrete-time systems.Noting that the basin is an invariant set of the nonlinear function, describing the system dynamics, conditions, under which the Hausdorff dimension of boundaries of invariant sets is positive, are obtained and the existence of fractal basin boundaries is shown. Furthermore, it is demonstrated that if periodic points with period three exist, then fractal basin boundaries appear.Secondly, the result obtained is applied to explore, the basin boundary of a class of one-dimensional nonlinear sampled-data control systems. Illustrative examples together with numerical experiments show the existence of fractal basin boundaries. These theoretical and numerical results reveal that in order to determine the sampling period, it is necessary to take into account the structure of the basin of the equilibrium.

Hausdorff Dimension of Fractal Basin Boundaries of a Class of One-dimensional Nonlinear Sampled-data Control Systems

In this paper, by calculating the Hausdorff dimension of basin boundaries, existing conditions of fractal basin boundaries are shown, concerned with a class of one-dimensional discrete nonlinear dynamical systems. The theoretical contribution of this paper is to clarify that if periodic points with period three exist, then fractal basin boundaries appear. By using this result, the fractal basin boundary of a class of nonlinear sampled-data control systems is explored. Illustrative examples together with numerical experiments show that if the sampling period becomes long, then the basin of an asymptotically stable equilibrium has fractal boundaries.

Analysis of a nonlinear sampled-data proportional navigation system having adjustable parameters

The proportional navigation system analysed in this paper is a complicated nonlinear sampled-data control system. The stability boundaries and limit cycles of the system are found by the stability-equation method. The results obtained are useful for analysing the tracking characteristics of the system, especially in the nonlinear region for which no analysis is given in the current literature.

Bifurcation and Chaos in Nonlinear Sampled-Data Control Systems

In this paper the bifurcation phenomenon and chaos in a nonlinear sampled-data control system are investigated. A C1 nonlinear function and a piecewise linear continuous function are considered. First, the fold bifurcation in an nth-order sampled-data control system is investigated, that is, it is shown that the fold bifurcation does not occur by changing the sampling period and, furthermore, methods to obtain a parameter sets for the fold bifurcation are studied. Next, the conditions for parameter sets for the fold, period doubling, and Hopf bifurcation in a second order sampled-data control system are made clear, and the chaotic behavior of the system is investigated by computer simulation. Several modes of chaos can be observed. It is revealed that an invariant closed curve is deformed and leads to strange attractors by the mutual effect of fixed points outside and inside the invariant closed curve.

Chaos in non-linear sampled-data control systems

Abstract In this paper, sufficient conditions for chaos in non-linear sampled-data control systems are investigated by applying Marotto's (1978) Theorem and Shiraiwa and Kurata's (1980) Theorem. It is shown that a state-feedback sampled-data control system with sampling period T is chaotic if T > T∗ for sufficiently largo T∗. It is also shown that if a sampled-data control system has an output-feedback and can be split into two subsystems, the existence of chaos in the system can be checked only by the lower-dimensional subsystem behaviour.

Limit-Cycles in Nonlinear Sampled Data Control Systems

Certain classes of nonlinear sampled data control systems are examined with regard to the possible existence of limit-cycles of a given period length. The systems treated here are quantized systems, that means, quantization in D/A- and A/D-conversion are considered. By help of the linear algebra necessary conditions for the existence of oscillations are presented. In order to take advantage of linear algebra, the autonomous nonlinear system is transformed into a nonautonomous linear system, where the nonlinearities determine the bounds of the input signal.In connection with a limit-cycle model a criterion for the absence of limit- cycles of a given period is presented that admits stronger or weaker statements depending on the structure of the nonlinearities. Two examples illustrate the application of the criterion.