Nonlinear Sampled-data Systems Research Articles

ℒ2-gain performance of nonlinear sampled-data systems with gain-scheduled control

This paper presents new sufficient conditions for stabilisation of sampled-data nonlinear systems, recast as quasi-linear parameter-varying models. The adopted control strategy considers gain-scheduled state-feedback controllers subject to induced input delay. The L 2 -gain performance is investigated in the sense of Lyapunov. After the proposition of a Lyapunov function and with the application of Wirtinger's inequality, the derived conditions are rewritten in terms of linear matrix inequalities. Aiming at the enlargement of the aperiodic sampling time and at the minimisation of the L 2 -gain, the effectiveness of the developed approach is assessed through numerical simulations.

Deterministic learning-based neural output-feedback control for a class of nonlinear sampled-data systems

Deterministic learning-based neural output-feedback control for a class of nonlinear sampled-data systems

Observer-based fault-tolerant control design for a class of sampled-data nonlinear systems with bounded disturbances

Observer-based fault-tolerant control design for a class of sampled-data nonlinear systems with bounded disturbances

Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems

Ensuring robust constraint satisfaction for an infinite time horizon is a challenging, yet crucial task when deploying safety-critical systems. We address this issue by synthesizing robust control invariant sets of perturbed nonlinear sampled-data systems. This task can be encoded as a non-convex program that we approximate by a tailored, computationally efficient successive convexification algorithm. Based on the zonotopic representation of invariant sets, we obtain an updated candidate for the invariant set and the invariance-enforcing controller by solving a single convex program. To obtain a possibly large region of safe operation, our algorithm is designed so that the sequence of candidate invariant sets is volume-wise monotonically increasing. We demonstrate the efficacy and scalability of our approach using a broad range of nonlinear control systems from the literature with up to 20 dimensions.

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.

On the stability of nonlinear sampled-data systems and their continuous-time limits

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between specific stability properties of the exact discrete-time model and stability properties of the continuous-time system that is obtained when the maximum admissible sampling period tends to zero. These results can be used to infer stability properties for the sampled-data system by direct inspection of the stability of the mentioned continuous-time system, a task which is typically easier than the analysis of the closed-loop sampled-data system. Compared to the literature, our results allow to prove stronger (asymptotic) sampled-data stability properties for nonlinear systems in cases for which existing results only guarantee practical stability.

Data-Driven Multimodel Predictive Control for Multirate Sampled-Data Nonlinear Systems

This paper is concerned with the asynchronous control problem of multi-rate sampled-data nonlinear systems. To solve this problem, the data-driven multi-model predictive control (DMMPC) strategy is proposed. First, a multi-model predictive control structure is designed such that each state variable of the multi-rate sampled-data nonlinear system can be controlled synchronously at all sampling instants. In this structure, the fuzzy neural network (FNN) is introduced to build the multi-model. Then, the prediction outputs of each state variable at all sampling instants are obtained to provide control information for the controller. Specially, the objective function with adaptive weight matrix (AWM) is designed to reduce the influence of the prediction error caused by nonlinear fitting on control performance. Then, the optimal control laws are calculated to improve the control precision. Finally, the convergence and stability of DMMPC are proved in detail. The numerical example and industrial application reveal that the proposed DMMPC can obtain considerable control performance for the multi-rate sampled-data nonlinear systems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The asynchronous control problem of the multi-rate sampled-data nonlinear system (MRSNS) may degrade the operation performance of closed-loop system. In this paper, a data-driven multi-model predictive control (DMMPC) strategy is designed for MRSNS without mechanism model. The strategy mainly consists of three parts: First, a multi-model prediction structure based on fuzzy neural network (FNN) is established to obtain the prediction output of all variables at each sampling point. The parameters of FNNs are corrected at each sampling point to ensure prediction accuracy. Second, an objective function with an adaptive weight matrix (AWM) is designed to compute the control law, in which AWM is used to reduce the influence of prediction error on control performance. Third, the effectiveness of DMMPC is verified by a numerical example and an industrial application of the wastewater treatment process. The experimental results show that DMMPC can achieve satisfied operation performance in control accuracy.

Nonlinear Sampled-data Systems—A lifting framework

This short note gives a new framework for dealing with nonlinear sampled-data systems. We introduce a new idea of lifting, which is well known for linear systems, but not successfully generalized to nonlinear systems. This paper introduces a new lifting technique for nonlinear, time-invariant systems, which are different from the linear counterpart as developed in Bamieh et al. (1991); Yamamoto (1994) etc. The main difficulty is that the direct feedthrough term effective in the linear case cannot be generalized to the nonlinear case. Instead, we will further lift the state trajectory, and obtain an equivalent time-invariant discrete-time system with function-space input and output spaces. The basic framework, as well as the closed-loop equation with discrete-time controller, is given. As an application of this framework, we give a representation for the Koopman operator derived from the given original nonlinear system.

Further Stability Criteria for Sampled-Data-Based Interval Type-2 Fuzzy Systems via a Refined Two-Side Looped-Functional Method

This article investigates the stability and stabilization problem of aperiodic sampled-data nonlinear systems in the framework of interval type-2 (IT-2) fuzzy models. First, by introducing two adjustable parameters and splitting the sampling intervals into four nonuniform intervals, a refined two-side looped-functional method is constructed to fully utilize inner state information during the whole aperiodic sampling interval. Simultaneously, the positive definiteness constraint for the individual matrix in Lyapunov–Krasovskii functional can be further relaxed. Then, via constructing a novel fuzzy Lyapunov–Krasovskii functional (FLKF) together with a fuzzy-dependent-switching scheme, the available features of fuzzy membership functions (FMFs) can be further taken into consideration to increase the design flexibility. Consequently, the stability condition and corresponding controller design approach for aperiodic sampled-data IT-2 fuzzy systems can be obtained with less design conservatism and larger sampling intervals. Finally, two simulation examples are employed to demonstrate the validity and superiority of the proposed method.

A Distributed Synchronisation-based Predictor for Lur'e-type Nonlinear Systems

This paper proposes a distributed state predictor for nonlinear systems using sampled measured data. In particular, we attempt to develop a distributed state predictor for Lur'e systems based on anticipating synchronisation. Anticipating synchronisation is a leader-follower synchronisation such that the follower system synchronises with the future values of the leader system by using delayed feedback. Since the prediction scheme has a closed-loop structure, it is expected to have robustness for disturbance and model mismatch. In this paper, we develop a distributed predictor that consists of networks of multiple predictors based on anticipatory synchronisation to achieve the state prediction for sampled-data nonlinear systems. First, we consider a distributed state predictor in the case where all measurements are sampled synchronously. After that, we develop a distributed state predictor based on asynchronously acquired measurements. The validity of the obtained results is illustrated in a numerical example.

Deterministic learning from neural control for a class of sampled-data nonlinear systems

This study investigates the deterministic learning and control issues for uncertain sampled-data nonlinear systems (SDNSs). The problem of how to acquire/learn knowledge from adaptive control for SDNSs with uncertain affine terms is studied. To be specific, an appropriate neural network-based (NNB) control strategy is first presented to ensure tracking performance. To further realize learning, the exponential stability (ES) of the integrated closed-loop system coupled with the estimation error of the NN weights is considered. As the uncertain affine term prevents learning from occurring, the integrated system is converted into a discrete linear time-varying (DLTV) perturbed system by employing the state conversion technique. Tracking convergence allows the persistent excitation condition (PEC) of the NNs to be established, which guarantees the ES of the integrated DLTV system. Thus, accurate modeling of closed-loop sampled dynamics is obtained. By reutilizing the experiential knowledge obtained, a knowledge-based controller is constructed for high-performance control. Finally, simulations are performed to verify the presented strategy.

Zonotopic Filtering for Uncertain Nonlinear Systems: Fundamentals, Implementation Aspects, and Extensions [Applications of Control

This tutorial provides a comprehensive perspective on the study of zonotopic filtering for nonlinear uncertain dynamical systems. Unlike stochastic methods that characterize the states by means of random vectors, set-based observers estimate deterministic sets that are guaranteed to contain the system states. Among many classes of sets, the focus here is on zonotopes due to their appealing properties that pursue a good tradeoff between precision and computational cost. We start by reviewing the fundamentals of zonotopic filtering together with illustrative examples. As nonlinear systems bring up many challenges for this topic, we choose one of the first nonlinear zonotopic observers proposed in the literature to guide a series of discussions. After presenting this algorithm and understanding its limitations, we extend it by incorporating state inequality constraints. In addition, we motivate the use of linear programs when solving minimum-volume intersections. Additionally, we give a practical discussion on the implementation of discrete-time zonotopic algorithms for sampled-data nonlinear dynamical systems. To better introduce the zonotopic approaches, we briefly review unscented Kalman filtering to trace parallels between the stochastic and set-theoretic frameworks. Then the presented algorithms are experimented and compared in a case study involving a quadrotor unmanned aerial vehicle.

Dissipativity-based framework for stability analysis of aperiodically sampled nonlinear systems with time-varying delay

In this paper, we provide novel conditions for stability analysis of aperiodically sampled nonlinear control systems subjected to time-varying delay. The proposed approach can also deal with cases in which delay is larger than the sampling interval. It is applicable to a general class of nonlinear systems and provides sufficient criteria for stability that aid in making trade-offs between control performance and the bounds on sampling interval and delay. As a stepping stone, a preliminary and generic result based on dissipativity, is introduced to analyse the exponential stability of a class of feedback-interconnected systems. The nonlinear sampled-data system is remodelled to consider the effects of sampling and delay in the dissipativity framework, as perturbations to the nominal closed-loop system. This leads to constructive stability conditions for a continuous time closed-loop system given by the feedback interconnection of the nominal closed-loop system and an operator(s) that captures the effects of sampling and delay. For Linear Time-Invariant (LTI) systems, we recover simple Linear Matrix Inequality (LMI) and frequency domain conditions previously proposed in the robust control framework.

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.

Sampled-Data Stabilization of a Class of Stochastic Nonlinear Markov Switching System with Indistinguishable Modes Based on the Approximate Discrete-Time Models

This paper investigates the stabilization issue for a class of sampled-data nonlinear Markov switching system with indistinguishable modes. In order to handle indistinguishable modes, the authors reconstruct the original mode space by mode clustering method, forming a new merged Markov switching system. By specifying the difference between the Euler-Maruyama (EM) approximate discrete-time model of the merged system and the exact discrete-time model of the original Markov switching system, the authors prove that the sampled-data controller, designed for the merged system based on its EM approximation, can exponentially stabilize the original system in mean square sense. Finally, a numerical example is given to illustrate the effectiveness of the method.

Stability analysis of non-linear sampled data systems with time varying sample period and delay in the feedback loop

In almost all practical applications of control, technological and economical considerations impose limits on communication speed, frequency of communication, and frequency of actuator adjustment. Such limits turned the analysis of sampled data systems into a flourishing field. Water systems pose a particular challenge: the systems are networks of canals and reservoirs spread over large areas, and the actuators are relatively large and exposed to the elements. In this study, a theorem on the local exponential stability of sampled data systems with variable control time step and variable delay in the communication between the non-linear continuous time process and the non-linear discrete time controller is presented. To illustrate the application of the theorem, it is applied to a simple water system.

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.

Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis

In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

Quality estimation of CPS network link based on non-uniformly sampling period

Cyber Physical System (CPS) is a fusion system integrating computing, communication and control functions with information task processing as the core. CPS needs real-time, highly efficient and reliable communication links to complete the dynamic feedback and control between the physical world and the information world effectively. Affected by many factors, the link quality of wireless communication environment is nonlinear randomness. Meanwhile, the sampled data of the system is non period signal. This study described it as a class of non-uniformly sampled nonlinear systems. Based on the Hierarchical Principle method, a stochastic gradient algorithm is proposed for non-uniformly sampled data nonlinear system. The algorithm can estimate the quality of CPS network link successfully. The results shows the validity of the algorithm, which can effectively guarantee quality of links and accomplish good dynamic feedback and control of the system.

Fault Detection for a Class of Uncertain Sampled-Data Systems Using Deterministic Learning.

In this article, we propose a learning-based fault diagnosis approach for a class of nonlinear sampled-data systems. First, the unmodeled sampled dynamics is acquired by the using deterministic learning method. The knowledge of the sampled dynamics of the normal and fault patterns is stored in the form of constant neural networks. Second, a fault detection scheme is designed in which memories of the learned knowledge can be recalled to give a rapid response to a fault. Third, analytical results concerning the fault detection condition and detection time are derived. It is shown that the mismatch function plays an important role in the performance properties of the diagnosis scheme. To analyze the effect of mismatch function on the residual, the concept of duty ratio is developed. Moreover, by comparing the constant neural networks of the normal and fault patterns, an extraction operator is designed to capture the feature of the mismatch function. By using this method, the performance of the diagnosis scheme can be improved. A simulation study is included to demonstrate the effectiveness of the approach.