Discrete-time Nonlinear Control Systems Research Articles

Observer-based model predictive control for uncertain NCS subject to hybrid attacks via interval type-2 T–S fuzzy model

In this study, an observer-based model predictive control (MPC) algorithm is addressed for an uncertain discrete-time nonlinear networked control system (NCS) subject to hybrid malicious attacks by using interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy theory. Hybrid malicious attacks, including two typical attacks, i.e., denial-of-service (DoS) attacks and false data injection (FDI) attacks, are considered in the communication networks. Under DoS attacks, the control signals will be interfered, which cause the degradation of signal-to-interference-plus-noise ratio, then lead to packets loss. Under FDI attacks, the false signals are injected and output signals are modified so that the system performance is deteriorated. For the NCS subject to hybrid attacks, a secure observer that can resist FDI attacks is devised and a fuzzy MPC algorithm that can solve the controller gains is proposed. Besides, by updating the bound of augmented estimation error, the recursive feasibility can be guaranteed. Finally, illustrative examples are given to show the effectiveness of proposed scheme.

A novel event-triggered constrained control for nonlinear discrete-time systems

<abstract><p>In this paper, a novel event-triggered optimal control method is developed for nonlinear discrete-time systems with constrained inputs. First, a non-quadratic utility function is constructed to overcome the challenge caused by saturating actuators. Second, a novel triggering condition is designed to reduce computational burden. Difference from other triggering conditions, fewer assumptions are required to guarantee asymptotic stability. Then, the optimal cost function and control law are obtained by constructing the action-critic network. Convergence analysis of the system is provided in the consideration of the system state and neural network weight estimation errors. Finally, the effectiveness and correctness of the proposed method are verified by two numerical examples.</p></abstract>

State-Space Region-Invariance of Discrete-Time Control Systems

In the paper, the so called region-invariance properties of discrete-time control systems are considered. An already known notion of positivity of control systems has been generalized (using a kind of geometric insight instead of a pure algebraic approach) to the general nonlinear discrete-time control systems, general regions in state-space, and controls from polyhedral cones in input-space. The class of such control systems has been characterized. Numerous numerical examples illustrating individual cases under consideration are presented in the paper.

Robust Learning-Based Predictive Control for Discrete-Time Nonlinear Systems With Unknown Dynamics and State Constraints

Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopman operator-based prediction model obtained off-line from pre-collected input-output datasets. Unlike classic tube-based MPC, in each prediction time interval of r-LPC, we use an actor-critic structure to learn a near-optimal feedback control policy rather than a control sequence. The resulting closed-loop control policy can be learned off-line and deployed online or learned online in an asynchronous way. In the latter case, online learning can be activated whenever necessary; for instance, the safety constraint is violated with the deployed policy. The closed-loop recursive feasibility, robustness, and asymptotic stability are proven under function approximation errors of the actor-critic networks. Simulation and experimental results on two nonlinear systems with unknown dynamics and disturbances have demonstrated that our approach has better or comparable performance when compared with tube-based MPC and LQR, and outperforms a recently developed actor-critic learning approach.

Observer-Based Asynchronous Control of Nonlinear Systems With Dynamic Event-Based Try-Once-Discard Protocol.

This work investigates the observer-based asynchronous control of discrete-time nonlinear systems with network-induced communication constraints. To avoid the data collisions and side effects in a constrained communication channel, a novel dynamic event-based weighted try-once-discard (DEWTOD) protocol is proposed. In contrast to the existing protocols, the DEWTOD scheduling regulates whether the sampling instant to release and which node to transmit the sampling instant simultaneously. In light of a hidden Markov model, the time-varying detection probability matrix is characterized by a polytopic set. By resorting to the polytopic-structured Lyapunov functional, sufficient conditions are derived such that the closed-loop dynamic is mean-square exponentially stable, and the observer-based controller is designed. In the end, two numerical examples are provided to explicate the validity of the attained methodology.

Event-triggered control for discrete-time delay systems

This study focuses on event-triggered control of nonlinear discrete-time systems with time delays. Based on a Lyapunov–Krasovskii type input-to-state stability result, we propose a novel event-triggered control algorithm that works as follows. The control inputs are updated only when a certain measurement error surpasses a dynamical threshold depending on both the system states and the evolution time. Sufficient conditions are established to ensure that the closed-loop system maintains its asymptotic stability. It is shown that the time-dependent portion in the dynamical threshold is essential to derive the lower bound of the times between two consecutive control updates. As a special case of our results, we demonstrate the performance of the designed event-triggering algorithm for a class of linear control systems with time delays. Numerical simulations are provided to demonstrate the effectiveness of our algorithm and theoretical results.

Observer-based sliding mode control for discrete-time nonlinear system with time-varying delay

This work deals with the design observer-based sliding mode control for discrete-time Takagi–Sugeno fuzzy models with time-varying delay and subject to measurement noises. The sliding surface is developed by introducing the state and input vectors to overcome the restrictive assumption in most existing sliding mode control schemes which forces the input matrices of all linear subsystems to be equal. Sufficient stability conditions of the error system and sliding mode dynamics with disturbance attenuation level are developed using the augmented Lyapunov–Krasovskii functional and free-weighting matrix. Finally, a simulation example is presented to demonstrate the efficiency of the proposed results.

A Fuzzy System Based Iterative Learning Control for Nonlinear Discrete-Time Systems with Iteration-Varying Uncertainties

In this paper, we consider an iterative learning control problem for a class of unknown discrete-time nonlinear systems with iteration-varying initial error, iteration-varying system parameters, iteration-varying external disturbance, iteration-varying desired output, and iteration-varying control direction. These iteration-varying uncertainties are not required to take any particular structure such as the high-order internal model and only need to satisfy certain boundedness conditions. We propose an iterative learning control law with an adaptive iteration-varying fuzzy system to overcome all the uncertainties and achieve the learning control objective. Furthermore, we present a sufficient condition for designing adaptive gains and prove the convergence of the learning error to a small value as the trial number is large enough. Finally, we use two simulation examples to demonstrate all the theoretical results.

Stability Verification in Stochastic Control Systems via Neural Network Supermartingales

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.

Kullback–Leibler control for discrete-time nonlinear systems on continuous spaces

Kullback-Leibler (KL) control enables efficient numerical methods for nonlinear optimal control problems. The crucial assumption of KL control is the full controllability of the transition distribution. However, this assumption is often violated when the dynamics evolves in a continuous space. Consequently, applying KL control to problems with continuous spaces requires some approximation, which leads to the lost of the optimality. To avoid such approximation, in this paper, we reformulate the KL control problem for continuous spaces so that it does not require unrealistic assumptions. The key difference between the original and reformulated KL control is that the former measures the control effort by KL divergence between controlled and uncontrolled transition distributions while the latter replaces the uncontrolled transition by a noise-driven transition. We show that the reformulated KL control admits efficient numerical algorithms like the original one without unreasonable assumptions. Specifically, the associated value function can be computed by using a Monte Carlo method based on its path integral representation.

Dynamic event-triggered gain-scheduling control of discrete-time quasi-LPV systems

This paper concerns the dynamic event-triggered gain-scheduling control of discrete-time nonlinear systems represented by quasi-linear parameter-varying (quasi-LPV) models. A novel dynamic triggering mechanism is proposed to cancel out the influence of asynchronous parameters induced by the event-based sampling. This new mechanism allows to derive constructive conditions to simultaneously design the gain-scheduled control law and the dynamic triggering mechanism to ensure the origin of the closed-loop system is asymptotically stable. As a sub-product, a co-design condition is readily derived to design static triggering mechanisms. Moreover, a convex optimization problem is proposed to enlarge the inter-event sampling and an estimate of the region of attraction of the closed-loop system is obtained. Numerical examples are provided to illustrate the effectiveness of the dynamic triggering strategy over its static counterpart.

Neural learning control for discrete-time nonlinear systems in pure-feedback form

Neural learning control for discrete-time nonlinear systems in pure-feedback form

Event-triggered data-driven control of discrete-time nonlinear systems with unknown disturbance

This paper is dedicated to event-triggered data-driven control of nonlinear systems with unknown disturbance via model free iterative learning approach. An extended state observer is employed to reconstruct the disturbance in system output. An event-triggered model free iterative learning control strategy is constructed by system input, system output and the reconstructed disturbance. Sufficient conditions are proposed to make the resultant tracking error system be uniform ultimate bounded. Simulation examples are provided to validate the effectiveness of the proposed scheme.

Event-triggered H–/L∞ fault detection observer design for discrete-time Lipschitz nonlinear networked control systems in finite-frequency domain

This paper proposes an event-triggered fault detection observer (FDO) design method for discrete-time Lipschitz nonlinear networked control systems (NCSs) in finite-frequency domain. First, a discrete event-triggered transmission scheme is proposed to mitigate the utility of limited network bandwidth. Second, with the aid of a reformulated Lipschitz property, the nonlinear error dynamics are converted into a linear parameter varying (LPV) networked system model. Third, based on this model, the finite-frequency index is used to measure the worst-case fault sensitivity performance and the norm from unknown disturbance to residual is used to measure disturbance robustness performance. Next, a residual evaluation and a dynamic threshold are synthesised based on the norm. Furthermore, sufficient conditions of the FDO design are derived and transformed by a set of linear matrix inequalities (LMIs). The proposed FDO design method can significantly reduce the data transmission to relieve the communication pressure, and can also achieve better FD performance than the full frequency domain. Finally, A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

Fixed-time control of nonlinear discrete-time systems with time-varying delay and uncertain parameters: state and output feedback approaches

Fixed-time control of nonlinear discrete-time systems with time-varying delay and uncertain parameters: state and output feedback approaches

Novel asynchronous premise reconstruction based adaptive event-triggered control for fuzzy systems with actuator failure

This paper explores the adaptive event-triggered (AET) based variable gains controller design problem for a category of discrete-time nonlinear networked control systems (NCSs) with actuator failure. An AET communication scheme is applied for NCSs to reduce the utilization of limited network bandwidth. For overcoming the asynchronous issue of premise variable caused by AET scheme, a novel asynchronous premise reconstruction technique is introduced. Meanwhile, a new variable gains controller is designed subject to AET approach, where the controller gains will be automatically updated by executing the online iteration algorithm. According to a discontinuous Lyapunov function, sufficient conditions are given to ensure that the closed-loop system is asymptotically stable and satisfies H∞ performance. Finally, in the simulation results, the validity of the proposed control method is verified and it is shown that the proposed scheme can achieve better system performances than the existing design technique with fixed threshold.

Nonfragile peak-to-peak filtering for discrete-time Takagi-Sugeno fuzzy systems with dynamic quantizations

This paper investigates the problem of nonfragile peak-to-peak filtering for a class of discrete-time nonlinear networked control systems with dynamic quantizations. The Takagi-Sugeno fuzzy model is applied to approximate the considered nonlinear networked control systems. The perturbations are also considered in the peak-to-peak filter to be designed. Unlike most work about the peak-to-peak filtering for dynamic systems with quantization, both the performance output signal and measurement output signal are quantized by two different dynamic quantizers in our work. The main attention is to design the nonfragile peak-to-peak filter which guarantees the filtering error system to be asymptotically stable and possess a peak-to-peak performance index. By employing the fuzzy basis-dependent Lyapunov function approach and the S-procedure, new sufficient conditions about designing the nonfragile peak-to-peak filter have been established, which are expressed in the form of linear matrix inequalities. In the end, a numerical example is offered to verify the effectiveness of the designed nonfragile peak-to-peak filter.

Closed-loop identification for a class of nonlinearly parameterized discrete-time systems

This paper studies the identification of discrete-time nonlinear parameterized control systems in given experiments. A necessary and sufficient condition of the closed-loop identifiability is established for the stable experiments and an algorithm is proposed to estimate the parameter. The estimates are shown to be strongly consistent with the convergence rate explicitly computed under some simple algebraic condition.

Compositional synthesis of opacity-preserving finite abstractions for interconnected systems

In this paper, we propose a compositional approach to construct opacity-preserving finite abstractions (a.k.a symbolic models) for networks of discrete-time nonlinear control systems. Particularly, we introduce new notions of simulation functions that characterize the distance between control systems while preserving opacity properties across them. Instead of treating large-scale systems in a monolithic manner, we develop a compositional scheme to construct the finite abstractions together with the overall opacity-preserving simulation functions based on those of the smaller subsystems. For a network of incrementally input-to-state stable control subsystems and under some small-gain type condition, an algorithm for designing local quantization parameters is presented to orderly build the local symbolic models of subsystems. We show that the network of those constructed symbolic models simulates the original network for an a-priori defined abstraction accuracy while preserving its opacity properties.

Echo state network-based online optimal control for discrete-time nonlinear systems

This paper investigates the online optimal control problem of discrete-time nonlinear systems using echo state network (ESN)-based adaptive dynamic programming (ADP) method. An online iterative learning algorithm is proposed to solve the partial differential Hamilton–Jacobi–Bellman (HJB) equation in real time. A novel neural networks (NN) critic-actor architecture is presented using two ESNs to implement the ADP method. Then, two online learning laws of the output weights are designed for searching the optimal cost function and control policy. The stability of system and output weights is analysed using Lyapunov approach. Three simulations are given to show the feasibility and effectiveness of the designed algorithm.