Discrete-time Systems Research Articles

Radial basis function neural network based data-driven iterative learning consensus tracking for unknown multi-agent systems

This paper provides a novel data-driven-distributed-consensus control protocol for unknown nonlinear non-affine discrete-time multi-agent systems (MAS) with repetitive properties. The leader’s commands are directed to the followers in the topological graph. The dynamic linearization technology (DLT) is used to build the distributed iterative learning (IL) controller along the iteration axis. In the iterative process, the control gain is automatically adjusted by updating the weight matrix of the high-order radial basis function neural network (RBFNN, HORBFNN). In global control, the higher order parameter (HOP) Newton method is used to achieve global convergence and stability of the control process. All the above processes do not require the understanding of dynamical equations or physical models for each agent, and only use local communication information of multi-agent to achieve consistent tracking of MAS leaders and followers. Based on the strong connection, the convergence performance, stability and boundedness properties of the proposed control protocol in the fixed topology as well as in the iterative topology are validated by a rigorous theoretical analysis. Simulation experiments are conducted to verify the effectiveness of the control protocol.

Stability of discrete-time system employing quantization and overflow nonlinearities

An investigation of exponential stability for externally interfered discrete-time systems under various concatenations of quantization and overflow nonlinearities is conducted in this article. A new criterion is proposed based on the passivity approach such that the interfered nonlinear discrete-time systems ensure passivity performance in terms of its storage function. The derived criterion not only considers the effects of overflow nonlinearity but also the consequences of quantization nonlinearity. Furthermore, the proposed criterion guarantees the passivity performance of the discrete-time system in the presence of external disturbance and exponential stability for zero disturbance. The reported conditions are defined in terms of linear matrix inequality, for easy tractability. Suitable examples are given to demonstrate the usefulness of the proposed work.

Model-free event-triggered resilient control for discrete-time nonlinear systems under sparse actuator attacks via GrHDP

Model-free event-triggered resilient control for discrete-time nonlinear systems under sparse actuator attacks via GrHDP

Distributed Nash equilibrium seeking for quadratic games in discrete-time systems with bounded control inputs

This paper considers the distributed Nash equilibrium seeking problem for quadratic games in discrete-time systems with bounded control inputs. First, a saturation gradient algorithm is proposed to seek the Nash equilibrium without considering the limitations of communication. Then the case that players can only communicate with their neighbors is considered, a distributed Nash equilibrium seeking algorithm is designed where a consensus protocol is adapted for information sharing. In the proposed distributed algorithm, each player has an estimate on others’ actions and the consensus of players’ estimates is achieved. By Lyapunov stability theory for discrete-time systems, it is shown that the Nash equilibrium of the game is globally asymptotically stable under certain conditions. Moreover, distributed Nash equilibrium seeking problem in hybrid systems with bounded control inputs is solved. Finally, two numerical examples are presented to verify the effectiveness of the proposed algorithms.

Assessing Stability in Discrete-Time Systems Impacted by Interference and State Delays: An Approach Using ISS

In this study, we introduce a criterion for addressing the input to state stability (ISS) problem inherent in nonlinear discrete systems featuring state delay, saturation overflow (SO), and external interference (EI). This paper proposes three novel theorems by employing the Lyapunov function to assure the stability of the targeted discrete time systems (DTS) under complex conditions such as state delay, SO, EI and the first theorem utilizes system information more effectively by considering EI, state delay and SO, the second theorem focuses on asymptotic stability (AS) analysis of the system when EIs are zero, the third theorem proposes the system is AS when state delays are zero. These theorems impose fewer constrains additionally these conditions are demonstrated to be more relaxed and computationally less intensive to existing criteria. The advantage of the suggested technique is proven through three numerical examples and comparison research.

Transient analysis of a SIQS model with state capacities using a non-homogeneous Markov system

In this paper, a novel stochastic model is proposed to model the spread of a virus in epidemics. The model is based on a discrete-time non-homogeneous Markov system with state capacities. In order to study the distributions of the state sizes, recursive formulae for their factorial and mixed factorial moments were derived in matrix form. As a consequence, the probability mass function of each state size can be evaluated in the transient period. To avoid the computational complexity of the proposed algorithm, an alternative method for the computation of the state size distributions was recommended. The proposed Markovian approach was then tailored to the characteristics of a SIQS (susceptible-infected-quarantined-susceptible) epidemic scheme, which took into account external infections and the potential for secondary infections. This epidemic model is well-suited for describing infections in computer networks, where the quarantine capacity can be likened to the number of working people (IT professionals) available to restore an infected computer. We presented numerical examples and sensitivity analysis to illustrate the behavior and performance of the system under different scenarios and parameter values. We show that the state capacities and the infection rates have significant effects on the evolution and extinction of the epidemic. We note that the optimal number of employed technicians can be identified, aiming to keep the computer network functional. Higher internal infection rates significantly affect the sustainability of the computer network, while controlling external infections is not always feasible. On the other hand, faster detection rates and higher malware elimination rates will considerably increase the number of computers that remain operational in the long term. Consequently, the quality of services provided by IT technicians plays a crucial role in the system’s viability.

Transient response improvement of predictive control under time domain constraints

In this paper, a novel predictive controller design approach within augmented structure base on convex optimization of an extra parameter is proposed in order to improve the transient response of discrete-time linear systems subject to input constraints. This methodology starts with the conception of an initial stabilizing predictive controller which ensures a fast closed loop response to the detriment of the other response specifications indexes (settling time, settling error, overshoot and control signal). Then, this controller is redesigned off-line using linear programming solver to meet a certain transient response specifications of the closed loop system determined before the design as time domain constraints. The resulting controlled output will track the reference as fast and as smooth as possible with a low energy consumption. Two examples are given to show the effectiveness of the developed controller.

Dynamic complexity of a discretized predator-prey system with Allee effect and herd behaviour

This paper investigates the dynamics of a discrete-time predator-prey system in which the prey population is impacted by the Allee effect. Possible fixed points in the system are studied for their existence and topological categorization. Moreover, the presence and direction of period-doubling and Neimark-Sacker bifurcations at the interior fixed point are examined through the application of bifurcation theory and the centre manifold theorem. A hybrid approach is adopted to control chaotic behaviour and prevent bifurcations. Numerical examples are provided to substantiate our theoretical findings. The Allee effect has been shown to affect the dynamics of the system using numerical simulations. The moderate Allee effect stabilizes predator and prey populations, facilitating ecological cohabitation and persistence.

Signed-network-based consensus control for nonlinear multi-agent systems: a dynamic encryption–decryption approach

Abstract This paper is concerned with the bipartite secure control issue for a class of discrete-time nonlinear multi-agent systems under a dynamic encryption–decryption approach. First, the coupling relationships between agents are portrayed through a signed graph topology containing the edges of positive and negative connection weights. Next, the information transmissions between agents and their neighbors are executed via a shared communication network. The dynamic encryption–decryption approach is implemented to transform original signals into ciphertexts. Under the assumption that the signed graph is structurally balanced, a signed-network-based bipartite secure controller is designed to achieve the desired state control for the nonlinear multi-agent system and sufficient conditions are obtained for the existence of the desired signed-network-based state controller. Furthermore, a precise definition of the minimum channel capacity is proposed to understand the factors affecting the minimum channel capacity. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.

Event-triggered fuzzy adaptive control for a class of MIMO discrete-time nonlinear systems with uncertain control gains

ABSTRACT An event-triggered output control technique is devised for the output anticipated trajectory tracking controller design problem for a class of unknown multiple-input-multiple-output (MIMO) discrete-time nonlinear systems. A parameterized state observer is established to estimate the non-measurable states accurately by utilizing the filter states and the gradient-based fuzzy parameter updated laws. A series of fuzzy filters are proposed to evaluate the immeasurable states, and a filter state observer is constructed to overcome the state estimation that is triggered by the unknown control gains and the coupling of control input. One non-zero parameter is added to a fuzzy logic system (FLS) to reduce the computed burden of the controller with several updating laws. A FLS with one non-zero parameter is introduced to reduce the calculated burden of the controller with fewer updating laws. The proposed method reduces the computed burden and communication consumption while realizing the immeasurable state estimations, guaranteeing the ultimately uniformly bounded (UUB) of the closed-loop system, and achieving a good tracking impact. Finally, simulation analyses are used as a numerical example to confirm that the proposed control strategy is valid.

Robust α-exponential estimate for polytopic uncertain positive discrete-time systems with bounded time-varying delay

In this paper, the problem of finding a robust α-exponential estimate for a class of perturbed positive discrete-time time-delay systems with polytopic uncertainties will be addressed. By proposing a linear parameter-dependent Lyapunov function, a condition for the existence of robust α-exponential estimates will be introduced. Some optimisation techniques are also incorporated to obtain a more accurate estimate. In particular, a procedure to reformulate a class of fractional programming problems into a linear programming problem which can be solved efficiently. A numerical example is presented to demonstrate the effectiveness of the proposed method.

Host-Parasitoid Systems are Vulnerable to Extinction via P-Tipping: Forest Tent Caterpillar as an Example.

Continuous-time predator-prey models admit limit cycle solutions that are vulnerable to the phenomenon of phase-sensitive tipping (P-tipping): The predator-prey system can tip to extinction following a rapid change in a key model parameter, even if the limit cycle remains a stable attractor. In this paper, we investigate the existence of P-tipping in an analogous discrete-time system: a host-parasitoid system, using the economically damaging forest tent caterpillar as our motivating example. We take the intrinsic growth rate of the consumer as our key parameter, allowing it to vary with environmental conditions in ways consistent with the predictions of global warming. We find that the discrete-time system does admit P-tipping, and that the discrete-time P-tipping phenomenon shares characteristics with the continuous-time one: Both require an Allee effect on the resource population, occur in small subsets of the phase plane, and exhibit stochastic resonance as a function of the autocorrelation in the environmental variability. In contrast, the discrete-time P-tipping phenomenon occurs when the environmental conditions switch from low to high productivity, can occur even if the magnitude of the switch is relatively small, and can occur from multiple disjoint regions in the phase plane.

Self-organizing neural intelligent control for nonlinear discrete-time systems with particle swarm optimization

Self-organizing neural intelligent control for nonlinear discrete-time systems with particle swarm optimization

H ∞ prescribed tracking performance-based fractional-order sliding mode control for disturbed discrete-time systems: an LMI approach

This paper presents a novel approach to the design of a discrete-time Fractional-Order Sliding Mode Control (FSMC) system for Single Input Single Output (SISO) applications, utilising the Autoregressive with exogenous input (ARX) method for system modelling. The proposed methodology emphasises the Prescribed Performance Control (PPC) to ensure minimal tracking errors through a transformation of tracking errors based on a specified performance function. A Fractional-Order Quasi-Sliding Mode Control (FQSMC) is subsequently developed to maintain the tracking error within predetermined bounds, effectively addressing the chattering phenomenon commonly associated with the traditional sliding mode control. The integration of fractional calculus enhances the smoothness of the output while ensuring accurate tracking, making it ideal for real-world applications. Additionally, a novel Linear Matrix Inequality (LMI) observer is introduced to bolster the system's resilience against uncertainties and disturbances without complicating the computational process. The effectiveness of the proposed Prescribed Performance Fractional-Order Quasi-Sliding Mode Control (PP-FQSMC) is validated through extensive MATLAB simulations and experimental studies conducted on a Tank system. Results demonstrate that the PP-FQSMC significantly outperforms traditional methods, with maximum tracking errors of 1.6 × 10−4 compared to 0.2 for the PP-QSMC and a Root Mean Square Tracking Error (RMSTE) of 1.3 × 10−3 compared to 1.2 × 10−4 for the PP-QSMC, ensuring strong tracking performance and stability. The findings indicate that the proposed controller effectively mitigates chattering in control signals while maintaining a smooth output. It showcases its potential for practical applications in environments characterised by model inaccuracies, time delays, and external disturbances.

Output feedback fault-tolerant Q-learning for discrete-time linear systems with actuator faults

This paper presents an innovative output feedback fault-tolerant Q-learning algorithm that can be implemented online without relying on explicit system models or fault details. In the face of actuator faults, finding optimal Fault-Tolerant Control (FTC) solutions that can stabilize the faulty system poses significant challenges. The proposed approach is implemented online without the need for system dynamics and actuator fault information. Furthermore, it operates without relying on full state measurements, utilizing only the input-output data of the faulty system. An innovative representation of the output feedback Fault-Tolerant Q-function (FTQF) is established using input-output data. Subsequently, a model-free optimal output feedback FTC policy is obtained from the developed FTQF. Then, a fault-tolerant Q-learning algorithm is formulated to iteratively acquire the optimal FTC policy in real-time, eliminating the necessity for system dynamics and actuator fault information. The proposed algorithm exhibits immunity to excitation noise bias, even without considering a discounting factor. Furthermore, the proposed Q-learning approach is proven to be effective in stabilizing faulty closed-loop system. Finally, the proposed algorithm's efficiency is validated through numerical simulations of F-16 autopilot aircraft dynamics.

On the Method for Constructing Null-Controllable Sets for Linear Discrete-Time Systems with Summary Control Constraints

On the Method for Constructing Null-Controllable Sets for Linear Discrete-Time Systems with Summary Control Constraints

Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies

In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.

Min–max group consensus of discrete-time multi-agent systems under directed random networks

This paper studies the min–max group consensus of discrete-time multi-agent systems under a directed random graph, where the presence of each directed edge is randomly determined by a probability and independent of the presence of other edges. Firstly, we propose a min–max consensus protocol without memory, and give the necessary and sufficient conditions to ensure that the multi-agent system can achieve the min–max group consensus in the sense of almost sure and mean square, respectively. Secondly, we design a novel consensus protocol with memory and a behavior mechanism. Using the stochastic analysis theory and the extremal algebra, some necessary and sufficient conditions are obtained for achieving the min–max group consensus in the sense of almost sure and mean square, respectively. It is shown that the protocol with memory can solve the loss problem of the maximum and minimum initial states. Finally, the effectiveness of the two group consensus protocols and the behavior mechanism is verified by four numerical simulations.

Interval estimation of sensor fault in rotary steerable drilling tools based on set-membership approach

The rotary steerable drilling tools (RSDTs) are invented for high-precision wellpath control. Fault diagnosis is essential for the RSDT as it can improve the reliability of the drilling processes. To estimate the sensor fault of the RSDT, this paper investigates the interval estimation problem for Lipschitz nonlinear systems with sensor fault via the set-membership approach. Firstly, the RSDT is modeled by a discrete-time Lipschitz nonlinear system with unknown inputs, noises, and parameter uncertainties. Next, based on the ellipsoid bundles, a set-membership fault estimator is presented, where the unknown inputs are decoupled. Additionally, a sufficient condition, which is derived based on the P-radius of the ellipsoid bundles, is put forward to design the parameters of the estimator with Lipschitz nonlinear terms. Then, the interval estimations of the states and fault are obtained via ellipsoid bundles. Finally, the efficiency of the proposed approach is evaluated through numerical simulations and experiments.

Leader-Following Sampled-Data Consensus of Multiagent Systems With Successive Packet Losses and Stochastic Sampling.

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that cause the sampling interval to deviate from the expected value and fluctuate according to a certain probability distribution. This probability distribution can be determined in advance through statistical analysis. Taking into account this stochastic sampling interval, this article focuses on addressing the leader-following sampled-data consensus problem for linear multiagent systems (MASs) with successive packet losses. First, the relationship of the equivalent sampling interval between two successive update instants is established, taking into account the double randomness introduced by both SPLs and stochastic sampling. Then, the equivalent discrete-time MAS is obtained, and the overall leader-following consensus problem is formulated as a stochastic stability problem of the equivalent system by incorporating the sampled-data consensus protocol and properties of the Laplacian matrix. Based on the equivalent the discrete-time system, a consensus criterion is derived under a directed graph by using the Lyapunov theory and leveraging a vectorization technique. By the introduction of a matrix reconstruction approach, the mathematical expectation of a product of three matrices, including the system matrix and its transpose, can be determined. Then, the consensus protocol gain is designed. Finally, an example is provided to validate our theoretical results.