Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities.

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov-Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.

Implementation of Parameter Observer for Capacitors.

This paper describes the implementation of a parameter observer (PO) intended to estimate the capacitance and equivalent serial resistance of a capacitor (ESR). The implemented observer consists of a dynamic second-order discrete-time system. The input signal of the observer is the voltage at the terminals of the capacitor measured during its discharge across a variable resistance in two steps. The implemented observer can be used in quasi-online or offline mode. The theoretical and experimental supporting materials provide a comprehensive picture of the implementation and conditions of use of the PO. The experimental verification was carried out with a microcontroller with Cortex®-M7 core architecture. The sampling time of the PO was 20 µs, and the estimation of the parameters was obtained before the end of the discharge of the capacitor. In the cases described in the paper, this means approximately 25 ms. Due to the PO's capabilities (estimation speed, reduced computational complexity and precision)-proved by the experiments carried out on three electrolytic capacitors of 100 µF, 220 µF and 440 µF-the implementation is of interest for several applications, primarily in the field of power electronic applications.

Model Dynamics and Optimal Control for Intervention Policy of COVID-19 Epidemic with Quarantine and Immigrating Disturbances.

A dynamic model called SqEAIIR for the COVID-19 epidemic is investigated with the effects of vaccination, quarantine and precaution promotion when the traveling and immigrating individuals are considered as unknown disturbances. By utilizing only daily sampling data of isolated symptomatic individuals collected by Mexican government agents, an equivalent model is established by an adaptive fuzzy-rules network with the proposed learning law to guarantee the convergence of the model's error. Thereafter, the optimal controller is developed to determine the adequate intervention policy. The main theorem is conducted to demonstrate the setting of all designed parameters regarding the closed-loop performance. The numerical systems validate the efficiency of the proposed scheme to control the epidemic and prevent the overflow of requiring healthcare facilities. Moreover, the sufficient performance of the proposed scheme is achieved with the effect of traveling and immigrating individuals.

On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems.

Given a discrete-time controlled bilinear systems with initial state x 0 and output function y i , we investigate the maximal output set Θ(Ω) = {x 0 ∈ ℝ n , y i ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝ p . Using some stability hypothesis, we show that Θ(Ω) can be determined via a finite number of inequations. Also, we give an algorithmic process to generate the set Θ(Ω). To illustrate our theoretical approach, we present some examples and numerical simulations. Moreover, to demonstrate the effectiveness of our approach in real-life problems, we provide an application to the SI epidemic model and the SIR model.

Ultimately Bounded Filtering for Time-Delayed Nonlinear Stochastic Systems with Uniform Quantizations under Random Access Protocol.

This paper investigates the ultimately bounded filtering problem for a kind of time-delay nonlinear stochastic systems with random access protocol (RAP) and uniform quantization effects (UQEs). In order to reduce the occurrence of data conflicts, the RAP is employed to regulate the information transmissions over the shared communication channel. The scheduling behavior of the RAP is characterized by a Markov chain with known transition probabilities. On the other hand, the measurement outputs are quantized by the uniform quantizer before being transmitted via the communication channel. The objective of this paper is to devise a nonlinear filter such that, in the simultaneous presence of RAP and UQEs, the filtering error dynamics is exponentially ultimately bounded in mean square (EUBMS). By resorting to the stochastic analysis technique and the Lyapunov stability theory, sufficient conditions are obtained under which the desired nonlinear filter exists, and then the filter design algorithm is presented. At last, two simulation examples are given to validate the proposed filtering strategy.

Security-guaranteed filter design for discrete-time Markovian jump delayed systems subject to deception attacks and sensor saturation.

This work is devoted the problem of a security-guaranteed filter design for a class of discrete-time Markov jump systems that are vulnerable to stochastic deception attacks and have random sensor saturation. Deception attacks, in particular, are taken into account in the filter when the attacker attempts to modify the broadcast signal in communication networks by inserting some misleading information data into the assessment output. The Bernoulli distribution is satisfied by two sets of introduced stochastic variables. It shows the likelihood that the broadcaster's data transmissions will be the focus of deception attacks and sensor saturation. The Lyapunov functional technique is established, and criteria are derived to ensure that the system is mean-square stable. Furthermore, explicit expression of the filter gains is obtained by solving a set of linear matrix inequalities. Lastly, two simulation examples including a synthetic genetic regulatory network are provided to further demonstrate the validity and efficiency of the suggested theoretical results.

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks.

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

Fully distributed consensus of discrete-time linear multi-agent systems with large input and communication delays.

This paper investigates the consensus problem for discrete-time leader-following multi-agent systems subject to large time delays. Building upon two assumptions, a novel fully distributed protocol is devised by utilizing a normalized weighting matrix, depending solely on the relative output measurement. It is shown that, for arbitrarily large yet bounded input and communication delays that are constant and exactly known, the consensus problem can be effectively addressed by both the proposed protocol and its truncated version. Assuming further that followers incorporate solely input delays, then the permitted delays can be time-varying and different. The proposed protocols do not rely on global information of the directed communication topology, thus ensuring robustness against alterations in the communication topology. A numerical example is employed to validate the effectiveness of the suggested approach.

Observer-based state estimation for discrete-time semi-Markovian jump neural networks with round-robin protocol against cyber attacks.

This paper investigates an observer-based state estimation issue for discrete-time semi-Markovian jump neural networks with Round-Robin protocol and cyber attacks. In order to avoid the network congestion and save the communication resources, the Round-Robin protocol is used to schedule the data transmissions over the networks. Specifically, the cyber attacks are modeled as a set of random variables satisfying the Bernoulli distribution. On the basis of the Lyapunov functional and the discrete Wirtinger-based inequality technique, some sufficient conditions are established to guarantee the dissipativity performance and mean square exponential stability of the argument system. In order to compute the estimator gain parameters, a linear matrix inequality approach is utilized. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed state estimation algorithm.

Discrete-time robust event-triggered actuator fault-tolerant control based on adaptive networks and reinforcement learning.

This paper focuses on the topic of fault-tolerant control for discrete-time systems with nonlinear uncertainties and actuator faults. It considers both passive and active faults as part of the analysis and design. The proposed adaptive controller, based on a nonlinear electronic circuit, handles offset-biasing, sensitivity variation, and dead-zone effects. An event-triggered mechanism, utilizing a sliding surface, enhances robustness and reduces data transmission. Adaptive networks called MiFRENs are employed, trained using reinforcement learning. Theoretical analysis guarantees boundedness of internal signals and tracking error. Experimental results validate the scheme, demonstrating required conditions, reduced data transmission, and robust performance. Comparative evaluations confirm its superiority.

Robust induced ℓ2-ℓ∞ optimal control of discrete-time systems having magnitude and rate-bounded actuators.

The design of robust state- and output-feedback control for uncertain discrete-time systems with physical magnitude and rate constraints on their actuator dynamics was addressed. Unlike the traditional methods such as anti-windup (AW) methods, nested ellipsoids, model predictive controllers (MPCs) and integral quadratic constraints(IQCs) formulated by sector bounded inequalities, this paper uses a transformation of the system dynamics to a form which considers control signal and its rate as controlled outputs and using discrete-time ℓ∞ induced (peak-to-peak) norm from disturbance inputs to these outputs. To cope with the magnitude and rate bound non-linearities together, the induced ℓ∞ norm from disturbance input to the outputs involving control signal and its rate is utilised. On the other hand, discrete-time(DT) induced ℓ2 norm from disturbance input to the main controlled output is used to mitigate the effects of disturbances. We can tackle this ambitious non-linear control problem in the domain of linear convex multi-objective optimal control problem, which can be solved by effective semi-definite optimisation methods by using the proposed transformation and handling the control constraints in terms of worst case peak-to-peak gain of the system. Extended Linear Matrix Inequalities (LMIs) and full block S-procedure based design conditions developed over Linear Fractional Representation(LFR) framework allow the user to obtain robust state- and output-feedback control solutions with reduced conservatism. For the first time, this paper introduces an extended LMI based robust output-feedback control design for magnitude and rate bounded (MRB) systems, using full block S-procedure. We demonstrate the performance of the proposed controller through several simulations over benchmark examples covering systems having multi-variable structures and uncertainties. Our study also involves comparison results with a recently introduced technique based on multi-stage AW technique. The simulation results show that the proposed method of this paper is much effective and less conservative compared to the recent AW method provided in the literature.

A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals.

Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.

Periodic event-triggered adaptive tracking control design for nonlinear discrete-time systems via reinforcement learning.

In this paper, an event-triggered control scheme with periodic characteristic is developed for nonlinear discrete-time systems under an actor-critic architecture of reinforcement learning (RL). The periodic event-triggered mechanism (ETM) is constructed to decide whether the sampling data are delivered to controllers or not. Meanwhile, the controller is updated only when the event-triggered condition deviates from a prescribed threshold. Compared with traditional continuous ETMs, the proposed periodic ETM can guarantee a minimal lower bound of the inter-event intervals and avoid sampling calculation point-to-point, which means that the partial communication resources can be efficiently economized. The critic and actor neural networks (NNs), consisting of radial basis function neural networks (RBFNNs), aim to approximate the unknown long-term performance index function and the ideal event-triggered controller, respectively. A rigorous stability analysis based on the Lyapunov difference method is provided to substantiate that the closed-loop system can be stabilized. All error signals of the closed-loop system are uniformly ultimately bounded (UUB) under the guidance of the proposed control scheme. Finally, two simulation examples are given to validate the effectiveness of the control design.

Epidemic model dynamics and fuzzy neural-network optimal control with impulsive traveling and migrating: Case study of COVID-19 vaccination.

To suppress the epidemics caused by a virus such as COVID-19, three effective strategies listing vaccination, quarantine and medical treatments, are employed under suitable policies. Quarantine motions may affect the economic systems and pharmaceutical medications may be recently in the developing phase. Thus, vaccination seems the best hope of the current situation to control COVID-19 epidemics. In this work, the dynamic model of COVID-19 epidemic is developed when the quarantine factor and the antiviral factor are established as free variables. Moreover, the impulsive populations are comprehended for traveling and migrating of individuals. The proposed dynamics with impulsive distractions are employed to generate the online data. Thereafter, the equivalent model is developed by using only the daily data of symptomatic infectious individuals and the optimal vaccination policy is derived by utilizing the closed-loop control topology. The theoretical framework of the proposed schemes validates the reduction of symptomatic infectious individuals by using fewer doses of vaccines comparing with the scheduling vaccination.

Asynchronous H∞ control of Markov jump discrete-time systems with incomplete transition probability and unreliable links.

In this study, an asynchronous H∞ state feedback controller is devised for Markov jump discrete-time systems (MJDTSs) with time-varying delay. "Asynchronous" means that the system switching mode θk, the controller mode ϑk and the quantizer mode λk are different from each other. The first one is homogeneous and the last two are non-homogeneous. In particular, as a promotion of existing work, we firstly attempt to propose the transition probabilities (TPs) of the three Markov chains (MCs) are not completely known. In addition, the discrete time-varying delay and its infinitely distributed ones are considered. Moreover, according to the Lyapunov stability theory and stochastic process, it is established for the sufficient criterion to ensure the stochastic stability of resulting closed-loop MJDTSs with an H∞ attenuation performance index. The feasibility and effectiveness of the proposed method are validated by three examples.

Fault reconstruction and resilient control for discrete-time stochastic systems.

In this paper, a novel resilient control technique is proposed for discrete-time stochastic Brownian systems with simultaneous unknown inputs and unexpected faults. Prior to previous work, the stochastic Brownian system under consideration is quite general, where stochastic perturbations exist in states, control inputs, uncertainties, and faults. Moreover, the unknown input uncertainties concerned cannot be fully decoupled. Innovative observer by employing augmented system approach, decomposition observer, and optimization algorithms is proposed to achieve simultaneous estimates of both states and faults. Furthermore, fault reconstruction-based signal compensation is formulated to alleviate the effects from actuator faults and sensor faults. An observer-based controller is eventually constructed to enhance the stability and robustness of the closed-loop dynamic system. The integrated resilient control technique can ensure the system has reliable output even under faults. Both linear systems and Lipschitz nonlinear systems are investigated and the design procedures are addressed, respectively. Finally, the proposed resilient control techniques are validated via an electromechanical servo-system, and an aircraft system.

Closed-loop control of tumor growth by means of anti-angiogenic administration.

A tumor growth model accounting for angiogenic stimulation and inhibition is here considered, and a closed-loop control law is presented with the aim of tumor volume reduction by means of anti-angiogenic administration. To this end the output-feedback linearization theory is exploited, with the feedback designed on the basis of a state observer for nonlinear systems. Measurements are supposed to be acquired at discrete sampling times, and a novel theoretical development in the area of time-delay systems is applied in order to derive a continuous-time observer in spite of the presence of sampled measurements. The overall control scheme allows to set independently the control and the observer parameters thanks to the structural properties of the tumor growth model. Simulations are carried out in order to mimic a real experimental framework on mice. These results seem extremely promising: they provide very good performances according to the measurements sampling interval suggested by the experimental literature, and show a noticeable level of robustness against the observer initial estimate, as well as against the uncertainties affecting the model parameters.

Non-fragile H∞ filtering for nonlinear discrete-time delay systems with randomly occurring gain variations.

In this paper,the problem of H∞ filtering for a class of nonlinear discrete-time delay systems is investigated. The time delay is assumed to be belonging to a given interval, and the designed filter includes additive gain variations which are supposed to be random and satisfy the Bernoulli distribution. By the augmented Lyapunov functional approach, a sufficient condition is developed to ensure that the filtering error system is asymptotically mean-square stable with a prescribed H∞ performance. In addition, an improved result of H∞ filtering for linear system is also derived. The filter parameters are obtained by solving a set of linear matrix inequalities. For nonlinear systems, the applicability of the developed filtering result is confirmed by a longitudinal flight system, and an additional example for linear system is presented to demonstrate the less conservativeness of the proposed design method.

Performance limitations in the tracking and regulation problem for discrete-time systems.

In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.