Discrete-time Context Research Articles

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.

Memory event-triggered scheme of positive systems: A dynamic weighted method

A novel memory event-triggered scheme for positive systems is proposed in this paper. To address the conservatism of the existing memory event-triggered scheme, the weight parameter on the left side of the memory event-triggered scheme is replaced with a dynamic function. This modification results in a dynamic weighted memory event-triggered scheme that can be applied in both continuous-time and discrete-time contexts. By adjusting the weight dynamically based on the system operation, the scheme can respond more effectively to changes in the system state. Compared to the memory event-triggered scheme, a more flexible balance is achieved between improving system performance and saving system resources. A joint design that combines the dynamic weighted memory event-triggered scheme and positive systems is presented for continuous linear systems, with the controller gain obtained by a linear programming strategy. The proposed co-design scheme is subsequently extended to discrete positive systems. To demonstrate the effectiveness of the proposed method, two practical applications are presented.

A novel strategy for fault estimation in Lipschitz nonlinear switched systems with discrete-time context using dissipativity theory

A novel strategy for fault estimation in Lipschitz nonlinear switched systems with discrete-time context using dissipativity theory

Discrete-Time Adaptive Control for Uncertain Scalar Multiagent Systems with Coupled Dynamics: A Lyapunov-Based Approach

Discrete-time architectures offer a distinct advantage over their continuous counterparts, as they can be seamlessly implemented on embedded hardware without the necessity for discretization processes. Yet, because of the difficulty of ensuring Lyapunov difference expressions, their designs, which are based on quadratic Lyapunov-based frameworks, are highly complex. As a result, various existing continuous-time results using adaptive control methods to deal with system uncertainties and coupled dynamics in agents of a multiagent system cannot be directly applied to the discrete-time context. Furthermore, compared to their continuous-time equivalent, discrete-time information exchange based on periodic time intervals is more practical in the control of multiagent systems. Motivated by these standpoints, in this paper, we first introduce a discrete-time adaptive control architecture designed for uncertain scalar multiagent systems without coupled dynamics as a preliminary result. We then introduce another discrete-time adaptive control approach for uncertain multiagent systems in the presence of coupled dynamics. Our approach incorporates observer dynamics to manage unmeasurable coupled dynamics, along with a user-assigned Laplacian matrix to induce cooperative behaviors among multiple agents. Our solution includes Lyapunov analysis with logarithmic and quadratic Lyapunov functions for guaranteeing asymptotic stability with both controllers. To demonstrate the effectiveness of the proposed control architectures, we provide an illustrative example. The illustrative numerical example shows that the standard discrete-time adaptive control in the absence of observer dynamics cannot guarantee the reference state vector tracking, while the proposed discrete-time adaptive control can ensure the tracking objective.

Variance optimality in constrained and unconstrained stochastic differential games

The purpose of this paper is to extend the variance optimality criterion to the settings of constrained and unconstrained two-person stochastic differential games. We give conditions that ensure the existence of Nash equilibria with minimal variance. This criterion is a complement to that of the average long-run expected reward of an ergodic Markov process. Our main contribution is that we give sufficient conditions to define and ensure the existence of relaxed strategies that optimize the limiting variance of a constrained performance index of each player in the continuous-time framework. To the best of our knowledge, this theoretical task has been approached only for unconstrained Markov decision problems in a discrete-time context. The applications of our research range from predator–prey systems to actuarial paradigms and cell growth modeling in patients diagnosed with cancer.

Total stability of equilibria motivates integral action in discrete-time nonlinear systems

Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. Inspired by the continuous-time literature, in this article we investigate the total stability properties of dynamical discrete-time nonlinear systems. Such a property locally relates phase plots of dynamical systems of the same dimension which are “similar enough”. As a consequence, it enables the analysis of robustness properties via simple model difference in the discrete-time context. First, we study how existence of equilibria for a nominal model transfers to sufficiently similar ones. Then, we provide results on the propagation of stability guarantees to perturbed systems. Finally, we relate such properties to the constant output regulation problem by motivating the use of discrete-time integral action in discrete-time nonlinear systems for model robustness purposes.

Interval Type-2 Fuzzy Control for HMM-Based Multiagent Systems via Dynamic Event-Triggered Scheme

This article discusses the interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy asynchronous controller design problem for nonlinear multiagent systems via a dynamic event-triggered scheme in the discrete-time context. To formulate the asynchronous phenomena between the system modes and the anticipant controller modes, the hidden Markov model is proposed. The primary attention is focused on the explicit design of the dynamic event-triggered strategy that can be dynamically adjusted in line with system information, which mitigates the communication burden efficiently. On this occasion, the information renewal of the controller is aperiodic. Furthermore, the nonlinear characteristics are effectually disposed through utilizing a unique IT2 T-S fuzzy model, which is with mismatched membership functions (MFs). As a result, the resulting closed-loop fuzzy multiagent systems are accompanied by mismatched MFs and asynchronous modes, whereafter, via solving the convex optimization problem, the desired controller gains are acquired. Eventually, the validity and practicability of the developed control scheme are illustrated by two examples.

Event-triggered filtering for uncertain semi-Markov jump systems with time-varying delay by using quantized measurement

This paper focuses on the extended dissipative filter design problem for a class of uncertain semi-Markov jump systems in the discrete-time context, where the parameter uncertainties are assumed to be occurred in a special probabilities way. The aim of this paper is to design a mode-dependent filter ensuring the stochastic stability of the resulting filtering error system. To reduce the burden of communication network, the event-triggered scheme and quantized measurement are employed. By constructing a new Lyapunov functional, the filter design methodology is put forward. Finally, two numerical examples are proposed to demonstrate the usefulness of the filter design methodology.

A Fair SINR Performance Comparison of FBMC/OQAM and FBMC/QAM Multicarrier Communication Systems in the Discrete-Time Framework

In the last couple of decades, multicarrier modulations have witnessed a considerable interest in wireless communication networks due to their ability to fight against multipath fading and offer multiple access with flexible resource sharing. One of the well known multicarrier modulation systems is filter-bank multi-carrier with an offset quadrature amplitude modulation (FBMC/OQAM), which was proposed as a powerful solution during the standardization of 5G. In this paper, we derive a closed-form expression of the signal to interference plus noise ratio (SINR) for FBMC/OQAM systems in the discrete-time context, for arbitrary wide sense stationary uncorrelated scattering (WSSUS) channels as well as transmitter (Tx) and receiver (Rx) waveforms. We quantify the potential gains in SINR brought by FBMC/OQAM, which exclusively operates on critical lattice density, with respect to FBMC/QAM, which have the flexibility to operate on critical or non-critical lattice densities. For completeness, we compare the performance of FBMC/OQAM in the discrete-time context, sweeping the discrete space of waveforms supports, with that of FBMC/OQAM in the continuous-time context, using the Hermite functions, and show how they perform similarly. Simulation results prove that FBMC/OQAM optimization algorithm, performing with the ping-pong optimized pulse shaping (POPS) paradigm, converges rapidly to excellent SINR values, even with small supports durations, in discrete-time context, which is equivalent to a reduced number of Hermite functions, in the continuous-time context.

Absolute Exponential Stability for Switching Positive Systems With Time-Delay Based on the Φ-Dependent ADT Strategy

The absolute exponential stability problem for the continuous- and discrete-time, respectively, switching positive nonlinear time-delay system is investigated under the nonlinearity of systems satisfying a certain sector condition in this paper. Two multiple co-positive Lyapunov-Krasovskii functionals (MCLKF) of such systems are constructed for the continuous- and discrete-time contexts respectively. By using the MCLKF and the Φ-dependent average dwell time switching strategy, more general stability conditions compatible with some existing works are established. Furthermore, the obtained results are generalized to other types of systems. A numerical example, finally, implies the validity and significance of the results proposed.

Asynchronous non-fragile control for persistent dwell-time switched singularly perturbed systems with strict dissipativity

This paper focuses on the problem of asynchronous non-fragile dissipativity control for a class of switched singularly perturbed systems (SPSs) governed by the persistent dwell-time (PDT) switching mechanism in the discrete-time context. Unlike some previous results, the modes of system and controller in this paper are assumed to be asynchronized, which conforms better with the practical scenarios. Besides, considering the case that the controllers may be affected by uncertain factors and can not be realized accurately during system operation, the non-fragile mechanism is introduced in the process of controller design to enhance the reliability and security of the SPSs. Based on Lyapunov stability theory and stochastic analysis theory, some sufficient conditions are obtained, which can ensure the exponentially mean-square stable (EMSS) and strict dissipative performance of the closed-loop system. Furthermore, the asynchronous non-fragile slow state variables feedback (SSVF) controller gains are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example and an inverted pendulum model are applied to demonstrate the superiority and the practicability of the developed control mechanism.

Distributed [formula omitted] state estimation for switched sensor networks with packet dropouts via persistent dwell-time switching mechanism

This paper addresses the distributed H∞ state estimation problem for a class of sensor networks with switching characteristics, where the switchings of parameters are presumed to obey persistent dwell-time switching mechanism rather than dwell time or average dwell-time ones in the discrete-time context. For the purpose of tracking the unavailable state of the target plant, a sensor network is formed by employing multiple sensor nodes distributed in space and worked cooperatively under a specific connection topology. The intention of the paper mainly centers on deriving some sufficient criteria for the addressed model to achieve the exponential mean-square stability with a prescribed H∞ performance, and the estimator gains corresponding to differently constructed estimators are further solved by means of the convex optimization method. Finally, the validity of the proposed approach is illustrated by a numerical example.

Fault-Tolerant Fuzzy Control for Semi-Markov Jump Nonlinear Systems Subject to Incomplete SMK and Actuator Failures

This article focuses on the problem of fuzzy-model-based fault-tolerant control for nonlinear semi-Markov jump systems in the discrete-time context. The discrete-time semi-Markov process is employed to describe the mode jumping among several subsystems in the investigated systems. Moreover, the nonlinear characteristics are effectively tackled through utilizing the Takagi–Sugeno fuzzy model. Unlike some previous results, the information of the semi-Markov kernel (SMK) in this article is assumed to be partially available, which conforms better with the practical scenarios. Besides, considering the case that actuators may encounter some unexpected failures during system operation, the fault-tolerant mechanism is introduced in the process of controller design to enhance the fault tolerance of the studied systems. By means of SMK approach and Lyapunov stability theory, some elapsed-time-dependent criteria for guaranteeing the mean-square stability of the closed-loop system are established. According to these criteria, the design methodology of the reliable fuzzy state feedback controller is developed. Eventually, in order to verify the practicability and rationality of the developed control scheme, a single-link robot arm model is presented.

Stability Analysis of Discrete-Time Switched Systems With Unstable Modes: An Improved Ratio-Based Tradeoff Approach

This brief investigates the stability of switched systems with unstable modes in discrete-time context. To enlarge the room for switching scheme design, a new multiple discontinuous Lyapunov functions (MDLFs) method is developed, and a novel mode-dependent average dwell time (MDADT) tradeoff strategy is explored. Subsequently, based on the new MDLFs method, stability criteria are achieved for the systems under arbitrary switching signals with the MDADT-based tradeoff switching scheme. Finally, the proposed results are applied to a Pulse-Width-Modulation driven boost converter to demonstrate the effectiveness.

Observed-Mode-Dependent State Estimation of Hidden Semi-Markov Jump Linear Systems

This paper is concerned with state estimation for a class of hidden semi-Markov jump linear systems governed by a two-layer stochastic process in the discrete-time context. A semi-Markov chain and an observed-mode sequence constitute the lower and upper layer of the process, respectively. With the aid of the emission probability, a novel filter, which is dependent both on the elapsed time within the activated mode and on the observed mode instead of the system mode, is constructed and called observed-mode-dependent (OMD) filter. A modified $\sigma$ -error mean square stability ( $\sigma$ -MSS) is proposed by considering the weight of expected operation time in each actual system mode. Based on the new $\sigma$ -MSS, together with a class of Lyapunov functions depending on both the system modes and the corresponding observed ones, numerically checkable conditions on the existence of the OMD filter are presented such that the estimation error system is $\sigma$ -MSS with a prescribed $\mathcal {H}_{\infty }$ disturbance attenuation level. A numerical example is presented to demonstrate the theoretical findings.

Finite‐time control of switched affine non‐linear systems based on the Lie derivative and iteration technique

In this study, the finite-time H ∞ control problem for a class of switched affine non-linear systems is discussed in both continuous-time and discrete-time contexts. Firstly, the concepts of finite-time boundedness are extended to switched non-linear systems in both continuous-time and discrete-time cases, respectively. Secondly, based on the Lie derivative and iteration technique, some sufficient conditions, which can guarantee that switched affine non-linear systems are finite-time bounded with a prescribed H ∞ performance, are derived by applying the mode-dependent average dwell time and the multiple Lyapunov functions. It is worth pointing out that each subsystem satisfies finite-time boundedness in the activation interval, and not in the whole time domain. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the obtained results.

Stability conditions of switched nonlinear systems with unstable subsystems and destabilizing switching behaviors

In this paper, the global uniform exponential stability (GUES) for a class of switched nonlinear systems is discussed in both continuous-time and discrete-time contexts. Different from multiple Lyapunov function and average dwell time in the previous work, a general multiple Lyapunov-like function and a modified admissible edge-dependent average dwell time switching scheme based on a directed graph are implemented in this paper. By further allowing the Lyapunov-like function to increase and decrease during the running time of active subsystems, and permitting the admissible transition edge-dependent weights (ATEDWs) to be greater or less than one, the extended stability results for switched systems in a nonlinear situation are first derived. Given a new amalgamation condition between the increasing ratio and decreasing ratio of the Lyapunov-like function at switching instants, the minimal admissible edge-dependent average dwell time (AEDADT) for admissible switching signals are is obtained. By contrasting with the results available on the subject, we allow that all the switching behaviors of the switching systems at switching instants are destabilizing, and the transition weights of admissible transition edge may be less than one1. More especially, even if some of the subsystems are not stable and all the switching behaviors of are destabilizing, the stability property of the switched system can still be preserved. Finally, two numerical examples are illustrated to show the validity of the proposed results.

A discrete-time optimal filtering approach for non-linear systems as a stable discretization of the Mortensen observer

In this work, we seek exact formulations of the optimal estimator and filter for a non-linear framework, as the Kalman filter is for a linear framework. The solution is well established with the Mortensen filter in a continuous-time setting, but we seek here its counterpart in a discrete-time context. We demonstrate that it is possible to pursue at the discrete-time level an exact dynamic programming strategy and we find an optimal estimator combining a prediction step using the model and a correction step using the data. This optimal estimator reduces to the discrete-time Kalman estimator when the operators are in fact linear. Furthermore, the strategy that consists of discretizing the least square criterion and then finding the exact estimator at the discrete level allows to determine a new time-scheme for the Mortensen filter which is proven to be consistent and unconditionally stable, with also a consistent and stable discretization of the underlying Hamilton-Jacobi-Bellman equation.

Mixed H∞ and passive filtering for switched Takagi-Sugeno fuzzy systems with average dwell time

This paper investigates the mixed H∞ and passive filtering problem for switched Takagi-Sugeno (T-S) fuzzy systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. To deal with this problem, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H∞ and passivity performance index. Based on this new performance index, the weighted H∞ filtering problem and the passive filtering problem for switched T-S fuzzy systems can be solved in a unified framework. Combining the multiple Lyapunov functions approach with a matrix decoupling technique, new sufficient conditions for the existence of mixed weighted H∞ and passive filters are obtained for switched T-S fuzzy systems. All these conditions are expressed in terms of linear matrix inequalities (LMIs). The desired filters can be constructed by solving these LMIs. Finally, numerical examples and practical examples are provided.

A novel approach to control synthesis of positive switched systems

This study addresses the control synthesis of positive switched systems in both continuous- and discrete-time contexts. First, a novel design approach to the state-feedback controller of continuous-time positive switched systems without time delay is presented by virtue of multiple linear copositive Lyapunov functions associated with linear programming. Then, the design approach is extended to discrete-time positive switched systems. It is shown that the presented approach is less conservative than existing ones through comparisons. Furthermore, the approach is developed to the stabilisation of positive switched systems with time delay. Some discussions on the presented approach are provided to show potential applications in corresponding control issues of positive switched systems. Finally, two examples are given to illustrate the theoretical findings.