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In inverse reinforcement learning (RL), there are two agents. An expert target agent has a performance cost function and exhibits control and state behaviors to a learner. The learner agent does not know the expert's performance cost function but seeks to reconstruct it by observing the expert's behaviors and tries to imitate these behaviors optimally by its own response. In this article, we formulate an imitation problem where the optimal performance intent of a discrete-time (DT) expert target agent is unknown to a DT Learner agent. Using only the observed expert's behavior trajectory, the learner seeks to determine a cost function that yields the same optimal feedback gain as the expert's, and thus, imitates the optimal response of the expert. We develop an inverse RL approach with a new scheme to solve the behavior imitation problem. The approach consists of a cost function update based on an extension of RL policy iteration and inverse optimal control, and a control policy update based on optimal control. Then, under this scheme, we develop an inverse reinforcement Q-learning algorithm, which is an extension of RL Q-learning. This algorithm does not require any knowledge of agent dynamics. Proofs of stability, convergence, and optimality are given. A key property about the nonunique solution is also shown. Finally, simulation experiments are presented to show the effectiveness of the new approach.

A fast non-negative latent factor (FNLF) model for a high-dimensional and sparse (HiDS) matrix adopts a Single Latent Factor-dependent, Non-negative, Multiplicative and Momentum-incorporated Update (SLF-NM2U) algorithm, which enables its fast convergence. It is crucial to achieve a rigorously theoretical proof regarding its fast convergence, which has not been provided in prior research. Aiming at addressing this critical issue, this work theoretically proves that with an appropriately chosen momentum coefficient, SLF-NM2U enables the fast convergence of an FNLF model in both continuous and discrete time cases. Empirical analysis of HiDS matrices generated by representative industrial applications provides empirical evidences for the theoretical proof. Hence, this study represents an important milestone in the field of HiDS matrix analysis.

This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection control problem, necessary and sufficient conditions for designing the suboptimal controller were presented, and the performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.

We propose a model that allows for conditional heteroskedasticity in the volatility of asset returns and incorporates current return information into the volatility nowcast and forecast. Our model can capture all stylised facts of asset returns even with Gaussian innovations and is simple to implement. Moreover, we show that our model converges weakly to the GARCH-type diffusion as the length of the discrete time intervals between observations goes to zero. Empirical evidence shows that our model has a better fit, a more efficient parameter estimator as well as more accurate volatility and VaR forecasts than other common GARCH-type models.

This article investigates the leader-follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader-follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader-follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed $i_{n}$ -step predictors, the leader's future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific ``learning rules,'' the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader-follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

A data-driven distributed formation control algorithm is proposed for an unknown heterogeneous non-affine nonlinear discrete-time MIMO multi-agent system (MAS) with sensor fault. For the considered unknown MAS, the dynamic linearization technique in model-free adaptive control (MFAC) theory is used to transform the unknown MAS into an equivalent virtual dynamic linearization data model. Then using the virtual data model, the structure of the distributed model-free adaptive controller is constructed. For the incorrect signal measurements due to the sensor fault, the radial basis function neural network (RBFNN) is first trained for the MAS under the fault-free case, then using the outputs of the well-trained RBFNN and the actual outputs of MAS under sensor fault case, the estimation laws of the unknown fault and system parameters in the virtual data model are designed with only the measured input-output (I/O) data information. Finally, the boundedness of the formation error is analyzed by the contraction mapping method and mathematical induction method. The effectiveness of the proposed algorithm is illustrated by simulation examples.

This article investigates the stability problem for discrete-time neural networks with a time-varying delay by focusing on developing new Lyapunov-Krasovskii (L-K) functionals. A novel L-K functional is deliberately tailored from two aspects: 1) the quadratic term and 2) the single-summation term. When the variation of the discrete-time delay is further considered, the constant matrix involved in the quadratic term is extended to be a delay-dependent one. All these innovations make a contribution to a quadratic function with respect to the delay from the forward differences of L-K functionals. Consequently, tractable stability criteria are derived that are shown to be more relaxed than existing results via numerical examples.

This study aims to analyse the robust exponential stability for neutral differential equations of the uncertain Takagi–Sugeno fuzzy system with distributed and discrete time interval delays by applying the Newton–Leibniz formula, the Lyapunov–Krasovskii functional, and the zero equations. By these methods, the less conservative exponential stability criteria are obtained for a special case of the generalized fuzzy of the neutral differential system. By applying Matlab LMI toolbox, the new conditions for exponential stability are obtained in the forms of linear matrix inequalities (LMIs), which can verify the numerical performance by the LMI toolbox of MATLAB. Finally, numerical examples are provided to manifest the efficiency and reduce the conservatism of the obtained results rather than the results which exist in the literature.

In this article, the stabilization problem of discrete-time power systems subject to random abrupt changes is studied via asynchronous control. In this regard, the transient faults in the power lines, and subsequent switching of associated circuit breakers are modeled as a Markov chain. Based on this, the power systems are described as discrete-time Markov jump systems. The focus is mainly to design the control for Markov jump-based power systems (MJPSs) when modes of the control asynchronously run with the modes of power systems. To do this, a hidden Markov model technique is used to characterize the nonsynchronization between the control and system. By constructing the mode-dependent stochastic Lyapunov function, the sufficient conditions are acquired in the form of linear matrix inequalities (LMIs), which ensure not only the stochastic stability of the resulting hidden MJPSs but also the existence of the desired control. Finally, the simulation example reveals the efficiency of the designed control law.

In this paper, an event-triggered output feedback adaptive fuzzy control scheme is developed for a class of uncertain discrete-time multi-input multi-output (MIMO) nonlinear systems with immeasurable states and unknown control gains. Due to the existence of unmeasured states, a set of fuzzy filters are designed, then a filter-based event-triggered adaptive fuzzy control scheme is developed for discrete-time MIMO nonlinear systems. To solve the problem of state estimation caused by the coupling of control input and unknown control gains, a fuzzy filters-based state observer is developed by combining filter states. And then, a parameterized state observe is constructed to effectively estimate immeasurable state signals by the combination of the fuzzy filter states and the gradient-based fuzzy parameter updating law. Based on filter states and estimation states, an event-based adaptive fuzzy control scheme is proposed by novel intermediate errors and backstepping. To overcome the causal problem caused by the low-triangular structure, the variable substitution and a predictor are, respectively, employed to forecast the future state and reference signals. A series of stability analyses illustrates that the proposed scheme achieves immeasurable state estimations, guarantees the ultimately uniformly boundedness of the closed-loop system, and obtains the good tracking performance, while reducing communication occupancy. Finally, simulation studies on a numerical and a practical example are conducted to demonstrate the effectiveness of the proposed scheme.

In this short paper, relaxed observer-based state estimation of discrete-time Takagi-Sugeno fuzzy systems is proposed via developing a new augmented matrix approach. In contrast with the recent method reported in the literature, a more advanced introduction mode of additional matrices is developed without any redundant constraint under the framework of homogeneous polynomials. Then, the proposed augmented matrices can be built in order to depict the characteristic information of each possible working mode in a superior way, and thus our obtained result is less conservative than the recent one. Moreover, it is worth noting that that the recent method belongs to the special case of ours. Finally, two numerical simulations are given to test and validate the superiority and generality of the developed method.

Autonomous vehicle path following performance is one of significant consideration. This paper presents discrete time design of robust PD controlled system with disturbance observer (DOB) and communication disturbance observer (CDOB) compensation to enhance autonomous vehicle path following performance. Although always implemented on digital devices, DOB and CDOB structure are usually designed in continuous time in the literature and also in our previous work. However, it requires high sampling rate for continuous-time design block diagram to automatically convert to corresponding discrete-time controller using rapid controller prototyping systems. In this paper, direct discrete time design is carried out. Digital PD feedback controller is designed based on the nominal plant using the proposed parameter space approach. Zero order hold method is applied to discretize the nominal plant, DOB and CDOB structure in continuous domain. Discrete time DOB is embedded into the steering to path following error loop for model regulation in the presence of uncertainty in vehicle parameters such as vehicle mass, vehicle speed and road-tire friction coefficient and rejecting external disturbance like crosswind force. On the other hand, time delay from CAN bus based sensor and actuator command interfaces results in degradation of system performance since large negative phase angles are added to the plant frequency response. Discrete time CDOB compensated control system can be used for time delay compensation where the accurate knowledge of delay time value is not necessary. A validated model of our lab Ford Fusion hybrid automated driving research vehicle is used for the simulation analysis while the vehicle is driving at high speed. Simulation results successfully demonstrate the improvement of autonomous vehicle path following performance with the proposed discrete time DOB and CDOB structure.

The present study concerns the dissipativity-based synchronization problem for the discrete-time switched neural networks with time-varying delay. Different from some existing research depending on the arbitrary and time-dependent switching mechanisms, all subsystems of the investigated delayed neural networks are permitted to be nondissipative. For reducing the switching frequency, the combined switching paradigm constituted by the time-dependent and state-dependent switching strategies is then constructed. In light of the proposed dwell-time-dependent storage functional, sufficient conditions with less conservativeness are formulated, under which the resultant synchronization error system is strictly (~X,~Y,~Z) - ϑ -dissipative on the basis of the combined switching mechanism or the joint action of the switching mechanism and time-varying control input. Finally, the applicability and superiority of the theoretical results are adequately substantiated with the synchronization issue of two discrete-time switched Hopfield neural networks with time-varying delay, and the relationship among the performance index, time delay, and minimum dwell time is also revealed.

This article is concerned with the development of a new event-triggered parity space fault detection (FD) scheme. A linear discrete-time system model with varying sampling periods is presented for handling the problem of event-triggered FD and a new parity relation is established. Based on this, an event-triggered residual generator is constructed and the generated residual is completely decoupled from event-triggered transmission error. The design of the parity matrix is formulated into an optimization problem and an optimal solution of the parity matrix is obtained by using singular value decomposition. The issue of residual evaluation is also considered in the event-triggering implementation. The novelties of this article are twofold. First, a new event-triggered parity relation is obtained and the parity space-based residual signal achieves complete decoupling with the event-triggered transmission error. Second, the calculation of the parity matrix is independent of event parameters. So the design of the parity space-based residual generator and event generator can be carried out independently. Finally, a simulation example is considered to demonstrate the effectiveness of the proposed method.

The linear quadratic (LQ) optimal control and stabilization problems for mean-field systems with input delay (MFSID) are investigated in this paper. The necessary and sufficient solvability conditions for LQ control of MFSID are first given in terms of a convexity condition and the solvability of equilibrium conditions. Consequently, by solving the associated mean-field forward and backward stochastic difference equations (MF-FBSDEs), the optimal control is derived in terms of the solution of a modified Riccati equation (MRE). Furthermore, for infinite horizon case, the stabilization problem for MFSID is studied, and the necessary and sufficient stabilizability conditions are obtained. We show that MFSID can be mean square stabilizable if and only if a modified algebraic Riccati equation (MARE) admits a unique positive definite solution.

The multivariable modeling of a servo actuating system consisting of multi-field multi-armature direct current (MFMADC) machine is extracted and a novel discrete time nonlinear algorithm is proposed for the corresponding system. The proposed control algorithm demonstrates robustness against modeling uncertainty and by utilizing its novel mathematical structure, decouples the dynamical interactions of the connected motors. The main contribution of this paper is the proposition of a new decoupling control algorithm that in which, the driving (commanding) voltages of the connected driving motors are extracted separately and independently using the Lyapunov principle in discrete time. In fact, the obtained coupled stabilizing convex inequalities of the controlling voltages, resulting from the evaluation of the Lyapunov functions, are analytically decoupled using elementary matrix operations. Consequently, each motor now has the capability to perform its controlling task (position control or torque control) with asymptotic stability and robustness against uncertainty. To assess the performance of the proposed controlling algorithm and its verification, a MFMADC machine is attached to a harmonic drive reducer (HDR) whose flex spline and circular spline are fabricated using viscoelastic polyesters PLA and thermoplastic PLA, respectively. A number of experiments are conducted where in the first test, the MFMADC is controlled in only-position mode while in the second test, the MFMADC is controlled in simultaneous position-torque control mode. Comparative assessments confirm that the MFMADC technology is needed when a high precision tracking of position, under high frequency disturbances, is desired.

This paper considers the stabilization problem of discrete-time semi-Markov jump singularly perturbed systems, in which the system operation mode is hidden but can be estimated by a detector with some emission probabilities. To model this circumstance, the hidden semi-Markov model with partially known emission probabilities is introduced, where the hidden state represents the real system operation mode while the emitted value represents the estimated value of the system operation mode and is available for the stabilizing controller. Based on the introduced hidden semi-Markov model, the stabilizing controller which only relies on the estimated value is designed to guarantee the $\delta$ -error mean square stability of the closed-loop system. A numerical example is used to verify the usefulness of the obtained results.

In order to address zero-sum game problems for discrete-time (DT) nonlinear systems, this article develops a novel event-triggered control (ETC) approach based on the deterministic policy gradient (PG) adaptive dynamic programming (ADP) algorithm. By adopting the input and output data, the proposed ETC method updates the control law and the disturbance law with a gradient descent algorithm. Compared with the conventional PG ADP-based control scheme, the present controller is updated aperiodically to reduce the computational and communication burden. Then, the actor-critic-disturbance framework is adopted to obtain the optimal control law and the worst disturbance law, which guarantee the input-to-state stability of the closed-loop system. Moreover, a novel neural network weight updating law which guarantees the uniform ultimate boundedness of weight estimation errors is provided based on the experience replay technique. Finally, the validity of the present method is verified by simulation of two DT nonlinear systems.

Aiming to addressing the nonrepetitive uncertainties of multiagent systems, this work proposes a discrete-time-distributed adaptive iterative learning control (DDAILC) scheme for an output consensus problem, where two fundamental requirements in the traditional distributed iterative learning control (ILC) methods, i.e., the identical initial states and the repetitive desired trajectories, are removed. Furthermore, the algorithm design and analysis are directly aimed at discrete-time nonlinear multiagent systems, rather than continuous-time ones, to meet the needs of practical implementations. The iteration-varying trajectory of the virtual leader is included in the learning control protocol for a compensation. The adaptive parameter-updating law works along the iteration dimension by using a general consensus error that contains the output data of adjacent agents. To ensure the estimation of the control gain to be nonzero, a semisaturator is utilized in the parameter-updating law. The convergence of the output consensus is shown rigorously. Both numerical and practical examples are used to test the theoretical results. Moreover, the DDAILC efficiently improves performance of the building heating, ventilation, and air conditioning (HVAC) system by utilizing both the distributed topology and the repetitive dynamic characteristic.

In this paper, the robust asynchronous filtering problem is investigated for a class of discrete-time T-S fuzzy complex dynamical networks subjected to random coupling delays and deception attacks. Specifically, the deception attacks are considered in the filter, where the adversary attempts to inject some false information data in the measurement output to modify the transmitted signal in the communication networks. We introduce respectively two sets of stochastic variables satisfying the Bernoulli distribution to depict the probability of the data transmitted by the network being subjected to time-varying coupling delays and deception attacks. By using Lyapunov-Krasovskii stability theory and Abel lemma-based finite-sum inequality, a new set of sufficient conditions is established which ensures the stochastic stability of the resulting error system with a prescribed mixed Hand passivity performance index. The proposed filter parameters are obtained by solving linear matrix inequalities. Ultimately, both the effectiveness and advantages of the proposed asynchronous filter with deception attacks are verified by two numerical examples including a tunnel diode circuit model.

The existing results of Lagrange stability for neural networks with distributed time delays are scale-free, which introduces conservativeness naturally. A class of Takagi-Sugeno fuzzy memrisive neural networks (FMNNs) on time scales with discrete time-varying and infinite distributed delays is brought in this paper. First, a new scale-limited Halanay inequality is demonstrated by timescale theory. Next, on the basis of inequality techniques on time scales, some new scale-limited algebraic criteria and linear matrix inequality criteria of Lagrange stability are obtained by comparison strategy and generalized Halanay inequality. All scale-limited sufficient criteria of Lagrange stability for FMNNs not only apply to continuous-time FMNNs and their discrete-time analogues, but also could deal with the arbitrary combination of them. Finally, two numerical simulations are given to verify the validity of the obtained theoretical results.

This article is concerned with the multiloop decentralized H∞ fuzzy proportional-integral-derivative-like (PID-like) control problem for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays under dynamical event-triggered mechanisms (ETMs). The sensors of the plant are grouped into several nodes according to their physical distribution. For resource-saving purposes, the signal transmission between each sensor node and the controller is implemented based on the dynamical ETM. Taking the node-based idea into account, a general multiloop decentralized fuzzy PID-like controller is designed with fixed integral windows to reduce the potential accumulation error. The overall decentralized fuzzy PID-like control scheme involves multiple single-loop controllers, each of which is designed to generate the local control law based on the measurements of the corresponding sensor node. These kinds of local controllers are convenient to apply in practice. Sufficient conditions are obtained under which the controlled system is exponentially stable with the prescribed H∞ performance index. The desired controller gains are then characterized by solving an iterative optimization problem. Finally, a simulation example is presented to demonstrate the correctness and effectiveness of the proposed design procedure.

We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex.

Semi-linear discrete-time control systems with periodic coefficients are considered. The problem of uniform global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has a Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic semi-linear discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Moreover, the converse Lyapunov Theorem on Lyapunov (non-asymptotic) stability is proved for complex and real linear periodic discrete-time systems. Finally, examples of using the obtained results are presented.

In this paper, a data-driven distributed leader-follower iterative learning consensus tracking control approach is proposed for unknown repetitive nonlinear non-affine discrete-time multi-agent systems. The leader's command is only communicated to a subset of the following agents and each following agent exchanges information only with its neighbors under a directed graph. A local iterative learning consensus control protocol is designed using only local measurements communicated among neighboring agents without the availability of physical and structural information of each agent by virtue of the dynamic linearization method both on the agent and the ideal distributed learning controller along the iteration axis. The convergent consensus properties of the tracking errors along the iteration axis are rigorously established under the strongly connected iteration-independent and iteration-varying communication topologies. One example is provided to validate the effectiveness of the proposed iterative learning consensus control protocol.

In this article, an event-driven output feedback control approach is proposed for discrete-time systems with unknown mismatched disturbances. To estimate the unavailable states and disturbances, a reduced-order extended state functional observer is proposed, and by introducing an event-driven scheduler, the ZOH-based event-driven output feedback disturbance rejection controller is designed, and the stability and disturbance rejection analyses are performed. To further save the network resources, the predictive event-driven output feedback disturbance rejection control approach is proposed, and the stability and disturbance rejection analyses of the systems with predictive control are also conducted. It can be shown that the disturbances are compensated completely in output channels of the systems, and compared with the time-driven control schemes. And event-triggering frequency is greatly reduced with the proposed event-driven control methods. Finally, the effectiveness of the provided control approaches is demonstrated by numerical simulations.

This short paper is devoted to the development of multi-instant gain-scheduling stabilization of discrete-time Takagi-Sugeno fuzzy systems by developing a time-variant balanced matrix approach. Many of the reported advances have provided more and more relaxed results via choosing higher order dependent gain matrices, which will be a trouble in the case of real-time implementation. Therefore, a multi-instant gain-scheduling fuzzy state-feedback controller with different working modes is given to stabilize the closed-loop systems by updating the enabled pair of lower order gain matrices in cycle. For each possible working mode, the real-time situation information of the normalized fuzzy weighting functions can be fully considered by using a set of time-variant balanced matrices in accordance to certain rules and thus much freedom is introduced for proposing less conservative results. More importantly, our relaxed result is obtained without requiring higher order dependent gain matrices than the existing ones, i.e, its conservatism is reduced in a more meaningful way and thus it is more conducive to real-time implementation. Finally, both the effectiveness and the superiority of the proposed results are discussed and validated in the numerical section.

This paper concentrates on the $l_{2}-l_{\infty }$ filtering problem of discrete-time fuzzy semi-Markov jump nonlinear system. The random jumps among the studied system are governed by the discrete-time semi-Markov process. Therefore, the storage characteristics of the transition probability between systems are fully considered. To analyze $\sigma$ -mean-square stability of the filtering error system, a filter, which is mode-dependent, based on the discrete-time fuzzy semi-Markov jump model is constructed to estimate the state of the system. Thereafter, based on the Lyapunov stability theory and the discrete-time semi-Markov kernel concept, a set of criteria to ensure the are proposed. In addition, by using Takagi-Sugeno fuzzy model, the nonlinear problem is effectively solved. Ultimately, an illustrative example of a tunnel diode circuit and a numerical example effectively and practicability reveal the developed filtering strategy.

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

This paper investigates the H bumpless transfer control problem for a class of discrete-time switched interval type-2 (IT2) fuzzy systems subject to dwell-time constraint. We proposed a novel description of bumpless transfer performance for discrete-time switched IT2 fuzzy systems. With the aid of the dwell-time-dependent Lyapunov function (DTDLF) approach and a novel mixed switching strategy, sufficient conditions ensuring the asymptotic stability with an H bumpless transfer performance are derived. More incisively, the bumpless transfer performance in this paper is only required over the subintervals of the active interval, which is more general and relaxes the limitation of traditional bumpless transfer performance in the existing results. Besides, dwell-time-dependent bumpless transfer IT2 fuzzy controllers are designed in the form of LMIs. Finally, a tunnel diode circuit model is employed to demonstrate the potential and effectiveness of the derived theoretical results.

A novel multi-instant gain-scheduling scheme is proposed in order to further improve the state estimation performance of discrete-time Takagi-Sugeno fuzzy systems in this paper. Different from those existing methods, the enabled working pattern at each sampling instant can be determined in cycle according to utilize the updated information of adjacent normalized fuzzy weighting functions in depth, and then the featured time-varying free matrices are introduced for each working pattern, which can remove those existing constraints on traditional free matrices. Consequently, the conservatism can be reduced significantly and it does broaden the range of applications for observer-based fuzzy state estimation. Despite the fact that the quantity of the free matrices becomes much bigger than before, it needs to be pointed out that the actual computational complexity only increases by a small amount through depressing the number of cycles. Given that the developed designing process belongs to an offline computation, it is an acceptable tradeoff between the increasement of computational burden and the reduction of conservatism. In the end, the effectiveness of the developed method is illustrated through the detailed analysis of numerical simulations.

This article investigates the event-triggered output consensus problem for a class of unknown heterogeneous discrete-time linear multiagent systems in the presence of unmodeled dynamics. The agents have individual nominal dynamics with unknown parameters, and the unmodeled dynamics are in the form of multiplicative perturbations. A novel design framework is developed based on an event-triggered internal reference model and a distributed model reference adaptive controller. To deal with the heterogeneity of the multiagent system, the event-triggered internal reference model is designed to generate a virtual reference signal for each agent with a dynamic event-triggering mechanism being adopted to reduce the communication burden between neighboring agents. To handle the unknown parameters and unmodeled dynamics, the robust model reference adaptive controller is then designed to follow the generated virtual reference signal. It is shown that if the unmodeled dynamics satisfy certain conditions, then the boundedness of all the signals and variables in the closed-loop system and convergence of consensus errors to a residual set are guaranteed. Moreover, the consensus errors will converge to zero asymptotically in the absence of unmodeled dynamics. Compared with existing related works, the proposed framework is able to deal with the agents with individual unknown nominal dynamics and unmodeled dynamics. Moreover, the proposed framework is fully distributed in the sense that no knowledge of any global information is needed. Finally, the performance of the proposed method is validated by examples.

This paper is concerned with H control problem for discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems with event-triggering scheme (ETS) and denial-of-service (DoS) attacks. Aperiodic DoS characterized by duration and frequency is introduced. In the light of DoS attacks and event-triggered fuzzy controller, the switched fuzzy Markov jump closed-loop system is established. Particularly, in order to address the issue of mismatched behavior between membership functions of fuzzy system and fuzzy controller, a novel ETS consisting of membership functions is developed. Then with the help of multiple Lyapunov function method and iterative technique, some sufficient conditions are provided to ensure the H performance of the resulting closed-loop system. Subsequently, the explicit parameter design of controller and ETS are provided. Finally, an example is employed to verify the validity of the proposed theoretical method.

In real world applications, sampled-data systems are often subject to undesirable physical constraints, which results in noisy sampling intervals that fluctuate around an ideal sampling period based on certain probability distribution. In the presence of noisy sampling intervals, this article is concerned with the stabilization problem for a class of sampled-data systems with successive packet dropouts. First, the relationship between two adjacent update times of zero-order hold is established. Then, by discrete-time approach, an equivalent discrete-time stochastic system is introduced. By the law of total expectation, together with confluent Vandermonde matrix, convolution formula and Kronecker product operation, the mathematical expectation of a product of three matrices including the system matrix and its transpose is calculated. Based on this, a stabilization controller is designed such that the closed-loop system is stochastically stable. Finally, an illustrative example is provided to verify the effectiveness of the proposed design approach.

This article investigates the design of the ℓ₂-ℓ∞ dynamic output-feedback (DOF) controller for interval type-2 (IT2) T-S fuzzy systems with state delay. For nonlinear systems, the IT2 fuzzy model is an efficient modeling method which can better express uncertainties than the (type-1) fuzzy model. In addition, state delay is also a general factor that affects system performance. After analyzing the stability of the system, based on convex linearization and the projection theorem, this article proposes a delay-dependent output-feedback controller design method. The IT2 membership functions (MFs) of the fuzzy controller are chosen to be different from those of the model so as to increase the freedom of controller selection. A membership-function-dependent (MFD) method based on the staircase MFs is applied to relax the stability analysis results. Finally, a numerical simulation example is given to illustrate the effectiveness of the results.

This paper presents a novel event-triggered near-optimal control (ETNOC) method for discrete-time (DT) constrained nonlinear systems. First, the tracking error system is constructed to convert the tracking control problem to the regulation problem. By introducing the tracking error system, the asymmetric control constraints design for the original constrained system can be converted to the symmetric control constraints design for the tracking error system. Second, a novel triggering condition is developed using the time-triggered optimal value function and control law. It is proven that the closed-loop system (CLS) is asymptotically stable under the developed ETNOC method, and there exists a predetermined upper bound for the real performance index. Then, to implement the developed ETNOC method, a parallel control approach with neural networks (NNs) and adaptive dynamic programming (ADP) techniques is proposed to predict the next state of the system and obtain the optimal value function and control law. The stability analysis of the CLS is provided in the consideration of the estimation errors of the NN weights and state. Finally, the effectiveness of the developed ETNOC method is validated by an application to a boiler-turbine system (BTS).

Considering disturbances, noise, and sensor faults, this paper investigates interval estimation for discrete-time Takagi-Sugeno fuzzy systems. To obtain precise estimation results and attenuate disturbances and noise in the system simultaneously, we integrate robust observers based on the H technique and reachability analysis. Two novel observer gain computation methods are proposed for different purposes. The time-invariant method relaxes the original design conditions by transforming the parameterized linear matrix inequality into a series of linear matrix inequalities to increase computational speed, while the time-varying method employs the parameterized linear matrix inequality directly and conducts calculation online. Furthermore, reachable set representations for error dynamics are formulated by making use of both time-invariant observer gain and time-varying observer gain. Two comparative numerical simulation examples are studied to illustrate the effectiveness and superiority of the developed methods.

This paper proposes a discrete-time differentiation algorithm of arbitrary order inspired by the continuous-time uniform robust exact differentiator and the continuous-time arbitrary order robust exact differentiator. As the well-known explicit Euler method is not suitable for discretizing algorithms with the fixed-time convergence property, a semi-implicit approach is proposed. The discrete-time differentiators of order 2 and 3 are studied in detail and it is proven that the estimation errors vanish independent of their initial condition in the unperturbed case. In the presence of perturbations it is shown that the origin of the estimation errors is surrounded by an attractive invariant set. Furthermore the performance of the proposed algorithm is evaluated via simulation studies.

With the rapid advancement of digital processors, filters have been commonly implemented using microcomputers. In this study, a low-cost and compact Arduino Uno development board was used to realize digital lead and lag compensators. Arduino boards are very affordable. Consequently, they were investigated to see if they were capable of preserving the frequency response of continuous-time compensators. The experiments required a set of equipment including a function generator, an Arduino Uno development board, a PC-based oscilloscope, and a laptop. The signal frequency was varied from 0 to 500 Hz. Two discretization methods were employed, namely bilinear transformation and matched pole-zero mapping. The results showed that an Arduino Uno board can be utilized to implement lead and lag compensators to some extent. The discrete-time compensator preserved the capability of filtering out certain frequencies. The change in DC gain was negligible, however, there was a significant difference in the cut-off frequency and transient slope. For both discretization methods, the frequency responses at high frequency experienced a rippling profile.

We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the underlying graph of the model. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n 2k+1 T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs, i.e., with at most linear number of edges. We prove λ + 1 cops suffice to capture the robber in any underlying graph with n − 1 + λ edges. Further, we define a family of underlying graphs with n−1+λ edges where λ−1 cops are necessary (and sufficient) for capture.

The current loop is the key to realizing high- precision permanent magnet synchronous motor (PMSM) drives. However,the performance of the current loop is deteriorated by the dc and ac disturbances. To deal with the problem,this paper proposes a discrete-time repetitive control-based active disturbance rejection control (DRC-ADRC) for the current loop. The DRC is embedded in the control law of the ADRC and operates in parallel with the discrete-time extended state observer (DESO),which is the core of the ADRC. The DRC is designed to compensate for the ac disturbance,while the DESO is designed to suppress the dc disturbance. The stability and anti-disturbance capability of the studied scheme are analyzed theoretically in the discrete-time domain,which can guide the tuning of control parameters. Compared with the existing ADRC-based PMSM control schemes,the proposed DRC-ADRC can suppress the dc and ac disturbances simultaneously,thereby improving dynamic- and steady-state performance of the current loop. Finally,the effectiveness of the studied DRC-ADRC is validated on a 4.4-kW PMSM drive platform.