Discrete-time Interconnected Systems Research Articles

Persistence Analysis of Discrete-Time Interconnected Positive Systems and its Application to Mobile Robot Formation

This paper addresses the analysis of discrete-time interconnected systems where each subsystem is stable and positive. Admissibility and persistence notions are derived similar to the continuous-time case and a condition for enforcing persistence is derived for the case when all subsystems are single-input single output. Results are applied on numerical examples including the formation control of mobile robots.

Finite-time fault detection filter design for discrete-time interconnected systems with average dwell time

In this paper, we present an approach to finite-time robust fault detection filter design for interconnected systems with disconnected interconnections among these subsystems. Taking various disconnected interconnections into account, a switched scheme is proposed to analysis these complex cases. By modeling these cases of disconnections into independent subsystems, a switching signal is introduced to specify which subsystem is activated. In the aid of the average dwell time method, sufficient conditions on existence of the desired filter are derived in term of linear matrices inequalities, which guarantee the augmented system is finite-time boundedness and achieve the H∞ performance. A numerical example is used to illustrate the effectiveness of the proposed approach.

Linear Hybrid Deterministic Dynamic Modeling for Time-to-Event Processes: State and Parameter Estimations

In this work, we initiate an innovative alternative modeling approach for time-to-event dynamic processes. The proposed approach is composed of the following basic components: (1) development of continuous-time state of dynamic process, (2) introduction of discrete-time dynamic intervention process, (3) formulation of continuous and discrete-time interconnected dynamic system, (4) utilizing Euler-type discretized schemes, and (5) introduction of conceptual and computational state and parameter estimation procedures. The presented approach is motivated by state and parameter estimation of time-to-event processes in biological, chemical, engineering, epidemiological, medical, military, multiple-markets and social dynamic processes under the influence of discrete-time intervention processes. The role and scope of our approach is exhibited by presenting several well-known hazard/risk rate and survival function estimates as special cases. Moreover, conceptual algorithms are illustrated by time-series data sets under the influence of intervention processes.

이산시간 상호결합 퍼지 시스템을 위한 관측기 기반 분산 퍼지 제어기 설계

In this paper, an observer-based decentralized fuzzy controller is designed for discrete-time interconnected fuzzy systems. Based on the fuzzy subsystem of the interconnected fuzzy system, the observer-based decentralized fuzzy controller is considered. By using the fuzzy subsystem and the observer-based decentralized fuzzy controller, the closed-loop system is obtained. From the closed-loop system, the stability condition with the maximum interconnection bound is developed, and its sufficient condition is represented as the linear matrix inequality (LMI). Finally, the numerical example is provided to verify the effectiveness of the proposed technique.

Design and Implementation of Feedback Resonance Compensator in Hard Disk Drive Servo System: A Mixed Passivity, Negative-Imaginary and Small-Gain Approach in Discrete Time

This paper presents a feedback resonance compensator designed in a simple and yet efficient way to suppress the effects of resonant modes of voice coil motor actuator used in hard disk drive (HDD) servo system. A velocity feedback controller is chosen as the feedback resonance compensator. Resonant modes of the actuator prohibit bandwidth to be pushed to higher frequencies and it causes large oscillations to the closed-loop system response. Therefore, effective compensation of mechanical resonant modes is one of the design challenges in HDD servomechanism. The proposed design is based on a mixed passivity, negative-imaginary and small-gain approach in discrete time which results in a robust stable controller. Firstly, stability of discrete-time interconnected system is analyzed using mixed passivity, negative-imaginary and small-gain properties. These results are analogous to previously established continuous-time case. Nowadays most of the control design is done in discrete time. Hence, this paper provides a base for discretization of mixed system with passivity, negative-imaginary and small-gain properties. Secondly, a velocity feedback controller for resonance compensation is designed using this mixed approach. Simulation and experimental results substantiate the effectiveness of the controller.

A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems

This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem.

Optimal Control Design Under Limited Model Information for Discrete-Time Linear Systems With Stochastically-Varying Parameters

The value of plant model information available in the control design process is discussed. We design optimal state-feedback controllers for interconnected discrete-time linear systems with stochastically-varying parameters. The parameters are assumed to be independently and identically distributed random variables in time. The design of each controller relies only on (i) exact local plant model information and (ii) statistical beliefs about the model of the rest of the system. We consider both finite-horizon and infinite-horizon quadratic cost functions. The optimal state-feedback controller is derived in both cases. The optimal controller is shown to be linear in the state and to depend on the model parameters and their statistics in a particular way. Furthermore, we study the value of model information in optimal control design using the performance degradation ratio which is defined as the supremum (over all possible initial conditions) of the ratio of the cost of the optimal controller with limited model information scaled by the cost of the optimal controller with full model information. An upper bound for the performance degradation ratio is presented for the case of fully-actuated subsystems. Comparisons are made between designs based on limited, statistical, and full model information. Throughout the paper, we use a power network example to illustrate concepts and results.

Positively Invariant Families of Sets for Interconnected and Time-Delay Discrete-Time Systems

Methods for the construction of positively invariant (PI) sets, both for interconnected and time-delay systems, either suffer from computational intractability or come with considerable conservatism, with respect to their ability to provide a nontrivial PI set as well as their ability to recover or even approximate the maximal positively invariant (mPI) set. Therefore, we apply the notion of PI families of sets to interconnected and time-delay systems. We show that for such systems, this notion enjoys computational practicability and, at the same time, is nonconservative, both in terms of the type of sets it produces and its ability to approximate and recover the mPI set. Moreover, this technique also provides a tractable stability analysis tool. In this paper, for both interconnected and time-delay systems, the properties of PI families of sets are analyzed, their use is illustrated via several examples, and their construction via convex optimization algorithms is discussed.

Integral Input-to-State Stability for Interconnected Discrete-Time Systems

In this paper, we investigate integral input-to-state stability for interconnected discrete-time systems. The system under consideration contains two subsystems which are connected in a feedback structure. We construct a Lyapunov function for the whole system through the nonlinearly-weighted sum of Lyapunov functions of individual subsystems. We consider two cases in which we assume that one of subsystems is integral input-to-state stable and the other is either input-to-state stable or only integral input-to-state stable.

Decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems

This paper presents a novel approach to address the decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems. The overall system is composed of a number of discrete-time interconnected nonlinear subsystems at the presence of multiple faults occurring at unknown time-instants. In order to deal with the unknown interconnection effects and changes in model dynamics due to multiple faults, both passive and active fault tolerant control design are considered. In the Active fault tolerant case an online approximation algorithm is applied to estimate the unknown interconnection effects and changes in model dynamics due to multiple faults. Besides, the decentralized control strategy is implemented for each subsystem with the model predictive control algorithm subject to some constraints. It is showed that the proposed method guarantees input-to-state stability characterization for both local subsystems and the global system under some predetermined assumptions. The simulation results are exploited to illustrate the applicability of the proposed method.

Stability analysis of spatially interconnected discrete-time systems with random delays and structured uncertainties

In this paper, robust stability analysis of spatially interconnected systems with random delays as well as structured uncertainties in discrete-time domain is presented. The random delays are represented as a series of Markovian jumping parameters with some transition probability. A sufficient condition to guarantee well-posedness, stochastic stability, and H∞ performance of the spatially interconnected systems is established. Through numerical simulations, the validity of the proposed approach is illustrated.

Resilient decentralized filtering of interconnected discrete-time systems

The objective of this paper is to propose new tools for robust and resilient filter design of a class of interconnected discrete-time systems with uncertain function of nonlinear perturbations by exploiting the decentralized information structure constraint. We seek to establish complete LMI-based procedures for linear filtering by basing all the computations at the subsystem level. The robustness property of filter design is assessed in terms of ℓ∞ performance while the resilience property is evaluated in face of additive gain variations that reflect the imprecision in filter implementation. By a suitable convex analysis, it is shown that both design problems can be formulated as convex minimization problem over linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the effectiveness of the developed design methods.

Decentralised - filtering of networked control systems: a jump system approach

We consider the problem of decentralised estimation of discrete-time interconnected systems with local estimators communicating with their subsystems over lossy communication channels. Assuming that the packet losses follow the Gilbert–Elliot model, the networked estimation problem can be formulated into a Markovian jump linear system framework. Modelling subsystem interactions as sum quadratic constrained uncertainties, we design mode-dependent decentralised -estimators that robustly stabilise the estimator system and guarantee a given disturbance attenuation level. The estimation gains are derived with necessary and sufficient rank-constrained linear matrix inequality conditions. Results are also provided for local mode-dependent estimators. Estimator synthesis is done using a cone-complementarity linearisation algorithm for the rank-constraints. The results are illustrated via an example.

Stability Analysis of Discrete-time Interconnected Positive Systems using Weighted l1-induced Norm

Stability Analysis of Discrete-time Interconnected Positive Systems using Weighted l1-induced Norm

Stabilization of Interconnected Discrete Systems with Quantization and Overflow Nonlinearities

In this paper, we address the problem of decentralized feedback control design for a class of linear interconnected discrete-time systems subject to quantization and overflow nonlinearities and unknown-but-bounded couplings. A decentralized quantized state feedback controller is designed at the subsystem level to render the closed-loop system asymptotically stable. When the local output measurements are available, a decentralized output-feedback quantized controller is developed attain similar asymptotic stability and guaranteed performance of the closed-loop quantized system. Several special cases of interest are derived and simulation results are provided.

Decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays

This article considers the decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H ∞ filter is designed for each subsystem. It is shown that the stability with H ∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.

Reliable decentralized control of interconnected discrete delay systems

In this paper, we study the problem of designing decentralized reliable state-feedback controllers under a class of actuator failures for a class of linear interconnected discrete-time systems having subsystem and coupling time delays. The failures take into consideration possible outages or partial failures in every single actuator. A decentralized stabilizing reliable feedback controller is derived at the subsystem level to give the closed-loop subsystem delay-dependent robust internal stability with a γ-level ℓ2-gain. The results developed are tested on a representative water quality control example.

Decentralized Optimal Control of a Class of Interconnected Nonlinear Discrete-Time Systems by Using Online Hamilton-Jacobi-Bellman Formulation

In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton-Jacobi-Bellman equation forward-in-time for the decentralized near optimal regulation of a class of nonlinear interconnected discrete-time systems with unknown internal subsystem and interconnection dynamics, while the input gain matrix is considered known. Even though the unknown interconnection terms are considered weak and functions of the entire state vector, the decentralized control is attempted under the assumption that only the local state vector is measurable. The decentralized nearly optimal controller design for each subsystem consists of two neural networks (NNs), an action NN that is aimed to provide a nearly optimal control signal, and a critic NN which evaluates the performance of the overall system. All NN parameters are tuned online for both the NNs. By using Lyapunov techniques it is shown that all subsystems signals are uniformly ultimately bounded and that the synthesized subsystems inputs approach their corresponding nearly optimal control inputs with bounded error. Simulation results are included to show the effectiveness of the approach.

Quantised feedback stabilisation of interconnected discrete-delay systems

The authors investigate in this study the problem of designing decentralised quantised ℋ∞ feedback control for a class of linear interconnected discrete-time systems. The system has unknown-but-bounded couplings and interval delays. The quantiser has an arbitrary form that satisfies a quadratic inequality constraint. A linear matrix inequality (LMI)-based method using a decentralised quantised output-feedback controller is designed at the subsystem level to render the closed-loop system delay dependent asymptotically stable with guaranteed γ-level. To show the generality of the authors' approach, it is established that several cases of interest are readily derived as special cases. The authors illustrate the theoretical developments by numerical simulations.

Delay-dependent stability of discrete-time interconnected systems

This paper studies the delay-dependent stability problem of discrete-time interconnected systems with time-varying delays. By using vector Lyapunov function approach and linear matrix inequalities (LMIs), new stability conditions are derived. These results proposed in this paper are all at subsystems level. After comparing with the existing results, it is shown that these conditions are less conservative. A numerical example is presented to demonstrate the effectiveness of the results.