A framework for discrete-time models of continuous-time systems

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.

Construction of discrete-time models for port-controlled Hamiltonian systems with applications

Nonlinear acoustic systems are often described by means of nonlinear maps which act as instantaneous constraints on the solutions of a system of linear differential equations. This description leads to discrete-time models exhibiting non-computable loops. This paper presents a solution to this computability problem by means of geometrical transformation of the nonlinearities and algebraic transformation of the time-dependent equations. The proposed leads to stable and accurate simulations even at relatively low sampling rates.

This work aims to propose a high-order fully actuated system (FAS) model for discrete-time strict-feedback systems with nonuniform dimensions. In most of existing works, the authors only consider strict-feedback systems with uniform dimension, i.e. all subsystems have the same dimension. In contrast, we assume that the subsystems may have different or nonidentical dimensions. In particular, the dimensions are assumed to be increasing. Both step-forward and step-backward FAS models for discrete-time strict-feedback systems with nonuniform dimensions are given, based on which the exponentially stabilised controllers can be directly obtained. We consider not only first-order strict-feedback systems but also second-order case.

The model of NCS(Networked Control Systems) with dynamic output feedback controllers is presented when the network-induced random time-varying delays are bounded and the upper bound of which is longer than one sampling period. Based on this, this paper discretizes the model of continuous-time systems and applies augmented state-space method to it, and then establishes a discrete-time jump system model governed by a finite state Markov process. Appling interior-point algorithm to design stabilizing controllers for the system, this paper proposed an approach to get the feasible initial solution. Theoretical analysis and simulation on a cart and inverted pendulum with random time delay show that the dynamic output feedback controllers can make the system stable.

This paper deals with an alterative definition of continuous-time models of discrete-time causal systems in a new approach to system theory, namely with the definition of continuous-time stochastic systems. Despite the general system theory has been intensively studied since 1960s, none of the developed theories has been fully accepted by professional community as sufficiently comprehensive up to now. The alternative system theory is based on quite new system paradigms consequent upon attentive observations and results in an axiomatic system theory with correctly and unambiguously defined notions.

Gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity

The discrete-time mathematical models for nonlinear systems with delayed control and measurement are established. Based on a linearization and a model transformation, the nonlinear system with delays is transformed to a formal nondelay system. Then the optimal control law with the state feedback term, the disturbance feedforward term, and the control memory term is derived from a discrete Riccati equation and a Stein equation. A high-gain observer is constructed such that the feedforward control law is physically realizable. Simulation results demonstrate the effectiveness of the optimal control law.

Switching funnel transformation function-based discrete-time sliding-mode control for servo systems with time-varying external disturbances

A discrete-time multi-server queueing model for opportunistic spectrum access systems

Performance optimization plays an important role in both applied and theoretical research. Recent research provides a unified view, with which the main results in many different areas can be derived or explained using two foundational sensitivities equations. With this approach, event-based optimization has been proposed to overcome the difficulties that the traditional approaches could not solve. However, most of the previous results are on discrete-time Markov systems. In the real world, many practical problems require the model of the continuous-time Markov systems. This paper focuses on extending the event-based optimization approach to the continuous-time Markov systems. As any Markov process can be viewed as a GSMP, we first give a standard description on the GSMP model and then slightly modify it to fit our problem setting. Compared with the event-based optimization with the discrete-time model, in the continuous-time case, in addition to control the probabilities of the controllable events, we need also control the rates of the triggerable events. The final result keeps as intuitive as that for the discrete-time Markov systems, and provides a natural framework for studying the event-based optimization problems.

This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of the control input onto the nullspace of the linearized constraints. We derive a fully constraint-compliant feedforward-feedback control update rule, for which we can solve efficiently with Riccati-style difference equations. We assume that the relative degree of all constraints in the discrete-time system model is equal to one, which often holds for robotics problems employing rigid-body dynamic models. Simulation examples, including a 6 DoF robotic arm, are given to validate and illustrate the performance of the method.

Dynamic output-feedback wide area damping control of HVDC transmission considering signal time-varying delay for stability enhancement of interconnected power systems

CONFIDENCE BOUNDS FOR FREQUENCY RESPONSE FUNCTIONS FROM TIME SERIES MODELS

This paper presents an optimized maneuver planning method for onboard gyro calibration in spacecraft, utilizing a Kalman filter-based approach. The calibration process focuses on estimating gyro scale factor errors and misalignments, which are critical for accurate attitude control. By integrating quaternion kinematics and gyro modeling, a discrete-time system model is developed, incorporating measurements from a star tracker to enhance estimation accuracy. An optimized sinusoidal maneuver trajectory is proposed to ensure the observability of gyro parameters, with the optimization aimed at minimizing estimation errors and improving convergence speed. Simulation results demonstrate that the optimized maneuver significantly reduces convergence time while maintaining high accuracy in estimating gyro biases, scale factors, and misalignments. The study highlights the importance of precise gyro calibration in spacecraft navigation and provides a robust framework for future applications in space missions.