Discrete-time Systems Research Articles

Boundary Value Problems for Linear and Nonlinear Discrete Systems: Solvability Conditions and Input-to-State Stability

This paper investigates boundary value problems (BVPs) for both linear and nonlinear discrete systems with a focus on input-to-state stability (ISS). We begin by analyzing homogeneous and nonhomogeneous linear systems, deriving explicit solution formulas using mathematical induction. Solvability conditions for these systems are established, providing necessary and sufficient criteria for the existence of solutions. The study is then extended to nonlinear discrete systems, where perturbation terms are introduced, and equivalent transformed BVPs are derived. By applying solvability conditions, we analyze the transition from nonlinear to linear cases as perturbations approach zero. The results contribute to the understanding of ISS properties in discrete-time dynamical systems and serve as a foundation for stability analysis and numerical methods in solving BVPs in discrete settings.

Difference flatness of discrete-time linear time-delay systems and transformation to fully actuated systems

This paper investigates the difference flatness of discrete-time linear time-delay systems (TDSs). Initially, by employing matrix augmentation techniques and model reduction methods, the discrete-time linear TDSs can be transformed into the discrete-time linear delay-free systems while preserving controllability equivalence. Subsequently, a coprime factorisation approach for the transfer function matrix of discrete-time linear delay-free systems is utilised to construct the flat output of the discrete-time linear TDSs. Based on this, the discrete-time linear TDSs can be equivalently transformed into the discrete-time fully actuated system (FAS) with the constructed flat output as the generalised state, and the pole assignment problem of discrete-time TDSs can be directly addressed. Numerical examples demonstrates the effectiveness of the proposed approach.

Resilience modeling for discrete-time multi-state systems based on aggregated Markov chains

Resilience modeling for discrete-time multi-state systems based on aggregated Markov chains

Data-driven event-triggered control of discrete-time nonlinear systems under mismatched input quantization and disturbance

Data-driven event-triggered control of discrete-time nonlinear systems under mismatched input quantization and disturbance

Adaptive model predictive control with one free control move for uncertain discrete-time linear systems with bounded disturbance

Adaptive model predictive control with one free control move for uncertain discrete-time linear systems with bounded disturbance

Event-triggered stabilization of discrete-time stochastic time-delay systems and its application to multi-agent systems consensus

Event-triggered stabilization of discrete-time stochastic time-delay systems and its application to multi-agent systems consensus

Privacy-preserving average consensus for second-order discrete-time multi-agent systems

Privacy-preserving average consensus for second-order discrete-time multi-agent systems

A Data-Driven Predictive Control Scheme for Nonlinear Discrete-Time Systems.

This article provides a new methodology to design a novel predictive control (PC) scheme for unknown nonlinear discrete-time systems, by deeply exploiting future ideal controllers and the dynamic linearization (DL) technique. The control input increment vector can be linearly parameterized with the time-varying control gain vector. The PC law is obtained by directly optimizing the control gain vector with the least square method. The system outputs are predicted through the parameterized PC law and the DL data model of the controlled system. The proposed PC scheme is data-driven, that is, it does not depend on the system dynamic model and the control gain vector is adaptively optimized by using only the measured input/output data. The monotonic convergency of the proposed PC scheme is theoretically guaranteed, and its effectiveness is validated by two illustrative examples, i.e., a complicated nonlinear system and a linear time-invariant system.

Estimation and output feedback stabilization for switched linear discrete-time systems with delayed-outputs

Estimation and output feedback stabilization for switched linear discrete-time systems with delayed-outputs

Efficient iterative learning model predictive control for uncertain nonlinear discrete-time systems

Efficient iterative learning model predictive control for uncertain nonlinear discrete-time systems

Discrete-Time Fractional-Order Sliding Mode Attitude Control of Multi-Spacecraft Systems Based on the Fully Actuated System Approach

In practical applications, most systems operate based on digital signals obtained through sampling. Applying fractional-order control to spacecraft attitude control is meaningful for achieving better performance, especially in the coordination of the multi-spacecraft attitude system. In this paper, a discrete-time fractional-order sliding mode attitude control problem is studied for multi-spacecraft systems based on the fully actuated system approach. Firstly, a discrete-time disturbance observer based on the fractional-order theory is constructed to estimate the disturbance. Secondly, a discrete-time fractional-order sliding mode controller is designed by combining the transformed fully actuated discrete-time system and the disturbance observer. Subsequently, every spacecraft can track the desired attitude under the designed controller. Finally, the simulation results show that the developed control method achieves faster convergence, smaller overshoot, and higher control accuracy.

Output Regulation Based on Zero-Sum Game for Discrete-Time System Driven by Exogenous Signal

Output Regulation Based on Zero-Sum Game for Discrete-Time System Driven by Exogenous Signal

Inverse reinforcement learning through expert imitation for discrete-time multi-player noncooperative games

This paper employs a model-free inverse reinforcement learning approach to address expert trajectory imitation control problem in linear discrete-time systems involving multi-player noncooperative games. Specifically, within an expert-learner framework, the learner reconstructs a cost function solely based on the expert's trajectory and its own input-output data, producing the same optimal feedback gain as the expert and thus imitating the expert's optimal response. The study develops an online off-policy inverse reinforcement learning algorithm without requiring knowledge of the system dynamics or the expert's control gains. Furthermore, a detailed convergence analysis of the algorithm is conducted. The results demonstrate that, with the inclusion of exploration noise to ensure persistent excitation, the algorithm guarantees an unbiased solution. Moreover, when the control gain of the learner agent reaches that of the expert agent, the cost function is not unique. Finally, the effectiveness of the algorithm is validated through simulation examples.

Event-Triggered Optimal Bipartite Consensus Control for Constrained Multiagent Systems via Internal Reinforce Q-Learning.

In this article, the event-triggered optimal bipartite consensus control problem is investigated for second-order discrete-time multiagent systems (MASs) with control input saturation and unknown system models. First, an instant reward signal with nonquadratic functions dealing with the control input saturation is defined, based on which a novel internal reinforce reward function is defined to facilitates agents to learn more intrinsic information from the local environment. Then, a novel event-triggered internal reinforce Q-learning (IrQL) algorithm is introduced. In contrast to conventional time-triggering Q-learning methods, the proposed event-triggered IrQL algorithm can not only fully exploit environment but also save the data computation and transmission resources. Based on elegant functional analysis techniques and Lyapunov stability theory, the internal reinforce reward function can be proved to be bounded and the tracking error dynamics of MASs are ensured asymptotic stability under the proposed event-triggered control policies. Then, data-driven reinforce-critic-actor neural networks are constructed to implement the event-triggered IrQL algorithm online with the proof of convergence. Finally, simulation examples show the validity and better performance over existing researches.

Inverse reinforcement learning for discrete-time nonlinear systems: applications in circuits and systems

This article proposes a novel inverse reinforcement learning (RL) algorithm to address the inverse optimal control (IOC) problem in discrete-time nonlinear circuits and systems with unknown performance function. We consider an expert-learner imitation structure, and adopt the learner to mimic the expert’s behaviour trajectories. Initially, a model-based value iteration inverse RL algorithm is developed, enabling the learner to reconstruct the unknown performance function utilising the observed demonstration behaviour trajectories from the expert. The algorithm includes a performance function learning stage derived from IOC and a control policy learning stage derived from optimal control. Subsequently, an actor-critic-based inverse RL algorithm is further implemented to obviate the need for information about the system dynamics for both the learner and expert. Finally, theoretical analysis is provided, and a boost converter circuit is used as an example to demonstrate the effectiveness of the proposed control algorithms.

Generalized Derivatives of Nonsmooth Discrete-Time Systems

Generalized Derivatives of Nonsmooth Discrete-Time Systems

Solvability, exact solution and momentum acceleration gradient-based iterative algorithm for general matrix equation $$ AXB+C\overline{X}D+EX^TF+GX^*H=J $$ and studying its applications in discrete-time antilinear systems and color image restoration

Solvability, exact solution and momentum acceleration gradient-based iterative algorithm for general matrix equation $$ AXB+C\overline{X}D+EX^TF+GX^*H=J $$ and studying its applications in discrete-time antilinear systems and color image restoration

Deterministic many-body dynamics with multifractal response

Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of nonergodic behavior in a many-body discrete-time dynamical system, specifically a multiperiodic response with multifractal distribution of equilibrium spectral weights at all rational frequencies. This phenomenon is observed in the momentum-conserving variant of the newly introduced class of the so-called parity check reversible cellular automata, which we define with respect to an arbitrary bipartite lattice. Although the models display strong fragmentation of phase space of configurations, we demonstrate that the effect qualitatively persists within individual fragmented sectors, and even individual typical many-body trajectories. We provide detailed numerical analysis of examples on 2D (honeycomb, square) and 3D (cubic) lattices. Published by the American Physical Society 2025

Neural-network-based accelerated safe Q-learning for optimal control of discrete-time nonlinear systems with state constraints.

Neural-network-based accelerated safe Q-learning for optimal control of discrete-time nonlinear systems with state constraints.

Self-triggered neural tracking control for discrete-time nonlinear systems via adaptive critic learning.

Self-triggered neural tracking control for discrete-time nonlinear systems via adaptive critic learning.