Discrete-time System Subject Research Articles

Data-driven integral sliding mode predictive control with optimal disturbance observer

In this paper, a novel data-driven integral sliding mode predictive control algorithm based on an optimal disturbance observer (DDISMPC-ODO) is proposed for a class of nonlinear discrete-time systems (NDTS) subject to external disturbances. The designed optimal disturbance observer realizes the precise observation of the lumped disturbance, thus ameliorating the accuracy of the controller and weakening problems with chattering. In this work, a robust pseudo-partial derivative (PPD) estimation algorithm is introduced, which not only improves the system performance, but also facilitates theoretical proof of parameter estimation and tracking accuracy. The convergence of the PPD estimation error and disturbance observation error is proved. It is also proved that the accuracy of the disturbance observation error can converge to O(T3) and then the magnitude of the sliding variable and the tracking error are also reduced to O(T3) respectively. Finally, the effectiveness of the proposed method is demonstrated by a simulation example and an experiment.

On positively invariant polyhedrons for discrete-time positive linear systems

In this paper, necessary and sufficient conditions for the polyhedron set to be a positively invariant polyhedron of a discrete-time positive linear system subject to external disturbances are established. By solving a set of inequalities, which is also a linear programming, necessary and sufficient conditions for the existence of positive invariant polyhedra for discrete-time positive linear systems are proposed, and the relationship between Lyapunov stability and positively invariant polyhedron is also investigated, numerical examples illustrate our results.

Semi-global Weighted Output Average Tracking of Discrete-time Heterogeneous Multi-agent Systems Subject to Input Saturation and External Disturbances

In this paper, we revisit the semi-global weighted output average tracking problem for a discrete-time multi-agent system subject to input saturation and external disturbances. The multi-agent system consists of multiple heterogeneous linear systems as leader agents and multiple heterogeneous linear systems as follower agents. A distributed state observer is designed for each follower agent that estimates the state of each leader agent. With these estimates, we design low-gain-based distributed control protocols. It is shown that, for any bounded set of the initial conditions, these control protocols cause the follower agents to track the weighted average of the outputs of the leader agents as long as the value of the low gain parameter is tuned sufficiently small. Simulation results illustrate the validity of the theoretical results.

Asymptotic Tracking of Discrete-Time Systems Subject to Uniform Output Quantization

This letter explores the internal model principle in order to achieve asymptotic tracking of discrete-time systems subject to output quantization. It is shown that, by artificially quantizing the reference signal, asymptotic tracking can be achieved for a class of systems and references: discrete-time positive real systems, and persistent references in the form of sums of sinusoids. Given the importance of discrete time positive real functions, a systematic way of constructing them is also provided as a contribution. The resulting controller relies on frequency domain tools and may be designed by traditional linear techniques.

Backstepping Control for a Class of Nonlinear Discrete-Time Systems Subject to Multisource Disturbances and Actuator Saturation.

In this article, the backstepping control scheme is designed for a class of systems with multisource disturbances, actuator saturation, and nonlinearities in the domain of discrete time. To address the multisource disturbances, we put forward a novel discrete-time hybrid observer, which can deal with both modeled and unmodeled disturbances. In virtue of the radial basis function neural networks, the unknown nonlinearities are approximated. In addition, the anti-windup technique is adopted to cope with the actuator saturation phenomenon, which is pervasive in engineering practice. Bearing all the adopted mechanisms in mind, the composite control strategy is designed in a backstepping manner. Sufficient conditions are established to guarantee that the states of the system ultimately converge to a small range with linear matrix inequalities. Finally, the effectiveness of the presented methodology is verified for the spacecraft attitude system.

Dynamic event-triggered H∞ filtering for discrete-time singular networked control system subject to cyberattacks

This paper investigates the event-triggered filtering problem for the discrete-time singular networked control systems (DSNCS) with random cyberattacks. To more effectively utilize the limited network resource, a new dynamic event-triggered mechanism is proposed, which can effectively reduce network information transmission and save bandwidth on the premise of ensuring system performance. By considering the effect of the event-triggered mechanism and two types of cyberattacks, the filtering error system model has been constructed. Two independent random variables obeying the Bernoulli distribution are introduced to describe the two types of cyberattacks. Sufficient conditions that can guarantee the admissibility of the filtering error system have been developed with Lyapunov stability theory and LMIs techniques. Moreover, the co-design method is present in terms of LMIs to derive the parameters of dynamic event-triggered mechanism and the designed [Formula: see text] filter synchronously. Finally, an illustrative example is employed to verify the usefulness of the proposed method.

Robust observer-based sliding mode [formula omitted] control for stochastic Markovian jump systems subject to packet losses

This paper studies the robust observer-based sliding mode H∞ control issue for discrete-time stochastic Markovian jumping systems (MJSs) subject to packet losses (PLs). Here, a state variable observer of an initial system is designed to estimate the state and a series of Bernoulli random variables is utilized to model the PLs, whose occurrence probability is allowed to be imprecise. Then, a linear switching function is constructed based on the estimated state space. The aim of our paper is to design an observer-based sliding mode H∞ control strategy such that, the stochastic stability conditions with prescribed H∞ performance are established for augmented MJSs under the PLs with imprecise occurrence probability, which is composed of the sliding mode dynamics and the error system. The linear sliding surface can be determined by solving some linear matrix inequalities (LMIs). In addition, by proposing an improved reaching condition, the desired robust observer-based H∞ controller is designed in discrete-time setting to drive the system state from any initial one onto the designated sliding surface. Finally, the usefulness of observer-based H∞ control method is demonstrated via some numerical simulations.

Robust networked ILC for switched nonlinear discrete systems with non-repetitive uncertainties and random data dropouts

In this article, a robust networked iterative learning control (ILC) method is presented for switched nonlinear discrete-time systems (NDTS) subject to non-repetitive uncertainties and random data dropouts. In the proposed robust networked ILC scheme, the switching law, iterative initial state, and disturbances, all of which vary with iterations, are well addressed. Corresponding to the actuator side and the measurement side of the networked switched NDTS, the random data dropouts occurred are compensated by the input signals at last iteration and the reference outputs, respectively. As a result, it is theoretically proved that under the non-repetitive uncertainties of the switched NDTS, the mathematical expectation of ILC tracking error remains bounded during the ILC process. While the non-repetitive uncertainties are progressively convergent in iteration domain, a precise tracking to the reference trajectory in mathematical expectation sense can be achieved. The effectiveness of the proposed networked ILC design is validated by a numerical example.

A New Approach to Characterize Successive Packet Losses in Stochastic Networked Systems

In this paper, we discuss the modeling and stabilization problems for a class of discrete-time stochastic networked systems (DSNSs) subject to successive packet losses. The system under consideration is transformed into a stochastic one with bounded stochastic delay. Considering that the stochastic delay is characterized by nonuniform distribution, a new equivalent model is then constructed that enables the DSNS’s controller design to benefit from knowing the probability characteristic of packet losses. Specially, to verify this feature, the probabilities of the delay can be explicitly obtained by utilizing the formula of total probability, which is critical to model transformation and analyze practical problems that exist in DSNSs. Based on the proposed model, sufficient conditions are established under which the globally mean-square asymptotic stability of resulting stochastic delay closed-loop system is guaranteed, and a delay-distribution-dependent design procedure is then proposed. A numerical example with simulation is provided to validate the analytical results and demonstrate the effectiveness of the design procedure.

Global Stabilization of the Discrete-Time Integrators System by Bounded Controls

This paper is concerned with global stabilization of discrete-time multiple integrators with bounded controls by utilizing the energy function based approach. First, a discrete-time double integrators system subject to input additive disturbances is stabilized by a bounded feedback whose formula involves a linear function of the state and a saturation function only. Next, this result is used to stabilize a discrete-time multiple integrators of arbitrary length by bounded control with the aid of a special canonical form. Compared with the existing results, the proposed controllers require fewer saturation functions, which allow a better use of the control energy. Moreover, some free parameters that are introduced into these controllers can help improve the transient performance of the closed-loop systems significantly. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Event-triggered Control for Heterogeneous Discrete-time Multi-agent Systems Subject to Uncertainties and Noises

This paper investigates the event-triggered control problem of heterogeneous discrete-time multi-agent systems (MASs) subject to uncertainties and noises. Based upon the output regulation theory, a new distributed event-triggered control scheme is proposed to reduce communication burden and attenuate effects of stochastic noises. Two types of event-triggered control laws based on dynamic state feedback and dynamic output feedback are designed, respectively. Moreover, to compensate parameter uncertainties, a p-copy internal model is synthesized into the designed controllers. It is shown that all tracking errors are exponentially ultimately bounded in the mean square sense regardless of uncertainties and noises. Several examples are finally given to demonstrate the validity of main results.

Network-based filtering for positive systems with random communication delays and deception attacks

This paper is concerned with the problem of network-based filtering for a discrete-time positive system subject to random communication delays and deception attacks. The delays and attacks are considered as phenomena occurring randomly via network communication, either passively or actively, and thus they can be suitably characterized by mutually independent Markov stochastic process and Bernoulli random variable. A novel resilient filter of a mode-dependent structure based on delayed and tampered sensor measurement is proposed. With such a mode-dependent filter, the network-based filtering error system is modeled by an augmented Markov jump linear system. Criteria by means of linear programming are then developed to determine the filter gain matrices such that the filtering error system guarantees its resiliency in terms of stochastic stability under a prescribed l1-gain while mitigating the simultaneous effects of random communication delays, deception attacks, disturbance, noise, and jumping system parameters. An illustrative example is given to test the feasibility of the conditions and verify the effectiveness of the resilient filter.

Designing a Switching Controller Based on Control Performance Assessment Index and a Fuzzy Supervisor for Perturbed Discrete-Time Systems Subject to Uncertainty

In this paper, a switching control strategy based on control performance assessment index namely Harris index and a fuzzy supervisor has been proposed for a perturbed discrete-time system subject to uncertainty. In the switching strategy, multiple controllers are utilized so that their virtues such as robustness, minimum output variance and minimum domain of control effort have been achieved simultaneously. Disadvantages of the used controllers like chattering and sensitivity to uncertainty are also improved. The Switching strategy has been designed in three steps. First of all, proper controllers have been designed which are minimum variance, incremental minimum variance and quasi sliding mode controllers. Then, Harris index and fuzzy supervisor are also designed in the next steps respectively. The Harris index has been determined to select proper controller among the available controllers for regulatory and tracking problems. The fuzzy supervisor is also designed to improve Harris index performance. The fuzzy supervisor is Sugeno type which can be used as a supervisor on Harris index operation, especially in presence of uncertainties. Finally, simulation results show that proposed control strategy improves the output variance effectively, reduces chattering domain of control input and sensitivity to uncertainty.

Design and flight experiments of a Tube-Based Model Predictive Controller for the AR.Drone 2.0 quadrotor

This paper focuses on the design, implementation and experimental validation of a Tube-Based Model Predictive Control (TBMPC) law for the stabilization of the horizontal dynamics of an Unmanned Aerial Vehicle (UAV) quadrotor. These dynamics are modelled by a discrete-time linear system subject to additive disturbance and polytopic constraints, which model is derived through an identification strategy from experimental flight data that is adapted to the subsequent design of invariant sets. The results obtained from a validation flight with the TBMPC law are presented to illustrate the robust state and control input constraints satisfaction.

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.

Exact recursive updating of state uncertainty sets for linear SISO systems

This paper addresses the classical problem of determining the set of possible states of a linear discrete-time SISO system subject to bounded disturbances, from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with time as new measurements become available. We present two theorems which give a complete description of the relationship between uncertainty sets at two successive time instants, and this yields an efficient algorithm for recursively updating uncertainty sets. Numerical simulations demonstrate performance improvements over existing exact methods.

Self-triggered Control for Uniform Ultimate Boundedness using Skewed Structured Singular Values

This paper proposes a self-triggered control approach that assures that the system state is uniformly ultimately bounded. In particular, a linear discrete-time system subject to both parametric uncertainties and disturbances is considered. The approach uses the skewed structured singular value for predictions to determine the next execution time. A numerical example is provided to illustrate the approach.

Local Stabilization of Nonlinear Discrete-Time Systems Subject to Amplitude Bounded Disturbances

The stabilization problem of nonlinear discrete-time systems subject to amplitude bounded disturbances by means of Takagi-Sugeno (T-S) fuzzy models is considered in this paper. The linear matrix inequality (LMI) approach is applied to design a state feedback fuzzy controller such that the system trajectories are ultimately bounded, that is, the state trajectory starting in a set of admissible initial conditions is guaranteed to converge in finite time to a nearby region of the state space origin. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems.

Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation

This technical note studies the robust output tracking controller design for a class of uncertain discrete-time systems subject to actuator saturation. To achieve this capability, a new controller is proposed by robustifying the discrete-time composite nonlinear feedback (DCNF) control law. Since, the proposed controller may be saturated; a precise analysis is done to show its robust performance in spite of presence of actuator saturation and time-varying external disturbances. Additionally, a theorem is given and proved which guarantees the disturbance attenuation via the proposed control law for three different cases of the saturation function and it is shown that even if the control signal is saturated, the proposed controller achieves steady-state error of order $O(T)$ for state regulation. Finally, computer simulations are performed for a practical system and the applicability of the proposed controller is shown.

A One-Step Approach to Computing a Polytopic Robust Positively Invariant Set

A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the solving of a single LP, a polytopic RPI set that is minimal with respect to the family of RPI sets generated from a finite number of inequalities with pre-defined normal vectors.