RHONN identifier-control scheme for nonlinear discrete-time systems with unknown time-delays

This work presents a neural identifier-control scheme for uncertain nonlinear discrete-time systems with unknown time-delays. This scheme is based on a neural identifier to get a model of the system and a discrete-time block control technique based on sliding modes to generate the control law. The neural identifier is based on a Recurrent High Order Neural Network (RHONN) trained with an Extended Kalman Filter (EKF) based algorithm. Applicability is shown using real-time test results for linear induction motors. Also, a Lyapunov analysis is added in order to prove the semi-globally uniformly ultimately boundedness (SGUUB) of the proposed neural identifier-control scheme.     

Discrete-time adaptive fuzzy speed regulation control for induction motors with input saturation via command filtering

A discrete-time adaptive fuzzy control method is introduced to achieve the speed regulation for induction motors (IMs) with input saturation via command filtering in this paper. First, the continuous model of IMs drive system is transformed into discrete-time form by using Euler formula. Then, the fuzzy logic systems are used to approximate the unknown nonlinear functions in the discrete-time drive system. In addition, the command filtering control method is introduced to overcome the “explosion of complexity” problem in the design process of traditional backstepping method. It is verified that all the closed-loop signals are bounded and the outputs can track the given reference signals well. Finally, simulation results illustrate the validity of the discrete-time control method.     

Discrete-time command filtered adaptive fuzzy fault-tolerant control for induction motors with unknown load disturbances

In this paper, a command filtered fault-tolerant control (CFFTC) approach is investigated for induction motors (IMs) discrete-time system in the presence of actuator faults and unknown load disturbances. Firstly, the IMs system discrete-time model is obtained by Euler method. Then, the fuzzy logic systems (FLSs) is utilized to compensate for unknown actuator faults. Besides, introducing the error compensation mechanism into discrete-time systems via command filters, “complexity of computation” and noncausal problem can be conquered, and the filtering error is avoided concurrently. Finally, simulation results demonstrate the validity of the presented fault-tolerant method for IMs system.     

Discrete-time recurrent high order neural networks for nonlinear identification

This paper focuses on the problem of discrete-time nonlinear system identification via recurrent high order neural networks. It includes the respective stability analysis on the basis of the Lyapunov approach for the NN training algorithm. Applicability of the proposed scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.     

Distributed semistable LQR control for discrete-time dynamically coupled systems

A distributed linear-quadratic-regulator (LQR) semistability theory for discrete-time systems is developed for designing optimal semistable controllers for discrete-time coupled systems. Unlike the standard LQR control problem, a unique feature of the proposed optimal control problem is that the closed-loop generalized discrete-time semistable Lyapunov equation can admit multiple solutions. Necessary and sufficient conditions for the existence of solutions to the generalized discrete-time semistable Lyapunov equation are derived and an optimization-based design framework for distributed optimal controllers is presented.     

Mean-square pinning control of fractional stochastic discrete-time complex networks

This paper considers the mean-square pinning control problem of fractional stochastic discrete-time complex networks. First, a new fractional stochastic discrete-time complex networks model with stochastic noise is established. Then, some pinning controllers and sufficient conditions are developed for the complex networks. By adopting Lyapunov energy function theory and matrix analysis theory, it proved that the synchronization of the fractional stochastic discrete-time complex networks can be achieved in a mean-square sense via pinning control. In addition, these results are extended to solve the synchronization problem of general fractional discrete-time complex networks without noise. Finally, several numerical examples are given to verify the correctness of the obtained theoretical results.     

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

This paper presents a discrete-time decentralized neural identification and control for large-scale uncertain nonlinear systems, which is developed using recurrent high order neural networks (RHONN); the neural network learning algorithm uses an extended Kalman filter (EKF). The discrete-time control law proposed is based on block control and sliding mode techniques. The control algorithm is first simulated, and then implemented in real time for a two degree of freedom (DOF) planar robot.     

Population extremal optimization-based extended distributed model predictive load frequency control of multi-area interconnected power systems

How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.     

Fault estimation and fault tolerant control for discrete-time nonlinear systems with perturbation by a mixed design scheme

This paper focuses on the observer-based fault-tolerant control problem for the discrete-time nonlinear systems with the perturbation and the fault signals. First, the nonlinear term with perturbation is put into the local nonlinear part so that the nonlinear system with perturbation can be described as an interval type-1 (IT1) T-S fuzzy system. Then, based on the unknown input observer technology, the IT1 T-S fuzzy fault estimation (FE) observer scheme is presented to obtain the real-time FE information and decouple the local nonlinear part from the estimation error system, where the design complexity and the computational burden are reduced simultaneously. Second, based on the real-time FE information, an FE-based interval type-2 (IT2) T-S fuzzy fault-tolerant control scheme is presented to achieve the compensation for the influence of the fault signal and the stabilization for the system. Different from the traditional methods, a mixed design scheme, which is based on the IT1 T-S fuzzy fault estimation observer method and the IT2 T-S fuzzy fault-tolerant controller method, is proposed in this paper. This strategy can not only reduce the computational burden, but also obtain a less conservative result. Finally, the effectiveness of the mixed design approach is illustrated by an example.     

Fault diagnosis and fault-tolerant tracking control for discrete-time systems with faults and delays in actuator and measurement

In this paper, the fault diagnosis (FD) and fault-tolerant tracking control (FTTC) problem for a class of discrete-time systems with faults and delays in actuator and measurement is investigated. In the first step, a discrete delay-free transformation approach is introduced for an constructed augmented system such that the two-point-boundary-value (TPBV) problem with advanced and delayed items can be avoided. Then, the optimal fault-tolerant tracking controller (OFTTC) is proposed with respect to an equivalent reformed quadratic performance index. Moreover, by using the real-time system output rather than the residual errors, a reduced-order-observer-based fault diagnoser for the augmented system is designed to diagnose faults in actuator and measurement, and solve the physically unrealizable problem of proposed OFTTC. Finally, the effectiveness of the proposed fault diagnoser and OFTTC is illustrated by a realistic design example for industrial electric heater.     

Model-based event-triggered control of switched discrete-time systems

In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method.     

Event-Triggered formation control for time-delayed discrete-Time multi-Agent system applied to multi-UAV formation flying

This paper studies the formation control for a time-delayed discrete-time multi-agent system (MAS). An event-triggered controller is proposed to reduce the communication load of the system. Based on the designed event-triggered condition and properties of Schur stable matrix, the stability of formation for discrete-time MAS is proved. Utilizing the virtual simulation platform integrated Robot Operating System (ROS) and Gazebo, a virtual scene with unmanned aerial vehicles (UAVs) models is built and the verification for the theoretical algorithm is completed. Finally, an experimental platform with four practical UAVs is constructed and the result shows that the expected formation is achieved and controller proposed can solve the formation control problem for time-delayed discrete-time MASs. Besides, the effectiveness of the event-triggered mechanism on reducing communication frequency is comfirmed in practical scenarios.     

Modeling of synchronous electric machines for real-time simulation and automotive applications

Recent research in the field of vehicle electrification has indicated that synchronous machines, which include the permanent magnet synchronous machine (PMSM) and the externally excited synchronous machine (EESM), represent a viable solution for electric propulsion. A challenging problem for synchronous machines drives employed in automotive applications is to obtain accurate mathematical models which can deal with parametric variation and which are suitable for real-time simulations and synthesis of control laws. The goal of this paper is to provide a mathematical modeling framework for synchronous machines that can answer to this challenging problem. To this end, using the rotor reference frame, the mathematical models of PMSMs and EESMs are constructed taking into account also the parametric variation due to magnetic saturation and temperature variation. Then, a complex state-space bilinear model for both EESM and PMSM with parametric variation due to magnetic saturation and temperature are developed. Considering the parametric variation as a polytopic bounded disturbance, it is then shown how to split the bilinear complex model in two PWA variable parameter state-space models suitable for a cascade control structure. Based on the developed models, a dynamic unified simulator was constructed in Matlab^®/Simulink^®. Measurement data obtained in a real test-bench system were used to verify the accuracy of the simulator. The discrete-time simulator was then integrated in an industrial hardware-in-the-loop test bench for real-time evaluation of a current control scheme in EESM drives.     

Iterative dynamic linearization and identification of a nonlinear learning controller: A data-driven approach

In this article, a nonlinear iterative learning controller (NILC) is developed using an iterative dynamic linearization (IDL) and a parameter iterative learning identification technique. First, the ideal NILC is transformed into a linear parameterized form by using a controller-oriented compact form IDL (controller-CFIDL) technique. Then an iterative learning identification approach is presented for tuning the parameters of the proposed controller using real-time I/O data. For the sake of analysis, a linear data model of the nonlinear plant is obtained by using the system-oriented IDL technology and a corresponding system parameter identification algorithm is developed in iteration domain. The convergence analysis is provided for the dynamically linearized nonlinear and nonaffine discrete-time system. The results are further extended by using a controller-oriented partial form iterative dynamic linearization (controller-PFIDL) method to gain a higher-order NILC utilizing additional control information from previous iterations. Simulations of two examples show the effectiveness of the proposed methods.     

A real-time estimation and control scheme for induction motors based on sliding mode theory

In this paper a sliding mode position control for high-performance real-time applications of induction motors is developed. The design also incorporates a sliding mode rotor flux estimator in order to avoid the flux sensors. The proposed control scheme presents a low computational cost and therefore can be implemented easily in a real-time applications using a low cost Digital Signal Processor (DSP). The stability analysis of the observer and the controller, under parameter uncertainties and load torque disturbances, is provided using the Lyapunov stability theory. Finally simulated and experimental results show that the proposed controller with the proposed observer provides a good trajectory tracking and that this scheme is robust with respect to plant parameter variations and external load disturbances.     

Robust finite-time sliding mode control for discrete-time singular system with time-varying delays

This paper explores the finite-time bounded issue for discrete-time singular time-varying delay system via sliding mode control method. A suitable discrete-time sliding mode control law is constructed to drive the state trajectories onto the specified sliding surface in a given finite time interval. Meanwhile, sufficient conditions for finite-time bounded to the closed-loop delayed system are provided in both reaching phase and sliding motion phase. In addition, the finite-time sliding mode controller gain matrix can be solved by using the linear matrix inequalities approach. Finally, three numerical examples are illustrated to demonstrate the superiority and practicability of presented results.     

Intersample optimization in a sampled-data control system using the redundancy of a dual-rate system

The present study discusses the design method for controlling a single-input/single-output linear time-invariant dual-rate system, where the sampling interval of the plant output is longer than the holding interval of the control input. In such a dual-rate system, the intersample output might oscillate even when the sampled output converges to the reference input in the steady state. In a conventional ripple-free method, an existing control law is extended by introducing an exogenous variable, which is independent of the discrete-time sampled response, and the exogenous variable is designed for eliminating the steady-state intersample ripples without changing the existing sampled response. In another method, since a control law is designed such that the intersample performance is optimized, the intersample ripples are eliminated in the transient as well as steady states. However, the preservation of an existing sampled response is not taken into account. The present study proposes a new design method for eliminating the intersample ripples subject to the existing sampled response. In the proposed method, the continuous-time index is optimized subject to the existing discrete-time response. As a result, the intersample ripples are eliminated in the transient as well as steady states, and the existing discrete-time sampled response is maintained. The proposed method is compared to the conventional dual-rate design methods in numerical examples, and the effectiveness of the method is demonstrated.     

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.     

Predictive control of discrete-time high-order fully actuated systems with application to air-bearing spacecraft simulator

This paper addresses an output tracking problem for discrete-time high-order fully actuated (DHOFA) systems and its application in the control of air-bearing spacecraft (ABS) simulator. A HOFA system model, as a novel system representation, is applied to establish the dynamics of discrete-time control systems. Accordingly, a HOFA predictive control scheme is presented to deal with this problem, which is composed of a HOFA feedback for stabilization and a HOFA predictive control for tracking. In this scheme, a Diophantine equation is exploited to construct an incremental HOFA (IHOFA) prediction model to substitute a reduced-order prediction model, and then a cost function involving tracking performance is minimized by using multi-step output predictions. A sufficient and necessary condition is proposed to discuss the stability and tracking performance of the closed-loop DHOFA systems, it is simple to utilize in system analysis and extend in practice. Two experiments of the control of ABS simulator are shown to illustrate the feasibility of the presented HOFA predictive control scheme.     

Modeling and stabilization of a wireless network control system with packet loss and time delay

The problem of modeling and stabilization of a wireless network control system (NCS) is considered in this paper, where packet loss and time delay exist simultaneously in the wireless network. A discrete-time switched system with time-varying delay model is first proposed to describe the system closed by a static state feedback controller. A sufficient criteria for the discrete-time switched system with time-varying delay to be stable is proposed, based on which, the corresponding state feedback controller is obtained by solving a set of linear matrix inequalities (LMIs). Numerical examples show the effectiveness of the proposed method.