Tracking Control Of Discrete-time Systems Research Articles

Pseudo-partial-derivative information-driven adaptive fault-tolerant tracking control for discrete-time systems

The fault-tolerant tracking control problem is studied for the discrete-time systems with actuator faults. To lessen adverse impacts of actuator fault, a PPD information-driven fault estimation algorithm is established to adaptively estimate actuator fault information online, which avoids the additional construction and training process of neural network. With the aid of the adaptive fault compensation, a model-free adaptive fault-tolerant tracking control algorithm is constructed to ensure that the expected output reference trajectory can be tracked by system output. Moreover, only input and output data are employed throughout the design process, system dynamics are not demanded. Ultimately, the availability of developed strategy is proved through a simulation.

Stochastic linear quadratic optimal tracking control for discrete-time systems with delays based on Q-learning algorithm

<abstract><p>In this paper, a reinforcement Q-learning method based on value iteration (Ⅵ) is proposed for a class of model-free stochastic linear quadratic (SLQ) optimal tracking problem with time delay. Compared with the traditional reinforcement learning method, Q-learning method avoids the need for accurate system model. Firstly, the delay operator is introduced to construct a novel augmented system composed of the original system and the command generator. Secondly, the SLQ optimal tracking problem is transformed into a deterministic one by system transformation and the corresponding Q function of SLQ optimal tracking control is derived. Based on this, Q-learning algorithm is proposed and its convergence is proved. Finally, a simulation example shows the effectiveness of the proposed algorithm.</p></abstract>

Optimal Tracking Control for Discrete-time Systems with Time-delay Based on the Preview Control Method

Abstract In this paper, the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method. First, a transformation is introduced. Thus, the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal. Then, by applying the preview control theory, an augmented system for the non-delayed system is derived, and a controller with preview function is designed, assuming that the reference signal is previewable. Finally, the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.

Output feedback preview tracking control for discrete-time polytopic time-varying systems

ABSTRACTThis paper focuses on the problem of static output feedback preview tracking control for discrete-time systems with time-varying parameters subject to a previewable reference signal. We develop a design method of a robust controller with integral and preview actions achieving robust tracking performance. First, an augmented error system including future information on reference signal is constructed by introducing two new related auxiliary variables to the original system state and input. This leads to a tracking problem being transformed into a regulator problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the augmented error system while considering a static output feedback. Meanwhile, the static output preview control gains are solved explicitly by the proposed conditions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

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.

Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.

Near-optimal tracking control for discrete-time systems with delayed input

This paper considers the near-optimal tracking control problem for discrete-time systems with delayed input. Using a variable transformation, the system with delayed input is transformed into a non-delayed system, and the quadratic performance index of the optimal tracking control is transformed into a relevant format. The optimal tracking control law is constructed by the solution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator and a near-optimal tracking control is obtained. Simulation results demonstrate the effectiveness of the optimal tracking control law.