Tracking Control Of Linear Systems Research Articles

Disturbance Observer-Based Data Driven Model Predictive Tracking Control of Linear Systems

Disturbance Observer-Based Data Driven Model Predictive Tracking Control of Linear Systems

Reinforcement Learning and Optimal Setpoint Tracking Control of Linear Systems With External Disturbances

In order to deal with optimal setpoint tracking (OST) problems, a discounted cost function has been introduced in the existing work. However, the optimal tracking controllers developed according to the discounted cost function may not ensure asymptotic tracking and the stability of the closed-loop systems. To overcome these limitations, in this article, we propose a novel adaptive optimal control method to minimize a cost function without a discount factor. The proposed method starts from a reformulation of the infinite-horizon OST problem for linear discrete-time systems with external disturbances. We derive an algebraic Riccati equation for solving the OST problem, whose solution is uniquely determined under mild conditions. It is proved that the obtained controller accommodates the disturbance and realizes the output tracking with zero steady-state error. In the framework of reinforcement learning, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -learning algorithm is devised to learn the suboptimal control policy by using measured data. The present learning algorithm does not require that the disturbance is measurable and can be implemented completely model-free. Finally, two examples on dc motor system and F-16 aircraft plant are provided to corroborate our design methodology.

Tracking Control of the Dynamic Input-Output Economic System Based on Data Fusion

In recent years, under the background of stable economic operation, people's research on economic systems has become increasingly popular. The dynamic input-output model reflects the change and development process of the input-output relationship of the economic system over a period of time. The main purpose of tracking control is to design a suitable controller so that the output of the control system can track the output of the reference system as much as possible. In the economic system, data is an important factor. Based on this, this paper mainly studies the tracking control of dynamic input-output economic system based on data fusion. This research takes the data fusion of the dynamic input-output economic system as the starting point and takes the optimal control and tracking of the economic system as the research object of this research. Based on data fusion technology, a new dynamic input-output economic system tracking and control is proposed. This paper studies the finite-time optimal tracking control of linear systems. Through numerical examples, comparing the finite-time and infinite-time optimal control simulation results, it is proved that the algorithm can achieve good tracking control. Experimental data shows that the optimal and suboptimal performance indicators for a limited time are 0.7729412 and 1.5687310, respectively. Therefore, compared with the infinite-time optimal control, the performance loss and the final tracking error of the suboptimal control proposed in this study are reduced.

Optimal Output Regulation for Square, Overactuated and Underactuated Linear Systems

This article considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique, which is most input energy efficient. Second, if exact tracking is infeasible, which control performs most accurately. These are typical challenges for overactuated systems and for underactuated systems, respectively. We formulate both goals as optimal output regulation problems. Then, we contribute two new sets of regulator equations to output regulation theory that provide the desired solutions. A thorough study indicates solvability and uniqueness under weak assumptions. For example, we can always determine the solution of the classical regulator equations that is most input energy efficient. This is of great value if there are infinitely many solutions. We derive our results by a linear quadratic tracking approach and establish a useful link to output regulation theory.

Set‐point output tracking problem for linear plants via periodic event‐triggered control

This study addresses event-triggered tracking control for linear systems with constant reference signals and disturbances. A remote observer-based proportional–integral controller, which communicates with the plant only at some discrete instants, is designed. The transmissions, involving both the sensor-to-controller and the controller-to-actuator channels, are scheduled by periodic event-triggered control. A new kind of summation-based triggering condition is proposed which can ensure that there exists a positive minimum inter-event time uniformly for a family of controllers parameterised by the verification periods. Then, it is proved that the proposed periodic event-triggered control can solve the set-point tracking problem asymptotically without the assumption that the reference signal is accessible to the sensor. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Output feedback adaptive fault‐tolerant compensation tracking control for linear systems based on the closed‐loop reference model

SummaryThis paper investigates the problem of output feedback adaptive compensation tracking control for linear systems subject to external disturbances and actuator failures including loss of effectiveness faults and bias faults. The impact of actuator faults on the transient performance of systems can be mitigated predicated on the closed‐loop reference model with an additional degrees of design freedom. Using the estimation information provided by the adaptive mechanism, an output feedback adaptive fault‐tolerant control strategy is developed to track closed‐loop reference model systems. It is shown that all the signals of the resulting closed‐loop system are bounded. Finally, simulation results are given to demonstrate the effectiveness of the proposed fault‐tolerant tracking control method.

Reinforcement Learning-Based Adaptive Optimal Exponential Tracking Control of Linear Systems With Unknown Dynamics

Reinforcement learning (RL) has been successfully employed as a powerful tool in designing adaptive optimal controllers. Recently, off-policy learning has emerged to design optimal controllers for systems with completely unknown dynamics. However, current approaches for optimal tracking control design either result in bounded tracking error, rather than zero tracking error, or require partial knowledge of the system dynamics. Moreover, they usually require to collect a large set of data to learn the optimal solution. To obviate these limitations, this paper applies a combination of off-policy learning and experience-replay for output regulation tracking control of continuous-time linear systems with completely unknown dynamics. To this end, the off-policy integral RL-based technique is first used to obtain the optimal control feedback gain, and to explicitly identify the involved system dynamics using the same data. Second, a data-efficient-based experience replay method is developed to compute the exosystem dynamics. Finally, the output regulator equations are solved using data measured online. It is shown that the proposed control method stabilizes the closed-loop tracking error dynamics, and gives an explicit exponential convergence rate for the output tracking error. Simulation results show the effectiveness of the proposed approach.

Robust Observer-Based Fault Tolerant Tracking Control for Linear Systems with Simultaneous Actuator and Sensor Faults: Application to a DC Motor System

This paper discusses the problem of observer-based sensor and actuator fault estimation for fault tolerant control systems subject to noise and disturbance. First, an extended state system is formulated by letting the sensor and actuator fault term be two auxiliary state vectors; then a single robust observer is constructed to achieve concurrent estimations of original system states and faults by using PI structure. Further, sufficient conditions for the robust stability of the proposed observer are formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved using LMI optimization techniques. Based on the idea of a corrective control law and a corrective measurement output, which have capability to compensate the presence of fault, the estimation results of the proposed observer are used to provide the fault tolerant control system without changing the existing nominal control law. Thus this approach can be applied to general control system. Finally, the validity and applicability of the proposed approach are shown by a numerical example of a DC motor system.

Stability Analysis andH∞Output Tracking Control for Linear Systems with Time-Varying Delays

The problem of stability analysis andH∞output tracking control for linear systems with time-varying delays is studied. First, by construction of a newly augmented Lyapunov-Krasovskii functional, a delay-dependent stability criterion for nominal systems with time-varying delays is established in terms of linear matrix inequalities (LMIs). Second, based on theH∞sense, the proposed method is extended to solve the problem of designing anH∞output tracking controller to track the output of a given reference model. Finally, three examples are included to show the validity and effectiveness of the presented delay-dependent stability and theH∞output tracking controller design.

Direct model reference adaptive control of linear systems with input/output delays

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for linear systems with unknown time varying input delays. This controller can also reject bounded disturbances of known waveform but unknown amplitude, e.g. steps or sinusoids. In this paper a robustness result is developed for DMRAC of linear systems with unknown small constant or time varying input delays using the concept of un-delayed ideal trajectories. We will show that the adaptively controlled system is globally stable, but the adaptive tracking error is no longer guaranteed to approach the origin. However, exponential convergence to a neighborhood can be achieved as a result of the control design. A simple example will be provided to illustrate this adaptive control method.

Adaptive Tracking Control of Linear Systems With Binary-Valued Observations and Periodic Target

This technical note studies the adaptive control for linear systems with set-valued observations to track a given periodic target. Based on the system parameters, accessorial parameters with the same order as that of the tracking targets are introduced and estimated. Considering the system parameters are unknown and set-valued observations can supply only limited information each time, a two-scale adaptive control algorithm is designed. Each control input is designed at the large time scale and lasts for a holding time (small scale), during which the parameter estimation algorithm is constructed. From the estimate of accessorial parameters, the control signal is updated at the large time scale by the certainty equivalence principle. As the holding time goes to infinity, the algorithm can be proved to be asymptotically efficient in a certain sense. Meanwhile, the adaptive tracking algorithm is shown to be asymptotically optimal. A numerical example is given to demonstrate the effectiveness of the algorithms and the main results obtained.

Dissipative Output Tracking Control of Linear Systems with Time Delay

The problem of dissipative output tracking control of linear systems with time delay is investigated. Firstly, an augmented system is constructed to describe dissipative output tracking control error, and the concept of dissipative output tracking is defined. Based on this, some sufficient conditions are derived in terms of linear matrix inequalities (LMIs) technique, which ensure that the augmented system is dissipative and stable; then design methods of dissipative output tracking state-feedback controller are provided, and the desired controller gain can be expressed through the solutions of LMIs. Finally, a numerical simulation example is given to illustrate the validity of the proposed results.

Unified Approximate Tracking Control of Linear Systems with Unacceptable Zeros

This paper addresses the problem of modeling and control of linear continuous-time systems with unacceptable zeros in a sense that they are on the right-half plane of the S-domain (non-minimum phase) or cause the controller to have undesired behavior. The unified approximation of output tracking control using output redefinition will result in approximate output tracking, yet insuring stable internal dynamics of the system. Four different types of output redefinition are presented in a unified way and shown to satisfy different forms of control objectives through a simulation example of small-signal model of boost converter.

Approximate design of optimal tracking controller for time-delay systems

Successive approximate design of the optimal tracking controller for linear systems with time-delay is developed. By applying the successive approximation theory of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV problems without delay and advance terms. The solution sequence of the linear TPBV problems uniformly converges to the solution of the original OTC problem. The obtained OTC law consists of analytic state feedback terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. By using a finite term of the adjoint vector sequence, a suboptimal tracking control law is revealed. Numerical examples show the effectiveness of the algorithm.

Tracking Controller for Linear Systems With Time Delays in Both State and Control Variables

Linear time invariant control systems with time delays in both state and control variables are studied. The problem is to design a controller so that the system response will follow a given reference input with zero steady-state error. The reference input is assumed to be a polynomial function of time. The controller is based on feeding forward the reference input and its delayed values. A method is derived for determining the feed-forward gain matrices. Necessary and sufficient condition for the existence of proposed tracking controller is also obtained. An example is given to illustrate the proposed method.