Preview Tracking Control Research Articles

Robust preview tracking control for LPV/LFR continuous-time systems

This study proposes a novel preview control method for linear parameter-varying (LPV) continuous-time systems (CTS) utilizing linear fractional representation (LFR). First, a formal system equivalent to the LFR of the LPV continuous system, which includes the preview compensation and tracking error, was developed to use the available reference signal values. In order to give innovative preview controller designs, the suggested conditions then depend on the utilization of decision matrices and slack variables related to the LFR technique. To provide minimal conservative synthesis criteria to the LPV/LFR continuous-time system, parameter-dependent Lyapunov functions and full-block multipliers were also taken into consideration. To create reliable state-feedback and output-feedback tracking controllers with preview actions, the design conditions were modeled as linear matrix inequalities (LMIs). Two scenarios were simulated to show how effective the suggested control strategy is.

Preview control for linear parameter‐varying discrete‐time systems using a linear fractional representation

AbstractIn order to create a mixed tracking controller for discrete‐time linear parameter‐varying (LPV) systems, this work introduces a unique control strategy employing a linear fractional representation (LFR). Under the premise that the reference signal can be previewable, a design strategy for a controller with preview compensations is suggested. First, a preview tracking control issue is changed into a regulator problem by adding two additional linked auxiliary parameters into the initial system state/input, which further creates more enhanced error systems incorporating future information of reference signals. The suggested conditions then depend on utilizing slack variables with decision matrices related to the LFR approach in order to give innovative preview controller designs. We also construct reduced conservative synthesis situations by taking into account parameter‐dependent Lyapunov functions and full‐block multipliers. In order to create state‐feedback and output‐feedback preview tracking controllers, design requirements are characterized as linear matrix inequalities. Two simulation studies are completed as the last step to highlight how successful the suggested control strategy is.

Robust fault-tolerant preview control of linear parameter-varying discrete-time systems

This study presents a new fault-tolerant preview tracking control (FTPTC) method using linear fractional representation (LFR) with regard to discrete-time linear parameter-varying (LPV) systems. To achieve preview tracking performance, a design strategy for a stable controller with integral, fault estimation, and preview actions is adopted. First, a fault estimation methodology for an LPV/LFR system with an actuator failure and external interference is developed utilizing the state observer approach. Next, based on the obtained fault estimation information, an equivalent augmented model including future information on reference signals, is developed, which converts preview tracking control (PTC) problem to a stabilization problem. Less conservative stability conditions for LPV have developed. Lastly, we performed two instances to validate the efficiency of the control approach that was proposed.

Dissipative sliding mode tracking control for discrete-time singular T-S fuzzy systems via a preview target mechanism

This study focuses on the dissipative sliding mode preview tracking control (SMPTC) of discrete-time singular T-S fuzzy systems (STSFSs) via a preview target mechanism. Due to the presence of singular matrix and input matrices with fuzzy rules in the system, the existing preview control approaches cannot be directly adopted. As a result, a novel singular augmented error system (AES) is derived based on a general method. Furthermore, the tracking problem has been translated into the stabilisation of singular AES. A linear sliding mode surface (SMS) is proposed for singular AES, and a suitably SMPTC law is presented. Sufficiency conditions for relaxation are derived to guarantee that the sliding mode dynamics is admissible with the dissipative criterion, and the sliding mode region (SMR) can be reached. The difference singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily. Finally, two examples have shown the effective tracking of the original output signal of system by utilising the proposed SMPTC law.

Preview controller synthesis for a class of linear parameter periodic systems

SummaryIn this study, the problem of preview tracking control (PTC) was considered with regard to the linear parameter periodic systems (LPPSs) subject to previewed signals. First, the difference operator approach was extended to derive an augmented error system (AES). As a result, the PTC problem was transformed into a stabilization problem via state/output feedback. Second, sufficient conditions guaranteeing the closed‐loop stability of the augmented error systems were derived, and the design of a periodic controller with preview actions was proposed through the approach of linear matrix inequalities (LMIs). Finally, a numerical simulation was performed to illustrate the effectiveness of the proposed periodic controller.

Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems

<p>In this paper, a novel observer-based robust preview tracking controller design method is proposed for a class of continuous-time Lipschitz nonlinear systems with external disturbances and unknown states. First, a state observer is designed to reconstruct unknown system states. Second, using differentiation, the state lifting technique, the differential mean value theorem, and several ingenious mathematical manipulations, an augmented error system (AES) containing the previewable information of a reference signal is constructed, thereby transforming the tracking control problem into a robust $ H_{\infty} $ control problem. Based on linear parameter-varying (LPV) system theory, a sufficient condition for asymptotic stability of a closed-loop system with a robust $ H_{\infty} $ performance level is established in terms of the linear matrix inequality (LMI). Furthermore, a tracking controller, which includes observer-based feedback control, integral control, and preview feedforward compensation, is established for the original system. In particular, the tracking controller design is simplified by computing the observer and tracking controller gains simultaneously via only a one-step LMI algorithm. Finally, numerical simulation results demonstrate that the proposed controller leads to superior improvement in the output tracking performance compared with the existing methods.</p>

Decentralized robust preview control for uncertain continuous-time interconnected systems

This paper investigates the problem of robust preview tracking control for uncertain continuous-time interconnected systems. We adopt the technology of decentralized control. The tracking controller for each uncertain isolated subsystem is first designed. With the help of an uncertain error system, the considered tracking problem is converted into a regulation problem. The preview tracking controller for the nominal system is obtained by utilizing existing results. A novel method is proposed to tackle the uncertainty in the systems. In this method, the uncertainty bound is incorporated into the cost function. As a result, the preview tracking controller of the nominal system can be treated as a robust preview controller of the uncertain isolated subsystem. Then, the controllers of the uncertain isolated subsystems are assembled as a robust preview controller of uncertain interconnected systems. Finally, an academic numerical example is presented to show the effectiveness and superiority of the proposed controller.

H∞optimal preview tracking control problem with disturbance attenuation

AbstractIn this paper, theH∞optimal preview tracking control problem of continuous‐time linear system with external disturbance is studied, where the reference signal is previewed and its amplitude does not decay. First, an augmented system with error vector, original system state derivative, and internal model state derivative is constructed, which transforms the tracking problem into theH∞optimal output regulation problem. Second, theH∞optimal control method is used to design the controller, and the output regulation of the augmented system is achieved by finding the upper bound of the discount factor. Then the optimal controller, including error integral, preview feed‐forward compensation, and internal model compensation, is obtained for the original problem, and meanwhile the sufficient conditions are also provided to guarantee the existence of the controller. Finally, both theoretical and simulation results show that under the proposed controller, the closed‐loop system can achieve asymptotic tracking and has robustness against the disturbance.

Design of an optimal preview controller for linear discrete-time periodic systems

In this paper, the preview tracking control problem for linear discrete-time periodic systems is considered. First, to overcome the difficulty arising from periodicity of the system, the linear discrete-time periodic system is transformed into an ordinary time-invariant system by lifting method. Secondly, the difference between a system state and its steady-state value is used to derive an augmented system instead of the usual difference between system states. Then, the preview controller for the augmented system is proposed by the preview control theory, which solves the preview tracking control problem for the periodic systems. Moreover, an integrator is introduced to ensure that the output can track the reference signal without static error. Finally, the obtained results are illustrated by the simulation examples.

Robust preview control for polytopic nonlinear control systems

In this paper, the preview tracking control problem for Lipschitz nonlinear system, where future reference signals over a finite horizon can be previewed. First, an augmented error system including previewed information is constructed, which transforms a preview tracking control problem into a regulation problem. Furthermore, sufficient conditions on polytopic nonlinear systems, which guarantee the corresponding closed-loop system to be asymptotically stable, are derived by employing parameter-dependent Lyapunov function. A linear matrix inequality approach for designing preview controllers in state feedback and output feedback settings is presented. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

H∞ decentralised output feedback preview tracking control via state observer for a class of nonlinear disturbed interconnected discrete systems

ABSTRACT This paper presents an observer-based decentralized output feedback preview tracking control method for a class of nonlinear disturbed interconnected discrete systems. The considered output tracking control problem, for the first time, is transformed into a controller design problem of N augmented error subsystems. For each subsystem, the suggested control law is formulated by a combination of integral control action, observer-based state feedback control action and preview feedforward action of this subsystem. Based on the Lyapunov function approach, the auxiliary matrix variable approach, and some special mathematical manipulations, the controller feasibility conditions are established in linear matrix inequality (LMI) framework to guarantee the existence of the offered observer-based decentralized preview tracking controller. And, the gain matrices of both decentralized observation and decentralized tracking control can be searched concurrently by only one-step LMI procedure. Finally, two examples are presented to verify the effectiveness and superiority of the proposed controller.

Preview Tracking Control of Linear Periodic Switched Systems with Dwell Time

This paper studies the preview tracking control problem for linear discrete-time periodic switched systems. Firstly, an augmented error system is constructed for each subsystem by stabilizing the augmented error systems through the method of optimal preview control, and the tracking problem of the switched system is transformed into the switched stability problem of closed-loop augmented error systems. Secondly, a switched Lyapunov function method is applied to search the minimal dwell time satisfying the switched stability of the closed-loop augmented error systems. Thirdly, the switched preview control input is solved from the controller of the individual augmented error system, and then the sufficient conditions and the preview controller can be obtained to guarantee the solvability of the original periodic switched preview tracking problem. Finally, numerical simulations show the effectiveness of the stabilization design method.

New results on observer-based robust preview tracking control for Lipschitz nonlinear systems

In this article, the observer-based robust preview tracking control problem is revisited for discrete-time Lipschitz nonlinear systems. The proposed observer-based preview control scheme is composed of the integral control action, the observer-based state feedback control action, and the preview feedforward action of the reference signal. Sufficient design condition of controller and observer gains, which are able to ensure the simultaneously convergence of both the estimation error and the tracking error toward zero, is established in terms of linear matrix inequality by applying the Lyapunov function approach and several mathematical techniques. Compared with the existing result, the system model is more general, which could describe a larger range of practical processes. The observer-based preview controller design is simplified by computing the gain matrices of both observer and tracking controller simultaneously by only one-step linear matrix inequality procedure. Robustness against external disturbance is analyzed via the H∞ performance criterion to attenuate its effect on the performance signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the suggested controller.

Observer‐based robust preview tracking control for a class of non‐linear systems

This study provides an observer-based robust preview tracking controller for Lipschitz non-linear systems. Firstly, the non-linear system dynamics is studied and the non-linear observer is designed. By introducing the Lyapunov function, the observer gain matrix is obtained through linear matrix inequalities (LMIs). To obtain an effective tracking control law, an augment error system which consists of difference of estimation error, tracking error, difference of estimated status and reference preview information is constructed. The sufficient solutions for observer-based robust preview controller are analysed using the LMI approach. Two numerical examples are provided to show the flexibility and effectiveness of the proposed robust preview tracking controller.

Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

Preview Tracking Control for Continuous-Time Singular Interconnected Systems

This paper proposes and investigates a problem of preview tracking control for a class of continuous-time singular interconnected systems. Firstly, the related items are deleted to obtain several isolated subsystems with low dimensions. An error system is constructed for each isolated subsystem so that the tracking error is included in the state vector of the error system; then, the tracking problem is transformed into a regulation problem. Secondly, the preview tracking controller is designed for each error system and obtained controllers are combined as the controller of the error system of the singular interconnected system. Thirdly, the Lyapunov function method is utilized to determine the constraints of the related terms so that the closed-loop system of the error system of the singular interconnected system is stable under the action of the controller obtained. Finally, the preview tracking controller of the singular interconnected system is obtained from the relationship between the error system and the original system. A numerical simulation algorithm for continuous-time singular systems is also proposed in this paper. The numerical simulation illustrates the effectiveness of the theoretical results.

Fault tolerant tracking control for a class of linear parameter varying systems using reduced-order simultaneous estimator and optimal preview policy

This paper considers the reduced-order estimator based fault tolerant preview tracking control problem for a class of linear parameter varying (LPV) systems. The main research contents are composed of two aspects. First, a scheduling-parameter-dependent reduced-order simultaneous state/fault estimator is designed based on model transformation method, unknown input observer theory, estimator parameterisation, and robustness optimisation. Second, a novel robust fault tolerant preview tracking control policy is constructed by integrating fault signal compensation, state feedback, preview action of reference signals, and integral regulation of tracking errors. Compared with the relevant studies, the merits can be summarised in two aspects. On one hand, the proposed design method of reduced-order estimator can be applied to more general LPV models because it does not depend on the traditional constraint operations, such as decomposition of system output equation, separated estimations of actuator and sensor faults, or derivative of output equation. On the other hand, the optimal preview policy including preview action and integral regulation is introduced to increase the design degree of freedom, which contributes to the optimisation of fault tolerant tracking performance even under influences of fault estimation errors and disturbances. Finally, the effectiveness of the proposed method is verified by three case studies.

Preview tracking control for a class of fractional-order linear systems

This paper studies the preview tracking control of a class of fractional-order linear systems. Firstly, we use the fractional derivative property to take the fractional derivative of both sides of the state equation several times, and we obtain a formal ordinary linear system. An augmented error system is constructed for the transformed ordinary linear system, the appropriate performance index function is introduced and relevant results of the optimal preview control are applied to design the optimal preview controller for the augmented error system when the reference signal is previewable. Based on the relationship between the original system and the augmented error system, the preview tracking controller of the original system can be obtained. It can guarantee the asymptotic tracking of the output of the original closed-loop system to the reference signal. The validity of the theoretical results is verified by numerical simulation.

Output feedback preview tracking control for time‐varying polytopic descriptor systems

SummaryThis paper focuses on the problem of static output feedback preview tracking control for discrete‐time descriptor systems with time‐varying parameters subject to a previewable reference signal. First, an augmented error system including the information of the future reference signal is constructed based on the error system approach. Second, a preview control policy is constructed by integrating output feedback, preview action, and integral operation. Relying on the augmentation modeling technique, a linear preview control design problem is transformed into an equivalent augmented output‐feedback control design problem. New design conditions guaranteeing the existence of a stabilizing controller are recast as an LMI‐based feasibility problem. The proposed preview controller design method requires neither special constraints on the state‐space system matrices nor a high‐dimensional augmented error system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Preview control for a class of linear discrete-time periodic systems

ABSTRACT This paper considers the problem of preview tracking control for linear discrete-time periodic systems subject to previewable reference and disturbance signals. First, the difference operator approach is introduced to derive an augmented error system that includes future information on the previewable signals. As a result, the problem of preview tracking control of the original system is transformed into a stabilisation problem via a periodic static output feedback. Second, sufficient conditions that guarantee the closed-loop stability of the augmented error systems are derived, and meanwhile, the design of a periodic controller with preview actions is proposed through the linear matrix inequalities approach. Finally, a numerical simulation example is presented to illustrates the effectiveness of the proposed method.