Model Reference Tracking Performance Research Articles

H∞$$ {H}_{\infty } $$ tracking control for uncertain switched stochastic systems with mixed time‐varying delays

AbstractThis article concerns the exponential tracking control problem of uncertain switched stochastic systems with mixed time‐varying delays including discrete delay and distributed delay. First, according to the multiple Lyapunov–Krasovskii functional described by the mixed time‐varying delays and the average dwell time method, a delay‐dependent sufficient conclusion is obtained, which makes the augmented system mean‐square exponential stable and satisfies the tracking performance. Then, the corresponding controllers are designed to ensure that the system has model reference tracking performance based on the above stability analysis. Finally, a numerical example and water quality preservation problems are employed to corroborate the usefulness of the method.

Stochastic Robust H∞ Decentralized Network Formation Tracking Control of Large-Scale Team Satellites via Event-Triggered Mechanism

The team formation of large-scale satellites for communication services of future smart cities in the 5G and 6G era is an important research topic currently. In this study, a robust H∞ with an event-triggered mechanism is proposed for the formation of large-scale satellites for communication tasks. At first, a satellite in the team formation is described by a nonlinear stochastic system with intrinsic random fluctuation, external disturbance, and coupling from other satellites. The proposed team formation tracking control for each satellite needs to consider the effect of network-induced delay and packet-dropout as well as save communication resources via an event-triggered mechanism. Further, the desired team formation of large-scale satellites can be prescribed by a set of reference models with the desired formation shape embedded in their reference inputs. Therefore, the large-scale team formation design problem can be simplified as an independentH∞ network model reference tracking control design problem for each satellite to efficiently attenuate the worst-effect of external disturbance, coupling of other satellites, intrinsic random fluctuation, network-induced delay, and packet-dropout on the model reference tracking performance. In order to avoid solving a nonlinear partial differential Hamillion-Jacobin inequality(HJI) for the H∞ decentralized network formation control for each satellite in the team the formation, the T-S fuzzy model is employed to interpolate several local linearized systems to approximate nonlinear satellite systems. Then the HJI in the H∞ decentralized network team formation design problem can be transformed into a set of linear matrix inequalities (LMIs) which can be easily solved by LMI TOOLBOX in MATLAB. Finally, a simulation example of team formation composed of ten satellites is given to illustrate the design procedure and to validate the proposed method in comparison with other methods.

H∞ tracking control for a class of asynchronous switched nonlinear systems with uncertain input delay

This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.

Stability analysis and robust stabilisation for a class of switched nonlinear systems with input delay

ABSTRACT This paper investigates stability analysis and robust model reference tracking control problem for a class of switched nonlinear systems with input delay and disturbance. Using a new Lyapunov–Krasovskii functional, free-weighting matrices and average dwell-time technique, new input-to-state stability conditions are derived in terms of linear matrix inequalities under a certain bound of delay. Then, based on the proposed Lyapunov–Krasovskii functional, robust model reference tracking control problem is studied. Finally, a kind of state feedback control law is proposed to guarantee robust model reference tracking performance. In addition, some examples are given to illustrate the effectiveness and feasibility of the proposed method.

Stability analysis and robust tracking control for a class of switched nonlinear systems with uncertain input delay

In this paper, the stability issue and tracking control problem for a class of switched nonlinear systems with uncertain input delay and disturbance are investigated. First, it is assumed a piecewise Lyapunov function exists for the nominal system (system without input delay and disturbance), and then, under the terms of the hypothetical piecewise Lyapunov function, a new Lyapunov-Krasovskii functional is constructed. By employing this new function and a switching signal which satisfies the average dwell time, the delay-dependent input-to-state stability under a certain delay bound is provided; also, a mechanism is invented to find the upper bound for input delay of switched system. In the next step, tracking control problem for this system is studied. Finally, a kind of state feedback control law which ensures conditions of aforesaid hypothetical piecewise Lyapunov function is proposed to guarantee the input-to-state stability and the robust model reference tracking performance. Simulation examples are given to illustrate the effectiveness of the proposed strategy.

LMI-based 2-DoF control design of a manipulator via T-S descriptor approach

Abstract This paper presents a method for the control design of a manipulator. The design goal is to achieve a guaranteed H∞ model reference tracking performance with respect to bounded reference inputs through a 2-DoF control scheme. To achieve this goal, the manipulator system is represented by a Takagi-Sugeno fuzzy model in descriptor form. The control scheme is based on a parallel distributed compensation controller. Furthermore, the stability of the nonlinear system is also guaranteed. Based on Lyapunov stability theory, the control design is formulated as an LMI optimization problem which can be effectively solved with numerical solvers. Simulation results carried out with the SimMechanics environment clearly demonstrate the effectiveness of the proposed method.

Robust Tracking Control of a Class of Switched Nonlinear Systems With Input Delay Under Asynchronous Switching

This paper concerns the problems of stability and robust model reference tracking control for a class of switched nonlinear systems with input delay under asynchronous switching. By proposing a new Lyapunov–Krasovskii functional, and using free-weighting matrices and average dwell-time (ADT) technique, new input-to-state stability (ISS) conditions are derived in terms of linear matrix inequalities (LMIs) under a certain delay bound. Then, robust model reference tracking control problem is studied based on the proposed Lyapunov–Krasovskii functional; Finally a kind of state feedback control law which guarantees robust model reference tracking performance is proposed. Illustrative examples are presented to demonstrate the efficacy and feasibility of results.

Multiobjective maximum power tracking control of photovoltaic systems: T-S fuzzy model-based approach

This paper presents a multiobjective maximum power point tracking (MPPT) control for photovoltaic (PV) system to guarantee both $$H_{2}$$ optimal control and $$H_{\infty }$$ model reference tracking performance simultaneously. First, the Takagi and Sugeno (T–S) fuzzy model is employed to describe the dynamic behavior of DC–DC boost converter. Then, based on this exact T–S fuzzy representation, multiobjective $$H_{2}/H_{\infty }$$ MPPT controller is designed to minimize concurrently the $$H_{2}$$ tracking error and $$H_{\infty }$$ disturbance attenuation level for the PV system. A specified T–S reference model is constructed to provide the desired trajectory which must be tracked. An MPP searching algorithm is also added in the global MPPT structure to generate the optimal PV current which is considered as input control for the T–S reference model. Finally, simulation results are given to illustrate the optimal tracking performance of the proposed fuzzy controller even when rapidly changing climatic conditions.

Design of a Stability Augmentation System for an Unmanned Helicopter Based on Adaptive Control Techniques

The task of control of unmanned helicopters is rather complicated in the presence of parametric uncertainties and measurement noises. This paper presents an adaptive model feedback control algorithm for an unmanned helicopter stability augmentation system. The proposed algorithm can achieve a guaranteed model reference tracking performance and speed up the convergence rates of adjustable parameters, even when the plant parameters vary rapidly. Moreover, the model feedback strategy in the algorithm further contributes to the improvement in the control quality of the stability augmentation system in the case of low signal to noise ratios, mainly because the model feedback path is noise free. The effectiveness and superiority of the proposed algorithm are demonstrated through a series of tests.

Tracking control for switched nonlinear systems with multiple time-varying delays

This paper investigates the problem of output tracking control for a class of switched nonlinear systems with multiple time-varying delays. Combining average dwell-time with free weighting matrix methods, a new exponential stability criterion is derived for switched nonlinear systems, which considers the time-varying delays and the rates of time delays. Then, the state feedback tracking controller is given by solving a set of linear matrix inequalities (LMIs) to satisfy the H∞ model reference tracking performance. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Observer-based tracking control for a class of switched fuzzy systems with fast switching controller

Observer-based robust tracking control for a class of switched fuzzy (SF) systems with time delay is investigated in this paper. An SF system, which differs from the existing systems, is first employed to describe a non-linear system. Next, a fast switching controller consisting of a number of simple sub-controllers is proposed. The designed controller based on measured output instead of the state information integrates the advantages of both the linear and switching state-feedback controllers but eliminates their disadvantages. Tracking hybrid control schemes, which are based upon a combination of the H∞ tracking theory, fast switching control algorithm and switching law design, are developed such that the observer-based H∞ model reference tracking performance is guaranteed. Sufficient conditions for the solvability of the tracking control problem are given for the case in which the state of system is not available. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are performed to demonstrate the effectiveness of the proposed control design approach.

State Feedback Tracking Control for Indirect Field- oriented Induction Motor Using Fuzzy Approach

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed model reference tracking performance. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear system in the synchronous d-q frame rotating with field-oriented control strategy. Then, a fuzzy state feedback controller is designed to reduce the tracking error by minimizing the disturbance level. The proposed controller is based on a T-S reference model in which the desired trajectory has been specified. The inaccessible rotor flux is estimated by a T-S fuzzy observer. The developed approach for the controller design is based on the synthesis of an augmented fuzzy model which regroups the model of induction machine, fuzzy observer, and reference model. The gains of the observer and controller are obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation and experimental results are given to show the performance of the observer-based tracking controller.

Robust Switching Rule Design for Boost Converters with Uncertain Parameters and Disturbances

This paper is concerned with the design problem of robust switching rule for Boost converters with uncertain parameters and disturbances. Firstly, the Boost converter is modeled as a switched affine linear system with uncertain parameters and disturbances. Then, using common Lyapunov function approach and linear matrix inequality (LMI) technique, a novel switching rule is proposed such that the model reference tracking performance is satisfied. Finally, a simulation result is provided to show the validity of the proposed method.

Fuzzy-Model-Based Piecewise H∞ Decentralized Tracking Control of Discrete-time Networked Nonlinear Interconnected Systems

This paper investigates the problem of H ∞ decentralized tracking control of discrete-time nonlinear interconnected systems under unreliable communication links via Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model consists of N interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, the decentralized control scheme is adopted and the communication links between the subsystem and controller are assumed to be imperfect, that is, data packet dropouts occur intermittently, which is often the case in a network environment. The data loss is modelled as a random process which obeys a Bernoulli distribution. A piecewise state feedback decentralized controller is designed to stabilize the networked interconnected fuzzy system in the sense of mean square and also achieve a prescribed H ∞ model reference tracking performance based on a piecewise Lyapunov function. Moreover, the required H ∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs). A simulation example is given to show the effectiveness of this approach.

Tracking control for a class of switched non-linear systems with time-varying delay

This paper investigates the problem of tracking control for a class of switched non-linear systems with time-varying delay. Firstly, based on the average dwell time method, a new exponential stability criterion for a class of switched non-linear systems with time-varying delay is derived; it is shown that this new criterion can provide fewer conservative results than those in the existing references. Then, tracking control for the systems is investigated, and a kind of state feedback control law and switching signal are proposed to satisfy the H∞ model reference tracking performance. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

RobustH∞fuzzy observer-based tracking control design for a class of nonlinear stochastic Markovian jump systems

This paper investigates the stochastic H∞ tracking control problem for a class of nonlinear stochastic Markovian jump systems. The attention is focused on the design of a fuzzy observer-based fuzzy controller such that an H∞ model reference tracking performance is guaranteed for admissible disturbances. A sufficient condition is established to guarantee the existence of the desired robust controller, which is given in terms of a set of coupled matrix inequalities. Moreover, a novel decoupled method is proposed to transform the sufficient condition into some linear matrix inequality (LMI) form such that observer gains and control gains can be simultaneously obtained by solving a set of LMIs. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Tracking control for switched linear systems with time‐delay: a state‐dependent switching method

AbstractTracking control for switched linear systems with time‐delay is investigated in this paper. Based on the state‐dependent switching method, sufficient conditions for the solvability of the tracking control problem are given. We use single Lyapunov function technique and a typical hysteresis switching law to design a tracking control law such that the H∞ model reference tracking performance is satisfied. The controller design problem can be solved efficiently by using linear matrices inequalities. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. It is highly desirable that a non‐switched time‐delay system can not earn such property. Simulation example shows the feasibility and validity of the switching control law. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

H ∞ Fuzzy Tracking Control Design for Nonlinear Active Fault Tolerant Control Systems

Abstract This paper studies the problem of H∞ fuzzy tracking control design for nonlinear active fault tolerant control systems based on the Takagi and Sugeno fuzzy model. Two random processes with Markovian transition characteristics are introduced to model the system component fault process and the fault detection and isolation decision process used to reconfigure the control law, respectively. The random behavior of the FDI process is conditioned on the fault process state. The parallel distributed compensation scheme is employed for the control design. As a result, a closed-loop fuzzy system with two Markovian jump parameters is obtained. Based on a stochastic Lyapunov function, a sufficient condition for stochastic stability of the closed-loop fuzzy system with a guaranteed H∞ model reference tracking performance is first derived. A linear matrix inequality approach to the control design is then developed to reduce the effect of the external disturbance and reference input on tracking error as small as possible. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

Tracking Control for Switched Linear Systems with Time-Delay

Tracking control for switched linear systems with time-delay is investigated in this paper. Sufficient conditions for the solvability of the tracking control problem are given respectively for the cases that the state of system is measurable and unmeasurable. When the state is measurable, we design a switching control law to achieve the H∞ model reference tracking performance. When the state is not available, the design of a switching control law based on measured output instead of the state information is considered. Lyapunov function methods are utilized to the stability analysis and controller design for the switched linear systems with time-delay. By using linear matrix inequalities and convex optimization techniques, the controller design problem can be solved efficiently. The simulation examples show the validity of the switching control laws.

Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H/sub /spl infin// model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.