Switched Linear Parameter-varying Systems Research Articles

Finite-time bumpless transfer control problem for switched LPV systems with guaranteed switching frequency

For the switched linear parameter-varying (LPV) systems, the finite-time bumpless transfer control (FTBTC) issue is addressed by utilising the parameter-dependent multiple piecewise Lyapunov function method. First, for the switched LPV systems, a finite-time bumpless transfer performance is proposed, which only demands that bumpless transfer inequation holds in the activated interval in place of entire intervals. Second, a switching law depending on external parameters, system state, dwell time is designed to guarantee switching frequency. Third, a time-varying switching controller is designed, under which a solvable condition of the FTBTC issue is presented. It allows the FTBTC issue of each subsystem to be unsolvable. Finally, an aero-engine model is established to confirm the availability of the proposed scheme.

An Integrated Design Approach for Fault-Tolerant Control of Switched LPV Systems With Actuator Faults

In this article, the active fault-tolerant control (FTC) issue is addressed for switched linear parameter varying (LPV) systems in the discrete-time domain. A general dwell-time property is considered in the system setup to govern the switching dynamics between subsystems, and the parameter variations within each subsystem are subjected to the polytopic uncertainties. The main innovation of the developed active FTC approach is to effectively cope with switched LPV models where both input and output matrices can be of parameter-dependent form. By virtue of a novel Lyapunov function approach depending on both dwell time and parameter variations, the joint task for fault detection, estimation, and compensation is fulfilled via an integrated design scheme. The input-to-state stability (ISS) conditions are obtained for the augmented faulty system satisfying a given ISS-gain performance requirement. The desired effect of active FTC is achieved in three critical steps: 1) construct a fault detection filter in terms of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> norm; 2) design an observer-based estimator to estimate the system states and faults simultaneously; and 3) synthesize a fault-tolerant controller with the LPV structure using the estimated states and faults for fault compensation. Finally, an application example is utilized to illustrate the efficiency and availability of the proposed control approach.

Zonotopic Set-Membership State Estimation for Switched LPV Systems

This paper addresses the state estimation problem for switched discrete-time Linear Parameter Varying (LPV) systems with mensurable and unmeasurable scheduling parameters. A zonotopic switched polytopic state estimator, considering parameter uncertainty, is proposed based on a Set-Membership Approach (SMA). Taking Average Dwell Time (ADT) into account, a new criterion is proposed to guarantee the convergence of the estimation. An application to vehicle lateral dynamics state estimation is used as case study. Simulation results reveal the effectiveness of the proposed algorithm and demonstrate advantages over the existing methods.

Fault-Tolerant Control of Switched LPV Systems: A Bumpless Transfer Approach

For switched linear parameter-varying (LPV) systems with possible actuator failures, the parameter-dependent multiple piecewise Lyapunov function is constructed to handle the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> bumpless transfer fault-tolerant control problem. First, a generalized bumpless transfer concept is presented for switched LPV systems to describe the transient performance, for which only the local bumpless transfer condition is required. Second, an event-triggered switching law, depending on the system states, external parameters, and dwell time, is designed to ensure a time span among adjacent switchings. Third, a solvability condition of the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> bumpless transfer fault-tolerant control problem is developed. A family of time-driven switching controllers with bumpless transfer constraint and fault-tolerant requirement are also designed. Finally, an application example of an aero-engine is given to verify the effectiveness of the developed methods.

Finite-time switched LPV control of quadrotors with guaranteed performance

This paper presents a novel finite-time switched linear parameter-varying (LPV) control method for quadrotors subject to large attitude angles and external disturbances. For controller design purpose, both the nonlinear attitude and position dynamics are modeled as a switched LPV system without the idealized assumption of linear approximation. A family of polytopic LPV controllers are designed and each of them is available for a specific parameter subspace of the quadrotor system. The persistent dwell time (PDT) switching logic is adopted to govern the switching behavior among these controllers, which is capable of addressing more general parameter variations than typically used dwell time or average dwell time. By applying an extended cost function, the established switched LPV control method ensures a guaranteed finite-time H∞/LQR performance for the error-tracking system of quadrotors. The advantages of the proposed method are demonstrated via simulations.

Switched linear parameter‐varying tracking control for quadrotors with large attitude angles and time‐varying inertia

AbstractThis paper is concerned with large‐angle attitude tracking control for quadrotors in the presence of time‐varying inertia and external disturbances using a switched linear parameter‐varying (LPV) system method. The attitude system of the quadrotor is divided into two parts, that is, the outer attitude‐angle loop and inner angular‐velocity loop. A feedback linearization controller is designed in the outer loop to generate the desired angular velocities. In the inner loop, the nonlinear quadrotor dynamics with time‐varying inertia is approximated by a switched LPV system that consists of a series of LPV models. The persistent dwell time (PDT) switching logic is adopted to describe the fast and slow switches coexist among these LPV models. Then, both the continuous‐time state‐feedback and dynamic output‐feedback controllers are designed, which ensure the globally uniformly asymptotically stability and external disturbance attenuation performance of the attitude tracking error system. Finally, the effectiveness of the proposed tracking control method of quadrotors is validated with an example.

On the robustness of cyber-physical LPV systems under DoS attacks

This paper addresses the state-feedback control problem for discrete-time linear parameter-varying (LPV) systems under the presence of exogenous disturbance and denial of service (DoS) attacks. The problem is modeled as a switched LPV system where the number of modes is connected with the number of consecutive DoS attacks. Three strategies are proposed, the use of a full packet of controllers, the hold strategy, and the zero-input strategy. The robustness of each scenario is assessed by using the H∞ performance from the exogenous input to the output of the switched LPV system. The employed Lyapunov function avoids the use of a duality argument to get the conditions. Additionally, in each considered scenario, it is possible to design, robust controllers, LPV controllers, and rational controllers to stabilize the system. Numerical experiments illustrate the behavior of the proposed strategies in different scenarios, confirming the effectiveness of the proposed method in providing robustness even under DoS attacks.

Optimal control of aero‐engine systems based on a switched LPV model

AbstractIn this paper, an optimal control problem for aero‐engines based on a switched linear parameter varying (LPV) model is solved. Firstly, according to the change of external flight conditions, a switched LPV model with different altitudes and Mach numbers is established for aero‐engines. Then, since the optimal control of the parameter‐dependent switched system cannot be dealt with by traditional methods, we thus propose an optimal control method for the switched LPV system, which includes solving the optimal continuous inputs and the optimal switching instants. Finally, simulations and a hardware in‐the‐loop test of an aero‐engine control system are presented to verify the effectiveness and superiority for the proposed optimal control method.

Dissipativity for Switched LPV Systems and Its Application: A Parameter and Dwell Time-Dependent Multiple Storage Functions Method

This paper investigates dissipativity and related properties for switched linear parameter-varying (LPV) systems by using parameter and dwell time-dependent multiple storage functions, which are different from traditional multiple storage functions because of the introduction of the external parameters into the storage functions construction. First, a novel concept relating to external parameters is proposed to describe the overall dissipativity property of switched parameter-varying systems in the absence of the conventional dissipativity property of the subsystems. Second, a state and parameter-triggered and time-driven switching laws is proposed, which avoids Zeno behavior by guaranteeing a dwell time among the adjacent switching. Third, several classic forms of dissipativity are addressed. For passivity and $ {L_{2}}$ -gain, under certain negative output feedback asymptotic stability is guaranteed with the aid of asymptotic zero state detectability. Finally, the effectiveness of the proposed result is illustrated by its application to a speed adjustment problem of an aero-engine.

Polytopic Model Weighted H∞ Output Feedback Control of Switched Lpv System Based on Mdadt

This paper provides and validates a class of weighted H∞ output feedback controllers of switched LPV (Linear Parameter Varying) systems based on the MDADT (Modal Dependent Average Dwell Time) method. First of all, the article uses a multi-lyapunov function to convert the linear parameter varying system into a polytopic model, and designs a switching law that can guarantee the system to be globally uniform and exponentially stable on the MDADT method. It can be shown that when the state is stable and can be measured in real time, the switching law and weighted H∞ controllers for each subsystem under the MDADT limit can be calculated. Finally, a numerical example is given to verify the feasibility of this method and the stability of the switched LPV system.

Event triggered control for a switched LPV system with applications to aircraft engines

The event triggered control for a kind of switched linear parameter varying (LPV) systems is studied. The authors present two event triggering schemes for such systems, depending on whether the controllers are pre-designed or to be designed. In the cases of pre-designed controllers, they present the state and parameters dependent event triggering scheme. In the case of controllers to be designed, two event triggering schemes are given, depending on the state and parameters, respectively. The feasible linear matrix inequality (LMI) conditions are given for designing controllers and event triggering thresholds. The minimum of trigger time intervals is obtained as a positive number. Under the average dwell time switching mechanism, the switched parameter-varying system is exponentially stable. Finally, the validity of designed approaches is verified through a simulation example for an aircraft engine model.

Feedback passification for switched LPV systems via a state and parameter-triggered switching with dwell time constraints

This paper addresses the issues of passivity and passification for switched linear parameter-varying (LPV) systems using multiple parameter-dependent storage functions which are not a simple extension of traditional multiple storage functions because of the introduction of the external parameter. Firstly, a state and parameter-triggered switching strategy is designed. The switching law is different from the existing results, which guarantees a dwell time constraint even when all subsystems are not passive. Then, an analysis condition ensuring the passivity for switched LPV systems is presented with the aid of the switching law. When passivity cannot be guaranteed by the designed switching law, the dual design scheme of parameter-dependent controllers for subsystems and a switching law is constructed to solve the problem of feedback passification for the switched LPV system. Finally, an aero-engine control example is provided to demonstrate the feasibility of the theoretical results.

H∞ bumpless transfer for switched LPV systems and its application

ABSTRACTIn this paper, the approach of the control bumps limitation is generalised and applied to the problem of H∞ bumpless transfer for a class of switched linear parameter-varying (LPV) systems. The H∞ bumpless transfer problem is to design a controller with the amplitude limitation and a parameter and modes-dependent switching law to reduce control bumps of the switched LPV systems and satisfy an H∞ performance index. The key point is to guarantee the bumps limitation constraint of the switched LPV systems by dual design of controllers and a switching law, even though the constraint for each subsystem is unsatisfied. First, a set of switching signals depending on parameters and modes are designed, and a family of switched LPV controllers with the bumps limitation objective are developed via multiple parameter-dependent Lyapunov functions. Then, a sufficient condition ensuring the H∞ bumpless transfer performance for a switched LPV system is presented in the format of numerically tractable conditions. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to the control design of an aero-engine.

Time‐weighted MR for switched LPV systems via balanced realisation

A new model reduction (MR) method is developed for continuous-time switched linear parameter-varying (LPV) systems based on time-weighted gramians. Using time-weighted energy functionals and parameter-independent multiple Lyapunov functions, the time-weighted controllability and observability gramians are obtained. With a balanced transformation matrix optimally derived, the authors show that a balanced realisation can be achieved for the original switched LPV systems. A series of low-order models for different weighting factors are yielded by state truncation or singular perturbation techniques. The reduced-order models can preserve the stability. The feasibility and effectiveness of the proposed MR method are illustrated by two examples including a three spring-mass system.

Output regulation for switched LPV systems with Markovian jump parameters and its application

This paper deals with the output regulation problem for switched linear parameter-varying (LPV) systems with Markovian jump parameters under partially unknown transition probabilities. Our aim is to find a feedback controller, such that the regulated output asymptotically converges to zero and the closed-loop system is stochastically stable when [Formula: see text]. Firstly, we give sufficient conditions for the solvability of the output regulation problem. Then, using the parameter-dependent stochastic Lyapunov functions method, we design a state feedback controller and a regulation observer-based controller for individual switched LPV subsystems to solve the output regulation problem for the given systems. Finally, the output regulation problem of an aero-engine model is investigated, and the effectiveness of the proposed control design scheme is illustrated by its application to a speed regulation problem of an aero-engine.

Simultaneous fault detection and control for switched LPV systems with inexact parameters and its application

ABSTRACTThis paper investigates the simultaneous fault detection and control problem for a switched linear parameter-varying (LPV) system. The inexact scheduling parameter-dependent fault detection filters and controllers are designed based on the output framework. To realise the detection and control goals, the inexact scheduling parameter-dependent sufficient LMI conditions are obtained by using multiple Lyapunov functions technique. A mode-dependent average dwell-time switching method is used, which is less strict than the general average dwell-time switching method. Simulation results on an aero-engine model show the feasibility and validity of the designed scheme.

Data assignment and parameter adaptation for Switched LPV system estimation

Most of the studies related to the special class of systems called Switched Linear Parameter Varying (LPV) systems are considered in terms of multi-Lyapunov analysis and control design. This issue attracted a lot of attention since a single controller with acceptable performance may not exist for LPV systems with a large parameter variation region. Even more, the mode sequence has mostly considered a priori known and independent of the system parameters and the regression vector. In this paper, a methodology is investigated for the estimation of the discrete state and parameters for a class of discrete-time (DT) Switched LPV systems. A clustering technique based on an interpretation of belief functions combined to the least squares algorithm is used to estimate the scheduled parameters. The simulation example demonstrates the effectiveness of the identification method by giving results in terms of discrete state estimation, parameter estimation and output fit.

Formula omitted] model reduction of switched LPV systems via semi-time-varying reduced-order model

This paper investigates the problem of model reduction for a class of switched linear parameter varying (LPV) systems with persistent dwell-time (PDT) switching property. The PDT switching generalizes the dwell-time and average dwell-time switching that are commonly concerned in the existing literature. To reduce the original high-order model with less conservatism, the constructed reduced-order model is both parameterized and semi-time-varying such that the model error system is uniformly stable over the PDT switching and guarantees an error performance in H∞ sense. A numerical example is used to verify the validity and advantage of the theoretical results.

Model reference adaptive control for switched LPV systems and its application

In this study, the problem of model reference adaptive control (MRAC) for switched linear parameter-varying (LPV) systems with parametric uncertainties is investigated. First, a switched LPV controller with the adaptive laws is designed. Then, the proposed LPV controller with the adaptive laws guarantees that all the closed-loop system signals remain bounded under a class of switching signals with average dwell time, and the state tracking error converges to a small ball centred at the origin whose radius can be made arbitrarily small by appropriately choosing the design parameters. Finally, a practical example about MRAC for a turbofan-engine is given to demonstrate the validity of the main results.

H∞ output tracking control for a class of switched LPV systems and its application to an aero‐engine model

SummaryThis paper aims to investigate the problem of H∞ output tracking control for a class of switched linear parameter‐varying (LPV) systems. A sufficient condition ensuring the H∞ output tracking performance for a switched LPV system is firstly presented in the format of linear matrix inequalities. Then, a set of parameter and mode‐dependent switching signals are designed, and a family of switched LPV controllers are developed via multiple parameter‐dependent Lyapunov functions to enhance control design flexibility. Even though the H∞ output tracking control problem for each subsystem might be unsolvable, the problem for switched LPV systems is still solved by the designed controllers and the designed switching law. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an H∞ speed adjustment problem of an aero‐engine. Copyright © 2016 John Wiley &amp; Sons, Ltd.