Switching Linear Parameter-varying Research Articles

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

SummaryThis paper proposes a set‐membership state estimation method for Switched Linear Parameter Varying (SLPV) systems subject to unknown but bounded parametric uncertainties, disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed at every time iteration. The size of this zonotope is designed to be convergent and bounded by satisfying ‐radius‐based and Average Dwell Time (ADT) conditions that are formulated in the Linear Matrix Inequality (LMI) framework. An extension of the state estimation method is presented to address the fault/disturbance estimation problem for SLPV systems. By using the state augmentation technique, the fault/disturbance estimation problem is transformed into a state estimation problem of the generated augmented descriptor switched LPV system. An application to vehicle lateral dynamics fault estimation is used for assessment purposes. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods.

Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks

This work studies the finite-time control problem for discrete-time nonlinear Markov switching linear parameter varying (LPV) systems with denial-of-service (DoS) attacks. The aperiodic DoS attacks are introduced into the systems with partially unknown transition probabilities. First, considering the characteristics of aperiodic DoS attacks, an appropriate feedback controller is designed according to that whether it is attacked or not. Furthermore, the finite-time stability criteria of closed-loop system are derived by means of iterative technique and multiple Lyapunov functions. Finally, a turbofan engine model is taken as an example to verify the effectiveness and feasibility of the proposed finite-time control method.

Design of Smooth Switching LPV Controller Based on Coprime Factorization and H∞ Performance Realization

This paper discusses the problem of designing smooth switching control based on the coprime factorization method. Aiming at the instantaneous chattering phenomenon generated by the linear parameter varying (LPV) controller during the switching moment, the moving region of the gain-scheduling variables is divided into a specified number of local subregions with overlapped region. Riccati inequality is used to solve the central controller for $H_{\infty} $ performance. The Youla free parameters are designed using the coprime factorization for each parameter sub-region by considering the system’s global and local performance requirements. Youla free parameter switching is used to improve the smoothness of switching and suppress transient response disturbance. Finally, the effectiveness of the method is verified by a simulation example.

H∞ bumpless transfer reliable control of Markovian switching LPV systems subject to actuator failures

In this paper, the H∞ bumpless transfer reliable control problem of Markovian switching linear parameter-varying (LPV) systems subject to actuator failures is addressed. A bumpless transfer reliable control constraint is introduced to describe the transient performance for such systems. By the use of the parameter-dependent Lyapunov function approach to reduce control bumps generated by the Markovian switching, a reliable switching controller which is also parameter-dependent is constructed to attenuate external disturbances. A criterion checking the solvability of the H∞ bumpless transfer reliable control problem is provided. As an application, a turbofan-engine model is used to verify the validity of the proposed design method.

Switching linear parameter‐varying control with improved local performance and optimized switching surfaces

SummaryThis paper presents a novel approach to designing switching linear parameter‐varying (SLPV) controllers with improved local performance and an algorithm for optimizing switching surfaces to further improve the performance of the SLPV controllers. The design approach utilizes the weighted average of the local L2‐gain bounds (representing the local performance) as the cost function to be minimized, whereas the maximum of the local L2‐gain bounds (representing the worst‐case performance over all subsets) is bounded with a tuning parameter. The tuning parameter is useful for taking the trade‐off between the local performance and the worst‐case performance. An algorithm based on the particle swarm optimization is introduced to optimize the switching surfaces of an SLPV controller. The efficacy of the proposed SLPV controller design approach and switching surface optimization algorithm is demonstrated on both a numerical example and a physical example of air‐fuel ratio control of an automotive engine.

Smooth switching linear parameter-varying fault detection filter design for morphing aircraft with asynchronous switching

This article deals with the problem of fault detection filters design for morphing aircraft with asynchronous switching. Considering time delay and intermittent measurements in the network environment, the morphing aircraft can be modeled as a switched linear parameter-varying (LPV) system. There always exists asynchronous switching phenomenon owing to time delay and data missing, which will lead to performance degradation. The parameter-dependent filters are established to generate the residual signal. In order to ensure the transient response of the morphing aircraft, the smooth switching LPV fault detection filters are designed by dividing the whole scheduling parameter set into subsets with overlaps. Meanwhile, the stability and prescribed performance of the system are guaranteed by combining multiple Lyapunov functional method and mode-dependent average dwell time method. The existing conditions and solution of filters are derived by linear matrix inequalities. Furthermore, an automatic partition method is proposed for the convenience of designing process. Simulation in the end demonstrates the superiority and effectiveness of the proposed method.

Switching LPV controller design under uncertain scheduling parameters

This paper addresses the problem of designing output-feedback switching linear parameter-varying (LPV) controllers under inexact measurement of scheduling parameters. The switching LPV controllers are robustly designed so that the stability and L2-gain performance of the switched closed-loop system can be guaranteed even under controller switching determined by measured (not actual) scheduling parameters. As for the switching rules, both hysteresis switching and average-dwell-time (ADT) switching are considered. Solvability conditions for the controller design problem are expressed in terms of parameter-dependent linear matrix inequalities and nonconvex switching surface conditions, with a line search parameter. The nonconvex conditions can be convexified for hysteresis switching controller design by imposing practical validity constraints, and for ADT switching controller design by adding equality constraints on some of Lyapunov variables on the switching surfaces. The effectiveness of the proposed method is demonstrated with a numerical example.

Design of a switched robust control scheme for drug delivery in blood pressure regulation

A control algorithm based on switching robust controllers is presented for a Linear Parameter Varying (LPV) time-delay system modeling automatic infusion of vasodilator drug to regulate postsurgical hypertension. The system is scheduled along a measurable signal trajectory. The prospective controllers are robustly designed at various operating points forming a finite set of robust controllers and then a hysteresis switching is performed between neighboring robust controllers for a larger operating range of the LPV system. The stability of the switching LPV system for the entire operating range is ensured by providing a sufficient condition in terms of bound on the scheduling signal variation using the concept of dwell time. Simulation results are provided to verify the performance of the designed control scheme.

A systematic method of smooth switching LPV controllers design for a morphing aircraft

This paper is concerned with a systematic method of smooth switching linear parameter-varying (LPV) controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as an LPV system, whose scheduling parameter is the variation rate of the wing sweep angle. By dividing the scheduling parameter set into subsets with overlaps, output feedback controllers which consider smooth switching are designed and the controllers in overlapped subsets are interpolated from two adjacent subsets. A switching law without constraint on the average dwell time is obtained which makes the conclusion less conservative. Furthermore, a systematic algorithm is developed to improve the efficiency of the controllers design process. The parameter set is divided into the fewest subsets on the premise that the closed-loop system has a desired performance. Simulation results demonstrate the effectiveness of this approach.

Smooth switching linear parameter‐varying control for hypersonic vehicles via a parameter set automatic partition method

This study presents a systematic approach to design smooth switching linear parameter-varying (LPV) controllers for hypersonic vehicles (HVs). Considering the switched LPV model of HVs, the smooth switching controllers are designed by means of dividing the scheduling parameter set into subsets with overlaps and the controllers in the overlapped subsets are smoothly scheduled between controllers in adjacent subsets. A switching law without constraint on average dwell time is obtained which makes the conclusion less conservative. To divide the parameter set automatically, a novel set partition method, in which the selecting of datum vertex and the handling of unpartitioned subset are innovative, is proposed. The switching LPV controllers that achieve a desired performance are constructed efficiently by solving a convex optimisation problem. Simulation results for HVs demonstrate the effectiveness of the proposed smooth switching LPV controllers and parameter set division method.

Smooth switching LPV controller design for LPV systems

This paper presents a method to design a smooth switching gain-scheduled linear parameter varying (LPV) controller for LPV systems. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching, and one gain-scheduled LPV controller is assigned to each of the local subregions. For each switching subregion, a function interpolating two local LPV controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices. The smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities. To find a solution to the feasibility problem, an iterative descent algorithm which solves a series of convex optimization problems is proposed. The usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball-screw drive system.

Adaptive Observer for Switching Linear Parameter-Varying (LPV) Systems

In this paper, the problem of joint state and parameter estimation in switching Linear Parameter-Varying (LPV) systems is considered. The proposed solution relies on an adaptive observer, which is designed finding a solution to a system of Trilinear Matrix Inequalities (TMIs). It is shown that, under certain assumptions, the TMIs can be reduced to Linear Matrix Inequalities (LMIs) that can be solved using available software. An example of a four wheeled omnidirectional mobile robot subject to unknown offsets in the motor voltages is used to illustrate the efficiency of the proposed approach.

Air-Fuel Ratio Control of Spark Ignition Engines Using a Switching LPV Controller

The three way catalytic converter (TWC) is a critical component for the mitigation of tailpipe emissions of modern spark ignition internal combustion (IC) engines. Because the TWC operates effectively only when the air-fuel ratio is very close to stoichiometric, accurate control of the air-fuel ratio is required. This paper uses a switching linear parameter varying (LPV) controller to regulate the air-fuel ratio. For controller design purposes, the dynamics of the fuel path is modeled as a time-varying first-order plus dead time (FOPDT) model, varying with the engine operating point, i.e., engine speed and air flow. Large variation of the FOPDT model across the engine operating range leads to a conservative LPV controller. Therefore, the operating range is divided into smaller subregions, an individual LPV controller is designed for each, and the LPV controllers are then switched based on the operating point. The LPV controllers are found by solving a convex optimization problem with linear matrix inequalities (LMIs) which can be efficiently solved using available LMI techniques. The resulting closed-loop system has guaranteed performance over the operating range of the engine. Simulations show the improved air-fuel ratio regulation of the switching LPV controller over the engine's operating range compared to that of an H∞ controller which is scheduled based on air flow only as well as a non-switching LPV controller.

On switching [formula omitted] controllers for nuclear steam generator water level: A multiple parameter-dependent Lyapunov functions approach

Poor control of the steam generator (SG) water level in the secondary circuit of a nuclear power plant can lead to frequent reactor shutdowns. From the viewpoint of economic operation, it is critical to keep the water level of SG in well control. This paper presents a new framework for addressing this problem based on switching control to linear parameter varying (LPV) systems. A family of LPV controllers are designed, and each of them is suitable for a specific operating range. Under the admissible switching logic, the closed-loop system remains stable and achieves prescribed H ∞ performance in the entire operating range. The approach is based on multiple parameter-dependent Lyapunov functions, which is less conservative than the employment of a single Lyapunov function. The switching LPV control scheme is then applied to the level control problem.

On switching [formula omitted] controllers for a class of linear parameter varying systems

We consider switching H ∞ controllers for a class of linear parameter varying (LPV) systems scheduled along a measurable parameter trajectory. The candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable. We provide sufficient conditions to guarantee the stability of the switching LPV systems in terms of the dwell time and the average dwell time. Our results are illustrated with an example, where switching between two robust controllers is performed for an LPV system.

Switching LPV control designs using multiple parameter-dependent Lyapunov functions

In this paper we study the switching control of linear parameter-varying (LPV) systems using multiple parameter-dependent Lyapunov functions to improve performance and enhance control design flexibility. A family of LPV controllers is designed, each suitable for a specific parameter subregion. They are switched so that the closed-loop system remains stable and its performance is optimized. Two switching logics, hysteresis switching and switching with average dwell time, are examined. The control synthesis conditions for both switching logics are formulated as matrix optimization problems, which are generally non-convex but can be convexified under some simplifying assumptions. The hysteresis switching LPV control scheme is then applied to an active magnetic bearing problem.

Modeling and H//sub∞/ control for switched linear parameter-varying missile autopilot

This paper presents a new method for designing a gain-scheduled missile autopilot. The nonlinear missile dynamics are modeled as a switched linear parameter-varying (SLPV) system, as is also common for many hybrid system models. A gain-scheduled autopilot for the SLPV system is then designed using a new synthesis technique that is based on a nonsmooth dissipation framework. The proposed algorithm extends previously published Lyapunov-based LPV approaches in three important ways: the SLPV system can provide a more accurate model of the missile dynamics; the nonsmooth Lyapunov function used in the synthesis is a more general class of Lyapunov functions; and the gridding technique typically used to solve the synthesis can be eliminated from the problem. As a result, the new approach yields a reliable gain-scheduled autopilot with better performance than the LPV controllers available in the literature.