LPV decoupling for control of multivariable systems

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.     

Design of LPV observers for LPV time-delay systems: an algebraic approach

The design of reduced order observer for linear parameter varying (LPV) time-delay systems is addressed. Necessary conditions guaranteeing critical structural properties for the observation error dynamics are first provided through nonlinear algebraic matrix equalities. An explicit parametrisation of the family of observers fulfilling these necessary conditions is then derived. Finally, an approach based on linear matrix inequalities is provided and used to select a suitable observer within this family, according to some criterion; e.g. maximisation of the delay margin or guaranteed suboptimal ?₂-gain. Examples from the literature illustrate the efficiency of the approach.     

基于输出反馈的欠驱动TORA系统的有界输入控制

针对欠驱动TORA (Translational oscillations with a rotational actuator)系统, 设计了一种具有执行器饱和约束的输出反馈控制器.与其他现有方法相比, 本文方法不仅考虑了执行器饱和约束和速度信号不可测情形, 而且考虑了旋转小球可能存在的循环行为.具体而言, 首先根据TORA系统模型分析了TORA系统的控制目标; 随后, 构造了一种新颖的能量函数, 在此基础上设计了一种考虑执行器饱和约束的输出反馈控制器, 并通过严格的数学分析证明了闭环系统关于平衡点的稳定性; 最后, 借助数值仿真测试检验了所提控制器的控制性能, 并与已有方法进行了对比.仿真测试结果表明本文所提方法具有更好的控制性能.     

Stability and performance analysis of time‐delay LPV systems with brief instability

Linear parameter‐varying (LPV) systems provide a systematic framework for the study of nonlinear systems by considering a representative family of linear time‐invariant systems parameterized by system parameters residing in a compact set. The brief instability concept in such systems allows the linear system to be unstable for some trajectories of the LPV parameter set, so that instability occurs only for short periods of time. In the present paper, we extend the notion of brief instability to LPV systems with time delay in their dynamics. The results provide tools for the stability and performance analysis of such systems, where performance is evaluated in terms of induced ??₂‐gain (or so‐called ??_∞ norm). The main results of this paper illustrate that stability and performance conditions can be evaluated by examining the feasibility of parameterized sets of linear matrix inequalities (LMIs). Using the results of this paper, we then investigate analysis conditions to guarantee the asymptotic stability and ??_∞ performance of fault‐tolerant control (FTC) systems, in which instability may take place for a short period of time due to the false identification of the fault signals provided by a fault detection and isolation (FDI) module. The numerical examples are used to illustrate the qualification of the proposed analysis and synthesis results for addressing brief instability in time‐delay systems. Copyright © 2010 John Wiley & Sons, Ltd.     

基于观测器的LPV系统故障检测方法

针对一类线性参数变化(LPV)连续系统的故障检测问题,通过构造合适的输出观测器,获得残差生成器,并通过优化设计步骤,实现对干扰的有效抑制和对故障的灵敏检测。利用依赖参数的Lyapunov函数,在保证残差生成器稳定性的基础上,给出观测器存在的充分条件。应用投影定理,借助附加矩阵解除了基于参数的Lyapunov函数矩阵与系统矩阵的耦合,得到以线性矩阵不等式(LMI)形式表示的求解条件。对于参数变化系统,基于LMI的求解条件为无穷维问题,借助基函数和参数网格化方法,使其转变为可求解的问题。仿真结果表明,应用该方法可以在一定程度上抑制干扰,并能灵敏有效地实现故障检测。     

Robust Stability and Stabilization Criteria for Discrete Singular Time‐Delay LPV Systems

This paper is concerned with establishing robust stability and stabilization criteria for discrete singular time‐delay linear parameter varying (LPV) systems. Firstly, a robust stability criterion is obtained for this class of systems by a delay‐partition approach, and thereby a less conservative sufficient condition which guarantees discrete singular time‐delay LPV systems to be admissible is given. Secondly, a class of state feedback controllers for stabilizing discrete singular time‐delay LPV systems is designed. Finally, compared with existing results, the numerical results of several examples illustrate the effectiveness of the approach proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Multi‐objective H2/L2 performance controller synthesis for LPV systems

This paper provides a kind of new matrix inequalities formulation for multi‐objective H2/L2 performance controller synthesis of linear parameter varying systems. These new matrix inequalities enable us to parameterize controllers without involving the Lyapunov variables in the formulation. Taking advantage of this feature, we can readily design multiobjective controllers with non‐common parameter‐dependent Lyapunov variables and two adjustable scalars. Furthermore, to obtain possibly lower values of performance criteria, a linear matrix inequalities (LMI)‐based optimal problem is solved by using the grid of the space that is combined with these two scalars. Finally, a numerical example is included to illustrate the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous‐time, uncertain, gridded, linear parameter‐varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency‐domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst‐case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst‐case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.     

Delay-scheduled state-feedback design for time-delay systems with time-varying delays—A LPV approach

This paper is concerned with the synthesis of delay-scheduled state-feedback controllers which stabilize linear systems with time-varying delays. In this framework, it is assumed that the delay is approximately known in real-time and used in the controller in a scheduling fashion. First, a new model transformation turning a time-delay system into an uncertain LPV system is introduced. Using this transformation, a new delay-dependent stability test based on the so-called full block -procedure is developed and from this result, a new delay-dependent stabilization result is derived. Since the resulting LMI conditions depend polynomially on the parameters, a relaxation result is then applied in order to obtain a tractable finite set of finite-dimensional LMIs. The interest of the approach resides in (1) the synthesis of a new type of controller scheduled by the delay value which has a lower memory consumption than controllers with memory (since it is not necessary to store past values of the state), and (2) an easy consideration of uncertainties on the delay knowledge.     

Quantized filtering for Markovian jump LPV systems with intermittent measurements

This paper investigates the problem of quantized filtering for a class of discrete‐time linear parameter‐varying systems with Markovian switching under data missing. The measured output of the plant is quantized by a logarithmic mode‐independent quantizer. The data missing phenomenon is modeled by a stochastic variable. The purpose of the problem addressed is to design a full‐order filter such that the filtering error dynamics is stochastically stable and the prescribed noise attenuation level in the sense can be achieved. Sufficient conditions are derived for the existence of such filters in terms of parameterized linear matrix inequalities. Then the corresponding filter synthesis problem is transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is utilized to demonstrate the usefulness of the developed theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Control of nonstationary LPV systems

This paper considers control of nonstationary linear parameter-varying systems, and is motivated by interest in the control of nonlinear systems along prespecified trajectories. In the paper, synthesis conditions are derived for such systems using an operator theoretical framework with the ?₂ induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semi-definite programming problem. The paper concludes with an in-depth example on the control of a two-thruster hovercraft along an eventually periodic trajectory.     

Model predictive control of constrained LPV systems

This article considers robust model predictive control (MPC) schemes for linear parameter varying (LPV) systems in which the time-varying parameter is assumed to be measured online and exploited for feedback. A closed-loop MPC with a parameter-dependent control law is proposed first. The parameter-dependent control law reduces conservativeness of the existing results with a static control law at the cost of higher computational burden. Furthermore, an MPC scheme with prediction horizon ‘1’ is proposed to deal with the case of asymmetric constraints. Both approaches guarantee recursive feasibility and closed-loop stability if the considered optimisation problem is feasible at the initial time instant.     

Finite‐time control for LPV systems with parameter‐varying time delays and exogenous disturbances

In this paper, we consider the stability analysis and control synthesis of finite‐time boundedness problems for linear parameter‐varying (LPV) systems subject to parameter‐varying time delays and external disturbances. First, the concepts of uniform finite‐time stability and uniform finite‐time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter‐varying time delays finite‐time bounded, are presented by using parameter‐dependent Lyapunov–Krasovskii functionals and free‐weight matrix technologies. Moreover, on the basis of the results on the uniform finite‐time boundedness, the parameter‐dependent state feedback controllers are designed to finite‐time stabilize LPV systems. Both analysis and synthesis conditions are delay‐dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior‐point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Performance‐oriented quasi‐LPV modeling of nonlinear systems

Polytopic quasi–linear parameter‐varying (quasi‐LPV) models of nonlinear processes allow the usage linear matrix inequalities (LMIs) to guarantee some performance goal on them (in most cases, locally, over a so‐called modeling region). In order to get a finite number of LMIs, nonlinearities are embedded on the convex hull of a finite set of linear models. However, for a given system, the quasi‐LPV representations are not unique, yielding different performance bounds depending on the model choice. To avoid such drawback, earlier literature on the topic used annihilator‐based approaches, which require gridding on the modeling region, and nonconvex BMI conditions for controller synthesis; optimal performance bounds are obtained, but with a huge computational burden. This paper proposes building a model by minimizing the projection of the nonlinearities onto directions, which are deleterious for performance. For a small modeling region, these directions are obtained from LMIs with the linearized model. Additionally, these directions will guide the selection of the polytopic embedding's vertices. The procedure allows gridding‐free LMI controller synthesis, as in standard LPV setups, with a very reduced performance loss with respect to the aforementioned BMI+gridding approaches, at a fraction of the computational cost.     

带有界扰动的一类非线性系统的鲁棒控制

对带有界扰动的一类非线性系统进行了状态反馈控制设计. 当状态反馈控制律作用于该系统时, 系统的状态能够收敛到原点的一个小邻域内.     

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.     

Active Disturbance Rejection Control for Teleoperation Systems with Actuator Saturation

In this paper, stabilization of a nonlinear bilateral teleoperation system with time delays and actuator saturation is investigated via active disturbance rejection control (ADRC). An linear extended state observer is introduced to deal with the lumped system uncertainties. Lyapunov functions are given to prove the stabilization of the closed‐loop bilateral teleoperation system. Two Phantom Premium 1.5 HighForce (HF) robot manipulators are used in experiments to demonstrate the effectiveness of the proposed method in this paper.     

Distributed control of LPV systems over arbitrary graphs with communication latency

This paper focuses on spatially distributed control systems where the controller sensing and actuation topology is inherited from that of the plant. Specifically, this paper considers distributed systems composed of discrete‐time linear parameter‐varying subsystems interconnected over general graph structures. These distributed systems are subject to a communication latency of one sampling period, where the information sent by a subsystem at the current time step is received by the target subsystem at the next time step. Analysis and synthesis conditions are derived for control design in this setting using a parameter‐dependent Lyapunov approach with the ?₂‐induced norm as the performance measure. Fast and easy‐to‐implement algorithms are also provided for constructing the controller in real time. The techniques developed are finally applied to a leader‐follower formation problem with intermittent communications.     

Fault‐tolerant fusion‐based MPC with sensor recovery for constrained LPV systems

In this paper, we present a robust fault‐tolerant control scheme for constrained multisensor linear parameter‐varying systems, subject to bounded disturbances, that utilises multiple sensor fusion. The closed‐loop scheme consists of a tube model predictive control‐based feedback tracking controller and sensor‐estimate fusion strategy, which allows for the reintegration of previously faulty sensors. The active fault‐tolerant fusion‐based mechanism tracks the healthy‐faulty transitions of suitable residual variables by means of set separation and precomputed transition times. The sensor‐estimate pairings are then reconfigured based on available healthy sensors. Under the proposed scheme, robust preservation of closed‐loop system boundedness is guaranteed for a wide range of sensor fault situations. An example is presented to illustrate the performance of the fault‐tolerant control strategy.