A Survey of Output Feedback Robust MPC for Linear Parameter Varying Systems

For constrained linear parameter varying(LPV)systems,this survey comprehensively reviews the literatures on output feedback robust model predictive control(OFRMPC)over the past two decades from the aspects on motivations,main contributions,and the related techniques.According to the types of state observer systems and scheduling parameters of LPV systems,different kinds of OFRMPC approaches are summarized and compared.The extensions of OFRMPC for LPV systems to other related uncertain systems are also investigated.The methods of dealing with system uncertainties and constraints in different kinds of OFRMPC optimizations are given.Key issues on OFRMPC optimizations for LPV systems are discussed.Furthermore,the future research directions on OFRMPC for LPV systems are suggested.

An iterative algorithm for solving ill-conditioned linear least squares problems

Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.

Polytopic LPV modeling and gain-scheduled switching control for a flexible air-breathing hypersonic vehicle

A novel gain-scheduled switching control method for the longitudinal motion of a flexible air-breathing hypersonic vehicle （FAHV） is proposed. Firstly, velocity and altitude are selected as scheduling variables, a polytopic linear parameter varying （LPV） model is developed to represent the complex nonlinear longitudinal dynamics of the FAHV. Secondly, based on the obtained polytopic LPV model, the flight envelope is divided into four smaller subregions, and four gain-scheduled controllers are designed for these parameter subregions. Then, by the defined switching characteristic function, these gain-scheduled controllers are switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a given tracking error performance criterion. The condition of gain-scheduled switching controller synthesis is given in terms of linear matrix inequalities （LMIs） which can be easily solved by using standard software packages. Finally, simulation results show the effectiveness of the presented method.

Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.

Feedback Control for Ecosystem Management:The Case of Wolf-Elk-Hunting Dynamics in the US Mountain West

The purpose of this paper is to explore the promise of utilizing some relatively new feedback control techniques in ecosystem management. First, we set forth a basic ecological-economic model of a predator-prey-hunting system in which both the predator and prey have use(flow) and non-use(stock) value and when the predator can inflict transboundary damages. We then use new data from the US Mountain West to show how a particular feedback approach—linear parameter-varying(LPV) control—can be utilized in this context. Our LPV model is able to quantify the cost of managing disturbances that inevitably arise as a manager tries to keep the actual path of the system "close" to its optimum. The results suggest management strategies in mountain ecosystems that feature large, mammalian carnivores.

Identification of LPV Models with Non-uniformly Spaced Operating Points by Using Asymmetric Gaussian Weights

In this paper, asymmetric Gaussian weighting functions are introduced for the identification of linear parameter varying systems by utilizing an input-output multi-model structure. It is not required to select operating points with uniform spacing and more flexibility is achieved. To verify the effectiveness of the proposed approach, several weighting functions, including linear, Gaussian and asymmetric Gaussian weighting functions, are evaluated and compared. It is demonstrated through simulations with a continuous stirred tank reactor model that the oroposed aonroach nrovides more satisfactory aonroximation.

HOSVD-based LPV modeling and mixed robust H_2/H_∞ control design for air-breathing hypersonic vehicle

This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.

LVP Modeling and Dynamic Characteristics Prediction of A Hydraulic Power Unit in Deep-Sea

A hydraulic power unit （HPU） is the driving ＂heart＂ of deep-sea working equipment. It is critical to predict its dynamic performances in deep-water before being immerged in the seawater, while the experimental tests by simulating deep-sea environment have many disadvantages, such as expensive cost, long test cycles, and difficult to achieve low-temperature simulation, which is only used as a supplementary means for confirmatory experiment. This paper proposes a novel theoretical approach based on the linear varying parameters （LVP） modeling to foresee the dynamic performances of the driving unit. Firstly, based on the varying environment features, dynamic expressions of the compressibility and viscosity of hydranlic oil are derived to reveal the fluid performances changing. Secondly, models of hydraulic system and electrical system are accomplished respectively through studying the control process and energy transfer, and then LVP models of the pressure and flow rate control is obtained through the electro-hydraulic models integration. Thirdly, dynamic characteristics of HPU are obtained by the model simulating within bounded closed sets of varying parameters. Finally, the developed HPU is tested in a deep-sea imitating hull, and the experimental results are well consistent with the theoretical analysis outcomes, which clearly declare that the LVP modeling is a rational way to foresee dynamic performances of HPU. The research approach and model analysis results can be applied to the predictions of working properties and product designs for other deep-sea hydraulic pump.

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional（LKF）, sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities（LMIs）. The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

LPV Flight Dynamics Modeling for Turbulent Wind Special Flight Analysis

A linear parameter varying(LPV)flight dynamics model(FDM)is proposed to cater for atmospheric disturbance analysis in special flight conditions.A novel FDM which is capable of addressing the influence of turbulent wind is derived under the wind frame.An affine parameter dependent LPV model with wind effects is built based on function substitution method.The optimal solution for the decomposing function of the LPV FDM is obtained by genetic algorithm(GA).The analysis of dynamic response indicates that the genetic-optimized LPV FDM approximates the nonlinear FDM evidently,since it identifies the instantaneous dynamics and flight states varying in a wide range.The simulations of approach and landing against wind shear show that the genetic-optimized LPV FDM captures the instantaneous dynamic response when flying through turbulent wind,indicating that the LPV model can be further applied to turbulent wind special flight analysis and control law design.

Identification of LPV system using locally weighted technique

The problem of linear parameter varying （LPV） system identification is considered based on the locally weighted technique which provides estimation of the LPV model parameters at each distinct data time point by giving large weights to measurements that are ＂close＂ to the current time point and small weights to measurements ＂far＂ from the current time point. Issues such as choice of distance function, weighting function and bandwidth selection are discussed. The developed method is easy to implement and simulation results illustrate its efficiency.

A Shortest Path Algorithm for Multi-stage Network with Linear Parameter

In this paper, we give the shortest path algorithm for multi-stage network with a linear parameter, and study its complexity.

The concise fractional Fourier transform and its application in detection and parameter estimation of the linear frequency-modulated signal

A concise fractional Fourier transform （CFRFT） is proposed to detect the linear frequency-modulated （LFM） signal with low signal to noise ratio （SNR）. The frequency axis in time-frequency plane of the CFRFT is rotated to get the spectrum of the signal in different an- gles using chirp multiplication and Fourier transform （FT）. For LFM signal which distributes as a straight line in time-frequency plane, the CFRFT can gather the energy in the corresponding angle as a peak and improve the detection SNR, thus the LFM signal of low SNR can be de- tected. Meanwhile, the location of the peak value relates to the parameters of the LFM signal. Numerical simulations and experimental results show that, the proposed method can be used to efficiently detect the LFM signal masked by noise and to estimate the signal＇s parameters accurately. Compared with the conventional fractional Fourier transform （FRFT）, the CFRFT reduces the transform complexity and improves the real-time detection performance of LFM signal.

Classical state feedback controller for nonlinear systems using mean value theorem： closed Ioop-FOC of PMSM motor application

The problem of state feedback controllers for a class of Takagi-Sugeno （T-S） Lipschitz nonlinear systems is investigated. A simple systematic and useful synthesis method is proposed based on the use of the differential mean value theorem （DMVT） and convex theory. The proposed design approach is based on the mean value theorem （MVT） to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients as linear parameter varying （LPV） systems. Using the Lyapunov theory, stability conditions are obtained and expressed in terms of linear matrix inequalities （LMIs）. The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for closed loop-field oriented control （CL-FOC） of permanent magnet synchronous machine （PMSM） drives is demonstrated through an illustrative simulation for the proof of these approaches. Furthermore, an extension for controller design with parameter uncertainties and perturbation performance is discussed.

Adaptive bolus chasing computed tomography angiography by a local linear time and space parameter varying model:modeling,control,identification,and experimental results

A high contrast to noise ratio(CNR)is always desirable for contrast-enhanced computed tomography angiography(CTA).To ensure a high CNR of the vascular images in CTA and potentially reduce the radiation exposure and contrast usage,an adaptive bolus chasing method is proposed and evaluated compared to the existing constant-speed method.The proposed method is based on a local time and space parameter varying model of the contrast bolus.Optimal scan time for the next segment of the vasculature is estimated and predicted in real time and guides the computed tomography(CT)scanner table movement that guarantees that each segment of the vasculature is scanned with the maximum possible enhancement.Simulations and experimental results show that the proposed bolus chasing method outperforms the conventional constant-speed method substantially.

Design of Adaptive Robust Guaranteed Cost Controller for Wind Power Generator

According to the increasing requirement of the wind energy utilization and the dynamic stability in the variable speed variable pitch wind power generation system, a linear parameter varying （LPV） system model is established and a new adaptive robust guaranteed cost controller （AGCC） is proposed in this paper. First, the uncertain parameters of the system are estimated by using the adaptive method, then the estimated uncertain parameters and robust guaranteed cost control method are used to design a state feedback controller. The controller s feedback gain is obtained by solving a set of linear matrix inequality （LMI） constraints, such that the controller can meet a quadratic performance evaluation criterion. The simulation results show that we can realize the goal of maximum wind energy capture in low wind speed by the optimal torque control and constant power control in high wind speed by variable pitch control with good dynamic characteristics, robustness and the ability of suppressing disturbance.

A Robust Control Strategy to Improve Transient Stability for AC-DC Interconnected Power System with Wind Farms

In view of the variable parameters that affect the transient stability of electromagnetic torque and mechanical torque balance in AC-DC system,and the uncertainty of wind power in large-scale interconnection of wind farm.This paper proposes a linear parameter varying(LPV)robust feedback control method for transient stability of interconnected systems.The proposed LPV robust feedback control method uses the DC channel power control and the mechanical power in the interconnected system as the control target to improve the transient stability of the interconnected system with wind farm channel.Firstly,aiming at the strong nonlinear characteristics of the interconnected system,the power balance and the wind power output uncertainty in the transient process,the transient process is designed as a linear model of variable parameters.Then,the H∞robust output feedback controller is designed according to the LPV model.The transient stability control strategy topology and transfer function of the interconnected system are proposed.Finally,the proposed scheme is verified by an interconnected system formed by four equal-value grids through AC and DC lines in a digital simulation platform.The results show that the LPV robust feedback control model proposed in this paper has better response characteristics and transient stability control effects for interconnected systems with wind power weak sendingend system.

On modeling and control of a flexible air-breathing hypersonic vehicle based on LPV method

This article develops a polytopic linear pa- rameter varying （LPV） model and presents a non-fragile H2 gain-scheduled control for a flexible air-breathing hypersonic vehicle （FAHV）. First, the polytopic LPV model of the FAHV can be obtained by using Jacobian linearization and tensor-product （TP） model transfor- mation approach, simulation verification illustrates that the polytopic LPV model captures the local nonlinear- ities of the original nonlinear system. Second, based on the developed polytopic LPV model, a non-fragile gain- scheduled control method is proposed in order to reduce the fragility encountered in controller implementation, a convex optimisation problem with linear matrix in- equalities （LMIs） constraints is formulated for designing a velocity and altitude tracking controller, which guar- antees//2 control performance index. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.

Gain self-scheduled H_∞ control for morphing aircraft in the wing transition process based on an LPV model

This article investigates gain self-scheduled H 1 robust control system design for a tailless fold- ing-wing morphing aircraft in the wing shape varying process. During the wing morphing phase, the aircraft＇s dynamic response will be governed by time-varying aerodynamic forces and moments. Nonlinear dynamic equations of the morphing aircraft are linearized by using Jacobian linearization approach, and a linear parameter varying （LPV） model of the morphing aircraft in wing folding is obtained. A multi-loop controller for the morphing aircraft is formulated to guarantee stability for the wing shape transition process. The proposed controller uses a set of inner-loop gains to provide stability using classical techniques, whereas a gain self-scheduled H 1 outer-loop controller is devised to guarantee a specific level of robust stability and performance for the time-varying dynamics. The closed-loop simulations show that speed and altitude vary slightly during the whole wing folding process, and they converge rapidly after the process ends. This proves that the gain self-scheduled H 1 robust controller can guarantee a satisfactory dynamic performance for the morphing aircraft during the whole wing shape transition process. Finally, the flight control system＇s robustness for the wing folding process is verified according to uncertainties of the aerodynamic parameters in the nonlinear model.

Direct thrust control for multivariable turbofan approach

A novel turbofan Direct Thrust Control(DTC)architecture based on Linear ParameterVarying(LPV)approach for a two-spool turbofan engine thrust control is proposed in this paper.Instead of transforming thrust command to shaft speed command and pressure ratio command,the thrust will be directly controlled by an optimal controller with two control variables.LPV model of the engine is established for the designing of thrust estimator and controller.A robust LPV H∞filter is introduced to estimate the unmeasurable thrust according to measurable engine states.The thrust estimation error system is proved to be Affinely Quadratically Stable(AQS)in the whole parameter box with a prescribed H∞performance indexγ.Due to the existence of overdetermined equations,the solving of controller parameters is a multi-solution problem.Therefore,Particle Swarm Optimization(PSO)algorithm is used to optimize the controller parameters to obtain satisfactory control performance based on the engine’s LPV model.Numerical simulations show that the thrust estimator can acquire smooth and accurate estimating results when sensor noise exists.The optimal controller can receive desired control performance both in steady and transition control tasks within the engine working states above the idle,verifying the effectiveness of the proposed DTC architecture’s application in thrust direct control problem.