A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

A new solution approach to polynomial LPV system analysis and synthesis

Based on sum-of-squares (SOS) decomposition, we propose a new solution approach for polynomial LPV system analysis and control synthesis problems. Instead of solving matrix variables over a positive definite cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.Comment: Preliminary version of the paper "Direct data-driven control of constrained systems" published in the IEEE Transactions on Control Systems Technolog

Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

A virtual actuator approach for the secure control of networked LPV systems under pulse-width modulated DoS attacks

In this paper, we formulate and analyze the problem of secure control in the context of networked linear parameter varying (LPV) systems. We consider an energy-constrained, pulse-width modulated (PWM) jammer, which corrupts the control communication channel by performing a denial-of-service (DoS) attack. In particular, the malicious attacker is able to erase the data sent to one or more actuators. In order to achieve secure control, we propose a virtual actuator technique under the assumption that the behavior of the attacker has been identified. The main advantage brought by this technique is that the existing components in the control system can be maintained without need of retuning them, since the virtual actuator will perform a reconfiguration of the plant, hiding the attack from the controller point of view. Using Lyapunov-based results that take into account the possible behavior of the attacker, design conditions for calculating the virtual actuators gains are obtained. A numerical example is used to illustrate the proposed secure control strategy.Peer ReviewedPostprint (author's final draft

Linear parameter varying (LPV) based robust control of type-I diabetes driven for real patient data

Due to increasing prevalence of diabetes as well as increasing management costs, the artificial control of diabetes is a highly important task. Model-based design allows finding more effective solutions for the individual treatment of diabetic patients, but robustness is an important property that can be hardly guaranteed by the already developed individualized control algorithms. Modern robust control (known as H∞) theory represents an efficient possibility to solve robustness requirements in a general way based on exact mathematical formulation (Linear Matrix Inequalities) combined with knowledge-based expertise (through real patient data, uncertainty weighting functions can be formulated). When the difference between the nominal model and real patient dynamics is bounded and known, this approach becomes highly reliable. However, this requirement poses the greatest limitation since a model always represents an approximation of the complex physiological process. Consequently, the uncertainty formulation of the neglected dynamics becomes crucial as robust methods are very sensitive to them. In order to formulate them, large amount of real patient data and medical expertise is needed to cover the different life-style scenarios (especially the worst-case ones) that define the control space by the accumulated knowledge. On the other hand, H∞–based methods represent linear control techniques; hence their direct nonlinear application is important for a physiological process. The paper presents a roadmap of using modern robust control in diabetes focusing on nonlinear model-based interpretation: how the weighting functions should be selected based on (knowledge-based) medical expertise, the direct nonlinear applicability of the method taking additional advantage of the recently emerged Linear Parameter Varying (LPV) methodology, robust performance investigation and switching control possibilities. During the control characteristics discussion, the trade-off between the medical knowledge-based empiricism and exact control engineering formulation is introduced through different examples computed under MATLAB on real diabetic patient data

Robust stabilization of LPV systems with structured uncertainty using minimax controllers

This paper addresses a robust control scheduling scheme for uncertain linear parameter-varying systems with structured uncertainty. A gain-scheduled controller is proposed which employs a set of minimax optimal robust controllers and incorporates an interpolation rule to achieve continuity of the controller gain over a range of operating conditions. Novel weighted time-domain integral quadratic constraints are introduced to assist in the derivation of the controller. The key idea of the interpolation for the structured uncertainty case is to transform the parameterized algebraic Riccati inequalities into equivalent linear matrix inequalities. For every fixed value of the system parameter, the proposed controller guarantees robust stability and a certain bound on the worst-case performance of the corresponding uncertain closed loop system. Furthermore, a bound on the rate of parameter variations is obtained under which the closed loop LPV system is robustly stable. To obtain the proposed controller, a set of semi-definite programming problems are introduced; this enables an efficient numerical solution to the problem under consideration. © 2007 IEEE

Development of linear parameter varying control system for autonomous underwater vehicle

The development and application of Linear Parameter Varying (LPV) control system for robust longitudinal control system on an Autonomous Underwater Vehicle (AUV) are presented. The LPV system is represented as Linear Fractional Transformation (LFT) on its parameter set. The LPV control system combines LPV theory based upon Linear Matrix Inequalities (LMIs) and - synthesis to form a robust LPV control system. The LPV control design is applied for a pitch control of the AUV to fulfill control design criteria on frequency and time domain. The final closed-loop system is tested for robust stability throughout the operational envelope