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

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Model Reduction of Multi-Dimensional and Uncertain Systems

We present model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation (LFT) on a repeated scalar uncertainty structure. These reduction methods can be interpreted either as doing state order reduction for multi-dimensionalsystems, or as uncertainty simplification in the case of uncertain systems, and are based on finding solutions to a pair of Linear Matrix Inequalities (LMIs). A related necessary and sufficient condition for the exact reducibility of stable uncertain systems is also presented

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

Design of wide-area damping control systems for power system low-frequency inter-area oscillations

The recently developed robust control theories and wide-area measurementtechnologies make the wide-area real-time feedback control potentially promising. Theobjective of this research is to develop a systematic procedure of designing a centralizeddamping control system for power grid inter-area oscillations by applying wide-areameasurement and robust control techniques while putting emphasis on several practicalconsiderations.The first consideration is the selection of stabilizing signals. Geometric measuresof controllability/observability are used to select the most effective stabilizing signals andcontrol sites. Line power flows and currents are found to be the most effective inputsignals. The second consideration is the effects of time-delay in the communication ofinput/output signals. Time-delays reduce the efficiency of the damping control system. Insome cases, large delays can destabilize the system. Time-delays should be modeled inthe controller design procedure so that the resulting controller can handle a range of timedelays.In this work, time-delays are modeled by Padé Approximations and the delayuncertainty is described by Linear Fractional Transformations (LFT). The thirdconsideration is the controller robustness. The synthesis of the controller is defined as aproblem of mixed H2/H∞ output-feedback control with regional pole placement and isresolved by the Linear Matrix Inequality (LMI) approach. The controller designed byrobust control techniques has satisfactory performance in a wide range of operatingpoints. The fourth consideration is the efficiency of the controller designed by lineartechniques in realistic nonlinear discrete environments. A tuning process and nonlinearsimulations are used to modify the controller parameters to ensure the performance androbustness of the controller designed with linear techniques. The last consideration is theselection of PMU data reporting rates. The performance of controllers designed in the sdomainis tested in digital environments and proper PMU data reporting rates are selectedwith consideration of the effects of time-delay.The design procedure of wide-area damping systems is illustrated by three studysystems. The first study system is a two-area four-machine system. The second one is theNew England 39-bus 10-machine system. The last one is a 29-generator 179-bus studysystem, which is a reduced order model of the Western Electricity Coordinating Council(WECC) system

Design of parameter-scheduled state-feedback controllers using shifting specifications

In this paper,the problem of designing aparameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H2 control and H1 control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H2 control and shifting H1 control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such away that different values of the separameters imply different regions where the closed-loop poles are situated, or different performances in the H2 or H1 sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, oventhough the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.Peer ReviewedPostprint (published version

Variance-constrained control for uncertain stochastic systems with missing measurements

Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we are concerned with a new control problem for uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design an output feedback controller such that, for all admissible parameter uncertainties and all possible incomplete observations, the system state of the closed-loop system is mean square bounded, and the steady-state variance of each state is not more than the individual prescribed upper bound. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of some free parameters, which may be exploited to achieve further performance requirements. An illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach