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

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

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

Robust multivariable controller design for flexible spacecraft

Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large

Decentralized event-triggered control over wireless sensor/actuator networks

In recent years we have witnessed a move of the major industrial automation providers into the wireless domain. While most of these companies already offer wireless products for measurement and monitoring purposes, the ultimate goal is to be able to close feedback loops over wireless networks interconnecting sensors, computation devices, and actuators. In this paper we present a decentralized event-triggered implementation, over sensor/actuator networks, of centralized nonlinear controllers. Event-triggered control has been recently proposed as an alternative to the more traditional periodic execution of control tasks. In a typical event-triggered implementation, the control signals are kept constant until the violation of a condition on the state of the plant triggers the re-computation of the control signals. The possibility of reducing the number of re-computations, and thus of transmissions, while guaranteeing desired levels of performance makes event-triggered control very appealing in the context of sensor/actuator networks. In these systems the communication network is a shared resource and event-triggered implementations of control laws offer a flexible way to reduce network utilization. Moreover reducing the number of times that a feedback control law is executed implies a reduction in transmissions and thus a reduction in energy expenditures of battery powered wireless sensor nodes.Comment: 13 pages, 3 figures, journal submissio

Mathematical modeling and vertical flight control of a tilt-wing UAV

This paper presents a mathematical model and vertical flight control algorithms for a new tilt-wing unmanned aerial vehicle (UAV). The vehicle is capable of vertical take-off and landing (VTOL). Due to its tilt-wing structure, it can also fly horizontally. The mathematical model of the vehicle is obtained using Newton-Euler formulation. A gravity compensated PID controller is designed for altitude control, and three PID controllers are designed for attitude stabilization of the vehicle. Performances of these controllers are found to be quite satisfactory as demonstrated by indoor and outdoor flight experiments

Probability-dependent gain-scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 John Wiley & Sons, Ltd.In this paper, the gain-scheduled control problem is addressed by using probability-dependent Lyapunov functions for a class of discrete-time stochastic delayed systems with randomly occurring sector nonlinearities. The sector nonlinearities are assumed to occur according to a time-varying Bernoulli distribution with measurable probability in real time. The multiplicative noises are given by means of a scalar Gaussian white noise sequence with known variances. The aim of the addressed gain-scheduled control problem is to design a controller with scheduled gains such that, for the admissible randomly occurring nonlinearities, time delays and external noise disturbances, the closed-loop system is exponentially mean-square stable. Note that the designed gain-scheduled controller is based on the measured time-varying probability and is therefore less conservative than the conventional controller with constant gains. It is shown that the time-varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the UK, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the National Natural Science Foundation of China under Grants 61028008, 61134009, 61074016, 61104125 and 60974030, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany

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This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem of H∞ loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-block H∞ synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV) system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter