Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result

H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements

In this paper, the H∞ output-feedback control problem is investigated for a class of two-dimensional (2-D) nonlinear systems with time-varying delays under imperfect measurements. Randomly occurring nonlinearities (RONs) are introduced in the system to account for probabilistic nonlinear disturbances typically caused by networked environments and governed by a sequence of random variables obeying the Bernoulli distribution. The imperfect measurement outputs are subject to both data missing and randomly occurring sensor saturations (ROSSs), which are put forward to characterize the network-induced phenomena such as probabilistic communication failures and limited capacity of the communication devices. The aim of this paper is to design an output-feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H∞ performance index is satisfied. Sufficient conditions are presented by resorting to intensive stochastic analysis and matrix inequality techniques, which not only guarantee the existence of the desired controllers for all possible time-delays, RONs, missing measurements and ROSSs but also lead to the explicit expressions of such controllers. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61174136, 61134009 and 61329301, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the “333 Project” Foundation of Jiangsu Province, the Programme for New Century Excellent Talents in University under Grant NCET-12-0117, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Decentralized and Fault-Tolerant Control of Power Systems with High Levels of Renewables

Inter-area oscillations have been identified as a major problem faced by most power systems and stability of these oscillations are of vital concern due to the potential for equipment damage and resulting restrictions on available transmission capacity. In recent years, wide-area measurement systems (WAMSs) have been deployed that allow inter-area modes to be observed and identified.Power grids consist of interconnections of many subsystems which may interact with their neighbors and include several sensors and actuator arrays. Modern grids are spatially distributed and centralized strategies are computationally expensive and might be impractical in terms of hardware limitations such as communication speed. Hence, decentralized control strategies are more desirable.Recently, the use of HVDC links, FACTS devices and renewable sources for damping of inter-area oscillations have been discussed in the literature. However, very few such systems have been deployed in practice partly due to the high level of robustness and reliability requirements for any closed loop power system controls. For instance, weather dependent sources such as distributed winds have the ability to provide services only within a narrow range and might not always be available due to weather, maintenance or communication failures.Given this background, the motivation of this work is to ensure power grid resiliency and improve overall grid reliability. The first consideration is the design of optimal decentralized controllers where decisions are based on a subset of total information. The second consideration is to design controllers that incorporate actuator limitations to guarantee the stability and performance of the system. The third consideration is to build robust controllers to ensure resiliency to different actuator failures and availabilities. The fourth consideration is to design distributed, fault-tolerant and cooperative controllers to address above issues at the same time. Finally, stability problem of these controllers with intermittent information transmission is investigated.To validate the feasibility and demonstrate the design principles, a set of comprehensive case studies are conducted based on different power system models including 39-bus New England system and modified Western Electricity Coordinating Council (WECC) system with different operating points, renewable penetration and failures

Performance comparison of structured H∞ based looptune and LQR for a 4-DOF robotic manipulator

We explore looptune, a MATLAB-based structured H1 synthesis technique in the context of robotics. Position control of a 4 Degree of Freedom (DOF) serial robotic manipulator developed using Simulink is the problem under consideration. Three full state feedback control systems were developed, analyzed and compared for both steady-state and transient performance using the Linear Quadratic Regulator (LQR) and looptune. Initially, a single gain feedback controller was synthesized using LQR. This system was then modified by augmenting the state feedback controller with Proportional Integral (PI) and Integral regulators, thereby creating a second and third control system respectively. In both the second and third control systems, the LQR synthesized gain and additional gains were further tuned using looptune to achieve improvement in performance. The second and third systems were also compared in terms of tracking a time-dependent trajectory. Finally, the LQR and looptune synthesized controllers were tested for robustness by simultaneously increasing the mass of each manipulator link. In comparison to LQR, the second system consisting of Single Input Single Output (SISO) PI controllers and the state feedback matrix succeeded in meeting the control objectives in terms of performance, optimality, trajectory tracking, and robustness. The third system did not improve performance in contrast to LQR, but still showed robustness under mass variation. In conclusion, our results have shown looptune to have a comparatively better performance over LQR thereby highlighting its promising potential for future emerging control system applications

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Survey on time-delay approach to networked control

This paper provides a survey on time-delay approach to networked control systems (NCSs). The survey begins from a brief summary on fundamental network-induced issues in NCSs and the main approaches to the modelling of NCSs. In particular, a comprehensive introduction to time-delay approach to sampled-data and networked control is provided. Then, recent results on time-delay approach to event-triggered control are recalled. The survey highlights time-delay approach developed to modelling, analysis and synthesis of NCSs, under communication constraints, with a particular focus on Round-Robin, Try-once-discard and stochastic protocols. The time-delay approach allows communication delays to be larger than the sampling intervals in the presence of scheduling protocols. Moreover, some results on networked control of distributed parameter systems are surveyed. Finally, conclusions and some future research directions are briefly addressed

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems