Stochastically Resilient Observer Design for a Class of Continuous-Time Nonlinear Systems

This work addresses the design of stochastically resilient or non-fragile continuous-time Luenberger observers for systems with incrementally conic nonlinearities. Such designs maintain the convergence and/or performance when the observer gain is erroneously implemented due possibly to computational errors i.e. round off errors in computing the observer gain or changes in the observer parameters during operation. The error in the observer gain is modeled as a random process and a common linear matrix inequality formulation is presented to address the stochastically resilient observer design problem for a variety of performance criteria. Numerical examples are given to illustrate the theoretical results

An LMI Approach to Discrete-Time Observer Design with Stochastic Resilience

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant or the measurement model. The present work addresses the important problem of stochastic resilience or non-fragility of a discrete-time Luenberger observer which is the maintenance of convergence and/or performance when the observer is erroneously implemented possibly due to computational errors i.e. round off errors in digital implementation or sensor errors, etc. A common linear matrix inequality framework is presented to address the stochastic resilient design problem for various performance criteria in the implementation based on the knowledge of an upper bound on the variance of the random error in the observer gain. Present results are compared to earlier designs for stochastic robustness. Illustrative examples are given to complement the theoretical results

Resilient Observer Design for Discrete-Time Nonlinear Systems with General Criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based resilient observer design approach is presented to guarantee the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of bounded perturbations on the gain. Some simulation examples are included to illustrate the proposed design methodology

Robust and Resilient Control Design and Performance Analysis for Uncertain Systems with Finite Energy Disturbances

This dissertation addresses the problem of robust and resilient control design with additional performance analysis for uncertain systems with finite energy disturbances. The control design is robust and resilient in the sense of maintaining certain performance criteria in the presence of perturbations in both system parameters and feedback gains. The performance analysis evaluates resilience properties of state feedback and dynamic (state estimate) feedback controllers. A resilient and robust state feedback controller is designed using linear matrix inequality (LMI) techniques for the characterization of solutions to the analysis and design problems posed in this work. Uncertainties are allowed in the linear and nonlinear parts of the system model and also in the feedback gain so that the designed controller is robust in addition to being resilient. The design of controllers for various performance criteria including asymptotic stability, H2, Hinf, input strict passivity, output strict passivity and very strict passivity are presented. In addition to the design problem, an approach is presented for performance analysis of the resilience property of perturbed controller and observer gains. The resilience property is defined in terms of both multiplicative and additive perturbations on the gains so that the closed loop eigenvalues do not leave a specified region in the complex plane, such as a vertical strip, disk, sector region, etc. The method presented allows maximum gain perturbation bounds to be obtained based on the designer’s choices of controller eigenvalue region. The LMI technique is used also for the analysis process. Both design and analysis problems are treated using Lyapunov functions. All work is conducted for both continuous- and discrete-time cases. Several illustrative simulation examples are included to show the effectiveness of the proposed design and analysis approaches

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

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

Observer-Based Non-Fragile Passive Control for Uncertain Nonlinear Sampled-Data System with Time-Delay

The problem of observer-based passive control for uncertain nonlinearsampled-data systems with time delay is investigated by using non-fragile passivecontrol. Attention is focused on the design of a non-fragile passive observer and acontroller which guarantees the passivity of the closed-loop system for all admissibleuncertainties. A sufficient condition for passivity and asymptotic stability of thecombined system is derived via linear matrix inequality (LMI). Finally, a simulationexample is presented to show the validity and advantages of the proposed method

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

Analysis and Synthesis Methods for Nonlinear Network Systems

Over the past two decades the interactions between systems and their control components have undergone some significant changes. These interactions are no more localized, but usually take place over a network and even the control components may be remotely located, thus involving aspects of communication in control systems. Furthermore, the last decade has also seen a surge in intermingling ideas from control and communication and their application to biological systems, power systems giving rise to new research areas like Networked Control Systems (NCS), Cyber-Physical Systems (CPS), Gene Regulatory Networks (GRN) to name a few. This has led researchers to study control systems with practical constraints imposed on them. One such practical constraint identified as a major challenge, is the fragility of control systems and performance degradation, when the interconnection is not reliable. Design of controllers and estimators for such systems needs to take into account these constraints and mitigate them, to ensure sufficient robustness against unreliability of the interconnection. Considerable research has been done over the past decade in analyzing these new challenges and developing design tools to extract desired performance. Control over communication channels is one such widely researched area where the effect of unreliable interconnection on the stability performance of the system has been studied. The reliability of communication could manifest in various ways like sensor failure at output measurement, control actuator failure, interconnection links failures in the form of packet erasure channel, fading channel, quantization etc. Significant research progress has been made, in areas of control and estimation over unreliable communication links, consensus over unreliable network interconnections, etc., albeit the work has dealt with linear time invariant (LTI) systems theory. This has led to fruitful results for special cases of packet-drop communication channel modeled as a Bernoulli erasure channel. In the case of linear systems these results have demonstrated a connection between the performance characteristics of the interconnection and the expansion or destabilizing characteristics of the linear system, in obtaining desired performance of the closed loop system. Most of the current research for control over communication channels have focused on LTI plant dynamics. Furthermore the results involving nonlinear plant dynamics have reverted to local linearization techniques. It is well-known that for nonlinear systems, results based on local linearization at an equilibrium point will be local in nature and does not account for the global dynamics of the nonlinear system. For the proposed applications of network control systems to electric power grid and biological networks it is essential to develop results for the analysis of nonlinear systems over networks. In this work, we are primarily interested in the interaction of nonlinear systems and controllers over unreliable interconnections modelled as a stochastic multiplicative uncertainty. We provide analysis and synthesis methods for the control and observation of uncertain nonlinear network controlled systems. Our analysis methods indicate, fundamental limitations arise in the stabilization and observation of nonlinear systems over uncertain channels. Our main result provides the limitation for observation of nonlinear system over erasure channel expressed in terms of the probability of erasure and positive Lyapunov exponents of the open loop nonlinear plant. The positive Lyapunov exponents are measure of dynamical complexity and comparing our results with existing results for LTI systems, we show that Lyapunov exponents emerge as a natural generalization of eigenvalues from linear to nonlinear systems. Entropy is another measure of dynamical complexity. Using results from ergodic theory of dynamical systems we also relate the limitation for stabilization and observation with the entropy corresponding to the invariant measure capturing the global dynamics of the nonlinear systems. Existing Bode-like fundamental limitation results for nonlinear systems relate limitation for stabilization with the entropy corresponding to the invariant measure at the equilibrium point. Our results are the first to connect the limitation for stabilization with the entropy corresponding to invariant measure other than the one associated with equilibrium point. Our synthesis methods for the design of robust controller and observer against uncertain channels revolves around special class of nonlinear systems -Lure systems. These systems are essentially linear systems with sector-bounded nonlinearity in the feedback loop. For this special class of nonlinear systems, we delve into the theoretical tools of absolute stability to obtain some synthesis methods which provide design criteria for nonlinear systems over unreliable interconnections. Stability of Lur\u27e systems is a special case of the stability of interconnected passive systems. Thus we can characterize the unreliability of the interconnection, that guarantees the desired performance for Lur\u27e systems, in terms of the passivity of the linear system. Passivity theory is a rich theory with wide spread applications to nonlinear controller design and observation, which extends ideas of system stability to input-output systems using the ideas of dissipativity. Our synthesis methods developed for Lure systems with input and output stochastic channel uncertainties provide natural extension of the powerful passivity based synthesis tools developed for deterministic Lure systems. In particular, our results help understand the trade-off between passivity and stochastic uncertainty in feedback control systems

Non-Fragile Guaranteed Cost Control of Nonlinear Systems with Different State and Input Delays Based on T-S Fuzzy Local Bilinear Models

This paper focuses on the non-fragile guaranteed cost control problem for a class of Takagi-Sugeno (T-S) fuzzy time-varying delay systems with local bilinear models and different state and input delays. A non-fragile guaranteed cost state-feedback controller is designed such that the closed-loop T-S fuzzy local bilinear control system is delay-dependent asymptotically stable, and the closed-loop fuzzy system performance is constrained to a certain upper bound when the additive controller gain perturbations exist. By employing the linear matrix inequality (LMI) technique, sufficient conditions are established for the existence of desired non-fragile guaranteed cost controllers. The simulation examples show that the proposed approach is effective and feasible