Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings

This study is concerned with the non-fragile H∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H∞ outputfeedback controller such that the closed-loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semidefinite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong 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.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

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

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

Nonlinear Tracking Control Using a Robust Differential-Algebraic Approach.

This dissertation presents the development and application of an inherently robust nonlinear trajectory tracking control design methodology which is based on linearization along a nominal trajectory. The problem of trajectory tracking is reduced to two separate control problems. The first is to compute the nominal control signal that is needed to place a nonlinear system on a desired trajectory. The second problem is one of stabilizing the nominal trajectory. The primary development of this work is the development of practical methods for designing error regulators for Linear Time Varying systems, which allows for the application of trajectory linearization to time varying trajectories for nonlinear systems. This development is based on a new Differential Algebraic Spectral Theory. The problem of robust tracking for nonlinear systems with parametric uncertainty is studied in relation to the Linear Time Varying spectrum. The control method presented herein constitutes a rather general control strategy for nonlinear dynamic systems. Design and simulation case studies for some challenging nonlinear tracking problems are considered. These control problems include: two academic problems, a pitch autopilot design for a skid-to-turn missile, a two link robot controller, a four degree of freedom roll-yaw autopilot, and a complete six degree of freedom Bank-to-turn planar missile autopilot. The simulation results for these designs show significant improvements in performance and robustness compared to other current control strategies

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