ROBUST FAULT DETECTION AND ISOLATION FOR UNCERTAIN LINEAR RETARDED SYSTEMS

A robust fault detection and isolation scheme is proposed for uncertain continuous linear systems with discrete state delays for both additive and multiplicative faults. Model uncertainties, disturbances and noises are represented as unstructured unknown inputs. The proposed scheme consists of a Luenberger observer for fault detection and a group of adaptive observers, one for each class of faults, for fault isolation. The threshold determination and fault isolation are based on a multi‐observer strategy. Robustness to model uncertainties and disturbances can be guaranteed for the scheme by selecting proper thresholds. All the signals, i.e., the fault estimate and the state and output estimation errors of each isolation observer can be shown to be uniformly bounded, and the estimate of the fault by the matched observer is shown to be satisfactory in the sense of extended H₂ norm. Furthermore, the sensitivity to fault and the fault isolability condition are analyzed also in the paper. Simulations of a heating process for detecting and isolating an actuator gain fault and an additive fault show the proposed scheme is effective.     

Event‐triggered observer‐based robust H∞ control for networked control systems with unknown disturbance

In this article, the event‐triggered robust H_∞ control is studied for a class of uncertain networked control systems (NCSs) subject to unknown state and variable disturbance. First, aiming to decrease the unnecessary transmissions of sampled data, an efficient adaptive event‐triggered scheme (AETS) is presented, which can reflect the full real‐time variation of addressed NCSs and help to reduce the conservativeness. Second, based on the triggered output signals and disturbance model, two effective observers are, respectively, exploited to estimate the state and disturbance, which are further utilized to reject the disturbance and design the controller. By using the overall closed‐loop system and selecting an augmented Lyapunov‐Krasovskii functional, two sufficient conditions on jointly designing the adaptive event scheme, observers, and controller are established via linear matrix inequality forms, which can guarantee the global exponential stability and ensure H_∞ performance. Finally, some simulations and comparisons in a numerical example are provided to demonstrate the effectiveness of the derived results.     

Robust H∞ observer design of linear time-delay systems with parametric uncertainty

This paper deals with the problem of H_∞ observer design for a class of uncertain linear systems with delayed state and parameter uncertainties. This problem aims at designing the linear state observers such that, for all admissible parameter uncertainties, the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified H_∞ norm upper bound constraint, independently of the time delay. The time delay is assumed to be unknown, and the parameter uncertainties are allowed to be norm-bounded and appear in all the matrices of the state-space model. An effective matrix inequality methodology is developed to solve the proposed problem. We derive the conditions for the existence of the desired robust H_∞ observers, and then characterize the analytical expression of these observers in terms of some free parameters. A numerical example demonstrates the validity and applicability of the present approach.     

How Do Two Observers Pool Their Knowledge About a Quantum System?

In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine independently obtained states of knowledge together to form a new state of knowledge, which is the state which would be possessed by someone having the combined information of both observers. Moreover, this combined state of knowledge can be found without reference to the manner in which the respective observers obtained their information. However, we show that in general this is not possible for quantum states of knowledge; in order to combine two quantum states of knowledge to obtain the state resulting from the combined information of both observers, these observers must also possess information about how their respective states of knowledge were obtained. Nevertheless, we emphasize this does not preclude the possibility that a unique, well motivated rule for combining quantum states of knowledge without reference to a measurement history could be found. We examine both the direct quantum analog of the classical problem, and that of quantum state-estimation, which corresponds to a variant in which the observers share a specific kind of prior information. PACS: 03.67.-a, 02.50.-r, 03.65.Bz     

Mixed H∞ and passive control for linear switched systems via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.     

Insensitive observers for discrete time linear systems

This paper considers the problem of designing an observer insensitive to system parameter variations in discrete time linear multivariable systems. A K-insensitive observer is defined as an observer that can reconstruct a linear function of the state vector in spite of the variations of system parameters, provided the initial state of the observer is suitably chosen. A deadbeat observer is defined to be an observer that reconstructs the linear function for an arbitrary initial condition of the observer. Then, the existence of the K-insensitive observer is examined, and the class of K-insensitive observers is characterized. A necessary and sufficient condition is derived under which the K-insensitive deadbeat observer can be designed, and a simple algorithm is proposed to design the observer. The resulting observer is shown to be stable. The order of the observer is evaluated. The condition for generic solvability of the problem is also given.     

Conditions for the existence of continuous storage functions for nonlinear dissipative systems

The problem of existence of continuous storage functions for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x_*, then, under certain assumptions, a continuous storage function can be constructed on a set of points accessible from x_* by concatenation of a finite number of forward and backward motions of the system. Most of these assumptions are weaker than certain controllability-type properties and can be checked using similar tests.     

Robust delay dependent fault estimation for a class of interconnected nonlinear time delay systems

This paper focuses on the problem of fault estimation for a class of interconnected nonlinear systems with time varying delays. In contrast to the common assumption imposed on the problem in most literature, here, there is no need for the delay rate to be less than one. Both actuator and component faults are considered within the general fault model invoked as multiplicative faults in this study. Robust adaptive observers are used to detect and estimate simultaneously the states and the parameter faults in each subsystem. The designed observers ensure a prescribed H _∞ performance level for the fault estimation error, irrespective of the uncertainties which are assumed here to be the unknown interconnections between the subsystems. With the aid of H _∞ performance index, the common assumption regarding the observer matching condition is no longer required. Sufficient conditions for asymptotic stability of the observers are derived via a matrix inequality approach with the aid of LyapunovKrasovskii function. Finally, a simulation example is presented to show the validity and feasibility of the proposed method.

     

Quantizing gravity using physical states of a superstring

A symmetric zero-mass tensor of rank two is constructed using the superstring modes of excitation, which satisfies the physical state constraints of a superstring. These states have a one to one correspondence with the quantized field operators and are shown to be the absorption and emission quanta of the Minkowski space Lorentz tensor, using the quantum field theory method of quantization. The principle of equivalence makes the tensor identical to the metric tensor at any arbitrary space-time point. The propagator for the quantized field is deduced. The gravitational interaction is switched on by going over from ordinary derivatives to co-derivatives. The Riemann-Christoffel affine connections are calculated, and the weak field Ricci tensor R _μν ⁰ is shown to vanish. The interaction part R _μν ^int is found, and the exact R _μν of the theory of gravity is expressed in terms of the quantized metric. The quantum-mechanical self-energy of the gravitational field in vacuum is shown to vanish. By the use of a projection operator, it is shown that gravitons are quanta of the general relativity field which gives the Einstein equation G _μν = 0. It is suggested that quantum gravity may be renormalizable by the use of the massless ground state of this superstring theory for general relativity, and a tachyonic vacuum creates and annihilates quanta of quantized gravitational field.     

H∞ optimal design of robust observer against disturbances

This paper considers the robust observer design problem for linear dynamic systems subject to the interference of external disturbances. For such systems, the state estimate from the conventional Luenberger is normally biased with respect to the true system state. To remedy this situation, this paper proposes a new structure for robust observers. With this new structure, the robust observer design problem is skillfully transformed into the well-known disturbance rejection control problem. The H_∞ optimal control design technique can then be applied to shape the proposed robust observer in the frequency domain. The proposed robust observer is a joint state and disturbance observer, which simultaneously estimates both the system state and unknown disturbances, and can be applied to non-minimum-phase systems.     

Time evolution of a system of two valued interacting elements : a microscopic interpretation of birth and death equations

We consider here one of the simplest possible systems with N interacting particles. It has the following features : (i) the state variable of each particle takes the values σ_i(= ?1 ; (ii) the interaction is chosen in such a way to preserve the symmetry of the distribution function p(σ₁, σ₂, [tdot], σ _N ; t) with respect to the σ _i and (iii) the evolution of the system is defined in a stochastic way by the transition probabilities of each particle as depending on the state of all other particles. The master equation of this Markov process is shown to be the equation of a general birth and death process in one dimension. More precisely, the birth and death process is : linear if the particles are independent ; quadratic if there is a binary interaction ; or cubic if there is a third-order interaction. We develop the reduced distribution equations hierarchy (which is the analogue of the BBGKY hierarchy) and we study under what conditions this hierarchy closes. Then we show that for specific systems there is a conserved quantity (in the mean) and we discuss for what kind of intercation there is respectively an H-theorem and a postulate of equal a priori probabilities at equilibrium. It appears in particular that this postulate should not be true in the strong form in which it is usually stated.     

Robust filtering for a class of discrete-time uncertain nonlinear systems: An H∞ approach

This paper deals with the H_∞ filtering problem for a class of discrete-time nonlinear systems with or without real time-varying parameter uncertainty and unknown initial state. For the case when there is no parametric uncertainty in the system, we are concerned with designing a nonlinear H_∞ filter such that the induced l₂ norm of the mapping from the noise signal to the estimation error is within a specified bound. It is shown that this problem can be solved via one Riccati equation. We also consider the design of nonlinear filters which guarantee a prescribed H_∞ performance in the presence of parametric uncertainties. In this situation, a solution is obtained in terms of two Riccati equations.     

H ∞ almost disturbance decoupling for a class of linear systems: a constructive approach

A new approach to H _∞ almost disturbance decoupling for a class of linear systems is proposed in this note by using a backstepping-like technique. It is shown that the H _∞ almost disturbance decoupling problem can always be solved for the class of linear systems, and one key advantage of the proposed approach is that the static state feedback control law for the H _∞ almost disturbance decoupling can be constructively obtained.     

Design of nonlinear observers with approximately linear error dynamics using multivariable Legendre polynomials

This paper presents a numerical approach to the design of nonlinear observers by approximate error linearization. By using a Galerkin approach on the basis of multivariable Legendre polynomials an approximate solution to the singular PDE of the observer design technique proposed by Kazantzis and Krener (see (Syst. Control Lett. 1998; 34 :241–247; SIAM J. Control Optim. 2002; 41 :932–953)) is determined. It is shown that the L₂‐norm of the remaining nonlinearity in the resulting error dynamics can be made small on a specified multivariable interval in the state space. Furthermore, a linear matrix equation is derived for determining the corresponding change of co‐ordinates and output injection such that the proposed design procedure can easily be implemented in a numerical software package. A simple example demonstrates the properties of the new numerical observer design. Copyright © 2006 John Wiley & Sons, Ltd.     

Supervisory control of hybrid systems within a behavioural framework

This contribution addresses the synthesis of supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. We find an l-complete approximation (abstraction) Σ_l for Σ, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists, we synthesize the maximally permissive supervisor for Σ_l. We show that it also solves the control problem for the hybrid system Σ. If no solution exists, approximation accuracy can be increased by computing a k-complete abstraction Σ_k, k>l. This paper is entirely set within the framework on Willems’ behavioural systems theory.     

Asynchronous hybrid systems with jumps – analysis and synthesis methods

In this paper we show that the H_∞ synthesis problem for a class of linear systems with asynchronous jumps can be reduced to a purely discrete-time synthesis problem. The system class considered includes continuous-time systems with discrete jumps, or discontinuities, in the state. New techniques are developed for the analysis of asynchronous time-varying hybrid systems which allow a particularly simple treatment, and provide an elementary proof for the sampled-data H_∞ problem.     

Adaptive observers for nonlinearly parameterized class of nonlinear systems

In this paper, one proposes adaptive observers for a class of uniformly observable MIMO nonlinear systems with general nonlinear parameterizations. The state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well-defined persistent excitation condition. Moreover, the gain of the observers involves a design function that has to satisfy a simple condition which is given. Different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function. The theory is supported by simulation results related to the estimation of the biomass concentration and the Contois model parameters in a bioreactor.     

Observer-based fuzzy control of fuzzy time-delay systems with parametric uncertainties

In this paper, non-linear systems with time-varying delays and parametric uncertainties are represented by an equivalent Takagi–Sugeno-type fuzzy model. Based on the Convex combination property, Lyapunov criterion and Razumikhin theorem, some sufficient conditions are derived under which the parallel-distributed fuzzy control can stabilize the whole uncertain fuzzy time-delay systems asymptotically. On the other hand, if the states are not all available, the fuzzy state observers are proposed to estimate all states of the fuzzy systems for fuzzy control. By satisfying some criteria, the stabilization, estimation and robustness of the fuzzy time-delay systems are also guaranteed. Moreover, if all the time-delays τ _i ( t ) of the fuzzy systems are the same for all the rules (i.e. τ _i (t) = τ _j (t) = τ for all i ≠ j), this paper proposes the simpler and less conservative criteria. The practical example based on the continuous stirred tank reactor model and a numerical example are given to illustrate the control design and its effectiveness.     

Globally exponential stability and stabilization of interconnected Markovian jump system with mode-dependent delays

This paper focuses on the problems of globally exponential stability and stabilization with H_∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H_∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.