Observer design for Linear Hybrid Systems with unknown inputs and Petri-net discrete dynamics

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario. Copyright © 2016 John Wiley & Sons, Ltd.

In this article, a full-order observer without unknown inputs reconstruction is suggested in order to achieve finite-time reconstruction of the state vector for a class of linear systems with unknown inputs. The observer is a simple one, its derivation being direct and easy. It will be shown that the problem of full-order observers for linear systems with unknown inputs can be reduced in this case to a standard one (the unknown input vector will not interfere in the observer equations). The effectiveness of the suggested design algorithm is illustrated by a numerical example (aircraft longitudinal motion), and, for the same aircraft dynamics, we make a comparison between our new observer and other already existing observers from the existence conditions and dynamic characteristics’ point of view; the superiority of the new designed observer is demonstrated.

In this article, a “Backward in Time Observer” has been designed for linear systems having time delays in output measurements and differences in the sampling rate of input and output measurements. With the proposed observer we are able to recover the performance of the system with no time delay and an equal sampling rate of input and output measurements. Different observers have been designed for time delayed systems by the researcher, but multi-rate time delayed systems have not been discussed so far, hence our proposed observer is able to cater for both of these problems in the system. The proposed observer is simulated for the seeker system of the missile for verification and illustration. Seeker system of missile is a linear time-invariant system having time delay in output measurement. Furthermore, the output measurement through IR camera of the seeker system has a lower sampling rate than its input signal from the gyro.

Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input

In this paper, an unknown input filter is proposed for discrete-time linear systems with quantized measurements. The approach uses a slightly modified model of the system to estimate both the system states and the unknown input simultaneously. Two well-known quantization methods, namely linear and logarithmic, are studied and a specific design procedure is derived for each case. For the linear case, the quantization error is modelled as measurement noise and for the logarithmic case, it is modelled as a norm-bounded uncertainty. In the end, simulation results are used to illustrate the effectiveness of the proposed filter.

In this paper, an optimal regulator design for fractional order linear systems with input time-delay is developed.Fractional systems are very sensitive to delay so delay is a critical factor.Here the input time-delay in linear fractional-order system is applied and the response shows an improvement of less than 0.001 ms.The input time-delay is considered at the beginning of the control design and no approximation and estimation are used in the control system Thus the system performance and stability can be guaranteed.Instability in responses might occur if a system with input time-delay is controlled by an optimal regulator design for fractional linear system that was designed with no consideration of input time-delay.The transformation model which is first presented, change the optimal regulator design for fractional order linear systems with input time-delay into a system without delay formally.Simulation graphs demonstrate better performance of the proposed optimal regulator design by fractional order with consideration of the value criterion.

This paper focuses on the joint input and state estimation for linear stochastic discrete-time systems. To obtain unique estimators that are optimal in the sense of being both least-squares and minimum-variance unbiased (MVU) and their recursive solution, an objective function of the sum of squared errors of outputs is first minimized with respect to an extended state vector including states and unknown inputs. A recursive solution of the extended state vector is then derived with the aid of matrix manipulations. Finally, appropriate matrix decomposition and transformation are used to extract the recursive solutions only involving the current states and unknown inputs from the recursive solution obtained in the previous step. This approach avoids excessive computation due to the dimensions of the matrices that increase with time. As a result, the resulting recursive solution is referred to as a general Kalman filter with unknown inputs (GKF-UI), which covers the most general case of unknown inputs so far in the literature without resorting to transforming the outputs and/or unknown inputs. The unknown inputs to be estimated by the proposed GKF-UI could be arbitrary signals without any prior information and the properties of the proposed GKF-UI are also examined. A numerical example with partial feedthrough from three unknown inputs is used to demonstrate the effectiveness and accuracy of the proposed algorithm.

Bond-Graph-Based Multivariable non linear UlO-type estimation

This paper concerns structured systems, namely linear systems where the state-space matrices have zeros in some fixed positions, and free parameters in all other entries. In particular, it focuses on discrete-time linear time-invariant systems affected by an unknown input. The goal is to study delay-L left invertibility, namely the possibility to reconstruct the input sequence from the output sequence, assuming that the initial state is known, and requiring that the inputs can be reconstructed at least up to L time steps before the current output. Under the assumption that the unknown input is scalar, this paper presents a simple graphical condition characterizing the structured systems which are generically delay-L left invertible.

The problem of state prediction for linear dynamic systems with discrete time is considered in the presence of unknown input and inaccurately specified parameters in the model. An algorithm with compensation for the constant component and estimation of the unknown variable input component by the least squares method is suggested. Results of statistical simulation are presented. The algorithm can be used for solving problems of processing information obtained as a result of observations over physical processes.

The topic of this paper is the backstepping-based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients. Thereby, a large class of outputs is considered, i.e., mixed distributed and pointwise in-domain or boundary outputs. The state feedback regulator design is based on the $\boldsymbol {p}$ -copy internal model principle. This results in a stabilization problem for a cascade of $\boldsymbol {m+p}$ boundary controlled transport partial differential equations (PDEs) with $\boldsymbol {p}$ ordinary differential equations (ODEs). For this, a systematic backstepping approach is presented, in which all design equations are explicitly solvable in backstepping coordinates. Furthermore, the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior. Robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations. A $\boldsymbol {4 \times 4}$ hyperbolic system with uncertain transport velocities and couplings in the transport PDEs illustrates the results of this paper.

In this paper, a step by step algorithm is given to design functional unknown input observer for nonlinear discrete time systems under the Polytopic Takagi-Sugeno framework (also known as multiple models systems). Applying the Lyapunov theory and the ℒ 2 attenuation, Linear Matrix Inequalities (LMI)s conditions are deduced which are solved for feasibility to obtain observer design matrices. To reject the effect of unknown input, classical approach of decoupling the unknown input for the linear case is used. A solver based solution is proposed. The novelty of the proposed approach consists in solving simultaneously both structural constraints and LMIs, which ensure a mean for the efficient design of the gains of the observers. To illustrate the proposed theoretical results, an application example of model reference tracking control applied to an electro-mechanical model of a motor with a time varying parameter is discussed.

Robust H ∞ controller design for linear uncertain systems with delayed state and control

For linear discrete random time-varying systems with unknown inputs, an improved two-stage Kalman filter algorithm is presented to simultaneously estimate the state and generalized deviation of the sensors in the micro-electromechanical system. Based on this algorithm, a multi-sensor fusion filter estimation is implemented. First, the offset dynamic model without unknown input is derived by dimension reduction decoupling; secondly, an auxiliary full-row rank matrix is added to decouple the bias noise from the observation noise; finally, a two-stage Kalman filter is constructed with a stateless offset filter and a state filter to estimate the state and bias. Then multi-sensor fusion filtering is performed based on this algorithm. The simulation results show that the system bias, state estimation error and root mean square error of the method and its fusion algorithm are significantly reduced. The improved accuracy proves that this method is very effective.KeywordsUnknown inputTwo-stage filterMulti-sensor fusion

Complements to full order observer design for linear systems with unknown inputs