Generic Delay-L Left Invertibility of Structured Systems with Scalar Unknown Input

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.

Interval observer design for unknown input estimation of linear time-invariant discrete-time systems

Generic properties and control of linear structured systems: a survey

This paper is concerned with the structural controllability analysis for discrete-time linear control systems with time-delay. By adding virtual delay nodes, the linear systems with time-delay are transformed into corresponding linear systems without time-delay, and the structural controllability of them is equivalent. That is to say, the time-delay does not affect or change the controllability of the systems. Several examples are also presented to illustrate the theoretical results.

For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.

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

This communication is concerned with stabilization via output static feedback of discrete-time linear time-invariant finite-dimensional systems. A new concept is introduced: output static stabilization in the relaxed sense. This (conservative) stabilization concept is defined so that it is characterized in terms of the discrete-time LQR problem. Properties, and alternative equivalent definitions of this new concept are analyzed. It is shown that for a particular class of plants, the stabilization problem in the above new sense can be cast as a convex programming problem (which moreover can be used as a tool for synthesis). A full characterization for the class of plants that are stabilizable in the above sense is presented. Important consequences of this characterization are somehow surprising. It is shown that the introduced new (conservative) stabilization concept is indeed much more important than it seems. The general problem of output static stabilization can be transformed into the stabilization problem in this new sense. A relationship between output static stabilizability and the discrete-time LQR problem is proved. Convex necessary and sufficient conditions, for joint stabilization (of multiple plants) in the above sense and for decentralized stabilization in the above sense, are presented.

As computer graphics technology becomes more popular, a large amount of 3-D model data is required for various purposes. Three-dimensional (3-D) digital modeling of object through 3-D optical scanners has been demonstrated in recent years. However, most current 3-D scanners are usually large, heavy, expensive, and commonly accurate (Mean Square Error is around 0.3mm). Presently, highly accurate, easy-to-use and cheap 3-D shape acquisition system provides viable solutions to meet the requirements of users. In this paper, we introduce a linear structured scanning system covers an area of 600mm by 400mm in width in a high accurate way (MSE is lower than 0.1mm). Hardware setup of the linear structured scanning system and the process of the shape acquisition for 3-D object modeling based on the linear structured scanning system are proposed in this paper. We also proposed a highly accurate calibration method which can overcome complicated calculations of camera parameters. This highly accurate calibration method can be widely applied to linear structured light measurement system. Then we describe the modeling approach of our linear structured scanning system. Finally, reconstruction and visualization results are illustrated and further analyses are discussed in this paper.

As with a continuous-time linear system, the predictor state feedback law for a discrete-time linear system with input delay is the product of a feedback gain matrix with the predicted state at a future time instant ahead of the current time instant by the amount of the delay, which is the sum of the zero input solution and the zero state solution of the system. The zero state solution for a discrete-time system is a finite summation that involves past input. The zero input solution is the product of the transition matrix and the initial state. The truncated predictor feedback (TPF), which results from discarding the finite summation part of the predictor feedback law, reduces implementation complexity. The delay independent TPF law further discards the delay-dependent transition matrix in the TPF law and is thus robust to unknown delays. It was pointed out in Lin (Commun. Inf. Syst. 7(3), 227–264 (2007)) and Zhou and Lin (IEEE Trans. Circuits Syst. I Regular Papers 58(11), 2741–2754 (2011)) that such a delay independent TPF law stabilizes a discrete-time linear system with all its poles at z = 1 or inside the unit circle no matter how large the delay is.

The Dynamic Regulation of Linear Discrete-time Systems with Unknown Input (A Design Method Using Adaptive State Observer)

Stability of Linear Discrete-Time Periodic Systems with Time-Delay

The paper presents the algorithm for robustness estimation of large deviations in free motion of linear discrete-time systems. A tracking discrete-time systems with the modal control law are discussed, where the modal control law is designed taking into account the value of delay and the deviation. Two cases of discrete-time systems with control signal delay are considered in the paper. The first case relates to predictable delay of control signal, and the second one relates to unpredictable delay of control signal. It is assumed that parameters of the system are linearly dependent on the uncertainties. The problem is solved with the state space approach and the sensitivity theory methods. An upper bound estimation of trajectory deviations for discrete-time systems is obtained. The estimation contains the condition number of the eigenvectors matrix of the system state matrix. Therefore, sensitivity functions of singular values of the eigenvectors matrix are used to calculate the robustness estimation of the deviations. Based on the obtained equations, an algorithm for the robustness estimation of large deviations in linear discrete-time systems with parametric uncertainties is proposed. The proposed method is compared with an alternative LMI based approach for the peak estimation problem. Advantages and disadvantages of both approaches are illustrated with examples.KeywordsDiscrete-time systemDelayLarge deviationsPeak effectSensitivity analysisUpper boundsRobustnessParametric uncertainty

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.

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

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