Stabilization of Uncertain Discrete-Time Linear System With Limited Communication

Abstract: The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

Abstract: This paper presents a model-free solution to the robust stabilization problem of discrete-time linear dynamical systems with bounded and mismatched uncertainty. An optimal controller design method is derived to solve the robust control problem, which results in solving an algebraic Riccati equation (ARE). It is shown that the optimal controller obtained by solving the ARE can robustly stabilize the uncertain system. To develop a model-free solution to the translated ARE, off-policy reinforcement learning (RL) is employed to solve the problem in hand without the requirement of system dynamics. In addition, the comparisons between on- and off-policy RL methods are presented regarding the robustness to probing noise and the dependence on system dynamics. Finally, a simulation example is carried out to validate the efficacy of the presented off-policy RL approach.

Abstract: Over the past few years, networked control systems (NCSs) have shown rapid progress and have indeed been very popular in terms of research as well as industrial applications. The issue of limited resources has been a fundamental problem in the translation of modern control techniques to NCS design. In order to address the aforesaid design challenge, an improved event-triggered adaptive backstepping control scheme is presented in this study for a class of uncertain NCSs with non-Lipschitz non-linearities under limited resources. Rather than a preselected constant threshold assumption, a well-designed and systematic triggering rule is derived based on the Lyapunov approach in order to satisfy bandwidth limitation and ensure system stability with acceptable transient performance. Relative to existing strategies in the literature, the proposed method leads to a substantially reduced number of transmissions with longer inter-event time. Thereby, the proposed algorithm exhibits more efficiency in resource utilisation. Simulation results on a networked control based robotic manipulator system illustrate the efficacy of the proposed adaptive scheme compared to benchmark control algorithms intended for a similar application.

Abstract: This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs). The considered system switches from one mode to another according to transition probability (TP) and evolves with mode-dependent average dwell time (MDADT), i.e., TP-based MDADT switching, which is more practical than classical average dwell time (ADT) switching. The logarithmic quantization technique is utilized to design mode-dependent quantized output controllers (QOCs). Noticing that external perturbations are unavoidable, actuator fault (AF) is also considered. New Lyapunov–Krasovskii functionals and analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. It is discovered that the TP matrix plays an important role in achieving the GES a.s., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lower bound of the DT of synchronized subsystems can be very small. An algorithm is given to design the control gains, and an optimal algorithm is provided for reducing conservatism of the given results. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

Abstract: This paper proposes the robust recursive least-squares (RLS) Wiener fixed-point smoother and filter in linear discrete-time stochastic systems with parameter uncertainties. The uncertain parameters exist in the observation matrix and the system matrix. The uncertain parameters cause to generate the degraded signal. In this paper, the degraded signal process is fitted to the finite order autoregressive (AR) model. The robust RLS Wiener estimators use the system matrices and the observation matrices for both the signal and the degraded signal, the variance of the state vector for the degraded signal, the cross-variance of the state vector for the signal with the state vector for the degraded signal, and the variance of the white observation noise. Also, this paper proposes the robust recursive fixed-point smoother and filter, by using the covariance information of the state vector for the degraded signal, the cross-covariance information of the state vector for the signal with the state vector for the degraded signal, the observation matrices for both the degraded signal and the signal besides the variance of the white observation noise. In estimating the signal process expressed by the second order AR model, the proposed robust RLS Wiener filter is superior in estimation accuracy to the robust Kalman filter and the RLS Wiener filter.

Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.

Abstract: First, we review some previous work on networked control systems (NCSs) and offer some improvements. Then, we summarize the fundamental issues in NCSs and examine them with different underlying network-scheduling protocols. We present NCS models with network-induced delay and analyze their stability using stability regions and a hybrid systems technique. Following that, we discuss methods to compensate network-induced delay and present experimental results over a physical network. Then, we model NCSs with packet dropout and multiple-packet transmission as asynchronous dynamical systems and analyze their stability. Finally, we present our conclusions.

Abstract: In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

Abstract: Part I presents two indirect methods of sampled-data controller design: These approaches include approximations to a real problem, which involves an analogue plant, continuous-time performance specifications, and a sampled-data controller Part II proposes a direct attack in the continuous-time domain, where sampled-data systems are time-varying The findings are presented in forms that can readily be programmed in, eg, MATLAB