Interval Prediction for Continuous-Time Systems with Parametric Uncertainties

The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.Comment: 6 pages, CDC 2019. Website: https://eleurent.github.io/interval-prediction

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou 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 recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

A Hybrid Observer for a Distributed Linear System with a Changing Neighbor Graph

A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at "event times" $t_1,t_2,\ldots$ using a local observer and a local parameter estimator. The local observer is a continuous time linear system whose input is $y_i$ and whose output $w_i$ is an asymptotically correct estimate of $L_ix$ where $L_i$ a matrix with kernel equaling the unobservable space of $(C_i,A)$. The local parameter estimator is a recursive algorithm designed to estimate, prior to each event time $t_j$, a constant parameter $p_j$ which satisfies the linear equations $w_k(t_j-\tau) = L_kp_j+\mu_k(t_j-\tau),\;k\in\{1,2,\ldots,m\}$, where $\tau$ is a small positive constant and $\mu_k$ is the state estimation error of local observer $k$. Agent $i$ accomplishes this by iterating its parameter estimator state $z_i$, $q$ times within the interval $[t_j-\tau, t_j)$, and by making use of the state of each of its neighbors' parameter estimators at each iteration. The updated value of $x_i$ at event time $t_j$ is then $x_i(t_j) = e^{A\tau}z_i(q)$. Subject to the assumptions that (i) the neighbor graph $\mathbb{N}(t)$ is strongly connected for all time, (ii) the system whose state is to be estimated is jointly observable, (iii) $q$ is sufficiently large, it is shown that each estimate $x_i$ converges to $x$ exponentially fast as $t\rightarrow \infty$ at a rate which can be controlled.Comment: 7 pages, the 56th IEEE Conference on Decision and Contro

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu 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.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany