Fault accommodation controller under Markovian jump linear systems with asynchronous modes

We tackle the fault accommodation control (FAC) in the Markovian jump linear system (MJLS) framework for the discrete-time domain, under the assumption that it is not possible to access the Markov chain mode. This premise brings some challenges since the controllers are no longer allowed to depend on the Markov chain, meaning that there is an asynchronism between the system and the controller modes. To tackle this issue, a hidden Markov chain ((Formula presented.), (Formula presented.)) is used where θ(k) denotes the Markov chain mode, and (Formula presented.) denotes the estimated mode. The main novelty of this work is the design of H∞ and H2 FAC under the MJLS framework considering partial observation of the Markov chain. Both designs are obtained via bilinear matrix inequalities optimization problems, which are solved using coordinate descent algorithm. As secondary results, we present simulations using a two-degree of freedom serial flexible joint robot to illustrate the viability of the proposed approach

Fault detection filter and fault accommodation controller design for uncertain systems

Model-based Fault Detection (FD) and Fault Accommodation (FA) approaches have been applied in a variety of cases. We propose several techniques to include uncertainties in the design process. First, we focus on the design of the Fault Detection Filter (FDF) and Fault Accommodation Controller (FAC) for Markovian Jump Linear Systems (MJLS). The MJLS framework allows us to include the network behavior (packet loss) during the design of the FDF and FAC.Second, we propose an FDF and FAC design for the MJLS, under the assumption that the Markov chain mode is not directly accessible. Since we are using the MJLS framework to model the network behavior, the assumption that the network state is not instantly accessible is useful because from a practical standpoint this is a truthful assumption. Third, from the results presented for the MJLS framework, we provided follow-up results using Lur'e Markov Jump System. This is compelling since on some occasions the non-linear behavior cannot be ignored. Therefore, applying the Lur'e MJS framework allows us to consider the same assumptions from MJLS, but now adds the non-linearities. Fourth, we propose the design Gain-Scheduled FDF and FAC for Linear Parameter Varying (LPV) systems, under the assumption that the schedule parameter is not directly acquired. We assume that the schedule parameter is subject to additive noise. This imprecision is included during the design, using change of variables and multi-simplex techniques. Finally, throughout the thesis, we provide some numerical examples to illustrate the viability of the proposed approaches

An Estimation Algorithm for a Class of Networked Control Systems Using UDP-Like Communication Schemes

In this work we consider a class of networked control systems (NCS) when the control signal is sent to the plant via a UDP-like communication protocol. In this case the controller sends a communication packet to the plant across a lossy network, but the controller does not receive any acknowledgement signal indicating the status of the control packet. Standard observer based estimators assume the estimator has knowledge of what control signal is applied to the plant. Under the UDP-like protocol the controller/estimator does not have explicit knowledge whether the control signals have been applied to the plant or not. We present a simple estimation and control algorithm that consists of a state and mode observer as well as a constraint on the control signal sent to the plant. For the class of systems considered, discrete time LTI plants where at least one of the states that is directly affected by the input is also part of the measurement vector, the estimator is able to recover the fate of the control packet from the measurement at the next timestep and exhibit better performance than other naive schemes. For single-input-single-output (SISO) systems we are able to show convergence properties of the estimation error and closed loop stability. Simulations are provided to demonstrate the algorithm and show its effectiveness

Detection of variance changes and mean value jumps in measurement noise for multipath mitigation in urban navigation

This paper studies an urban navigation filter for land vehicles. Typical urban-canyon phenomena as multipath and GPS outages seriously degrade positioning performance. To deal with these scenarios a hybrid navigation system using GPS and dead-reckoning sensors is presented. This navigation system is complemented by a two-step detection procedure that classifies outliers according to their associated source of error. Two different situations will be considered in the presence of multipath. These situations correspond to the presence or absence of line of sight for the different GPS satellites. Therefore, two kinds of errors are potentially “corrupting” the pseudo-ranges, modeled as variance changes or mean value jumps in noise measurements. An original multiple model approach is proposed to detect, identify and correct these errors and provide a final consistent solution

Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics

Automated synthesis of provably correct controllers for cyber-physical systems is crucial for deployment in safety-critical scenarios. However, hybrid features and stochastic or unknown behaviours make this problem challenging. We propose a method for synthesising controllers for Markov jump linear systems (MJLSs), a class of discrete-time models for cyber-physical systems, so that they certifiably satisfy probabilistic computation tree logic (PCTL) formulae. An MJLS consists of a finite set of stochastic linear dynamics and discrete jumps between these dynamics that are governed by a Markov decision process (MDP). We consider the cases where the transition probabilities of this MDP are either known up to an interval or completely unknown. Our approach is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS. We formalise this abstraction as an interval MDP (iMDP) for which we compute intervals of transition probabilities using sampling techniques from the so-called 'scenario approach', resulting in a probabilistically sound approximation. We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.Comment: 14 pages, 6 figures, under review at QES

The Generalized Area Theorem and Some of its Consequences

There is a fundamental relationship between belief propagation and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detail in a companion paper. This paper investigates the extension to general memoryless channels (paying special attention to the binary case). An area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed. We show that this area theorem gives rise to an upper-bound on the maximum a posteriori threshold for sparse graph codes. In situations where this bound is tight, the extrinsic soft bit estimates delivered by the belief propagation decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold. More generally, it is conjectured that the fundamental relationship between the maximum a posteriori and the belief propagation decoder which was observed for transmission over the binary erasure channel carries over to the general case. We finally demonstrate that in order for the design rate of an ensemble to approach the capacity under belief propagation decoding the component codes have to be perfectly matched, a statement which is well known for the special case of transmission over the binary erasure channel.Comment: 27 pages, 46 ps figure

Controle amostrado ótimo de sistemas lineares com saltos markovianos através de realimentação de estados

Orientador: José Cláudio GeromelTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Este trabalho é inteiramente dedicado ao desenvolvimento de uma lei de controle ótimo amostrado aplicada a sistemas lineares com saltos markovianos, cujo principal uso são os sistemas controlados através da rede (NCS - Networked Control System). Neste contexto, duas características da rede são consideradas simultaneamente: a limitação da largura de banda, tratada através da existência de sinais amostrados no sistema, e a perda de pacotes, modelada através de uma cadeia de Markov a tempo contínuo. A fim de alcançar este objetivo, a abordagem geral adotada é dividida em quatro etapas: análise de estabilidade e cálculo de norma no contexto da norma H2; análise de estabilidade e cálculo de norma no contexto da norma Hoo; projeto de controle amostrado ótimo que minimiza o índice de desempenho J2 baseado na norma H2, o qual pode ser expresso em uma formulação convexa baseada em LMIs; projeto de controle amostrado ótimo que minimiza um certo índice de desempenho Joo baseado na norma Hoo, o qual também admite uma formulação convexa baseada em LMI, embora uma análise matemática mais aprofundada seja necessária. Cada uma destas etapas possui a mesma estrutura descrita a seguir. Primeiro, os resultados teóricos são matematicamente desenvolvidos e provados. Segundo, alguns casos particulares são derivados a partir destes resultados teóricos. Terceiro, um algoritmo convergente é proposto para resolver cada um dos casos mencionados. As convergências também são provadas. Finalmente, um exemplo teórico ilustra os principais desenvolvimentos em cada caso. A teoria aqui desenvolvida é nova, não havendo resultado similar na literatura atual. Para uma visão prática dos resultados desta dissertação, três exemplos são considerados e adaptados de trabalhos disponíveis: dois deles correspondem a sistemas físicos controlados através de uma rede sendo um originalmente estável e o outro instável, e o terceiro corresponde a um sistema econômico cujas políticas de controle são aplicadas a tempo discretoAbstract: This work is entirely devoted to develop an optimal sampled-data control law applied to Markov jump linear systems, whose main usage is Networked Control Systems (NCS). In this context, two network characteristics are simultaneously considered: the bandwidth limitation addressed by the existence of sampled-data signals in the system, and the packet dropouts modeled by a continuous-time Markov chain. In order to accomplish this goal, the general adopted approach is broken in four steps: stability analysis and norm evaluation based on the H2 norm; stability analysis and norm evaluation in the Hoo context; the optimal sampled-data control design that minimizes a J2 performance index based on the H2 norm, which can be expressed in a convex formulation based on LMIs; the optimal sampled-data control design that minimizes a certain Joo performance index based on the Hoo norm, which also admits a convex formulation based on LMIs, even though a deeper mathematical analysis is required. Each step has the same structure described in the sequel. First, the theoretical results are mathematically developed and proved. Second, some particular cases are derived from these theoretical results. Third, a convergent algorithm is proposed to solve each of the mentioned cases. The convergence of the algorithms are also proved. Finally, a numerical example illustrates the main developments in each step. The theory developed here is new and there is no similar result in the current literature. For a practical view of the outcomes, three practical examples are borrowed and adapted from available works: two of them are physical systems controlled through an NCS, where one is originally stable and the other unstable, and the third one is an economical system whose policy is applied in a discrete-time basisDoutoradoAutomaçãoDoutora em Engenharia Elétrica2012/23634-2FAPES

Genetic-Algorithm-Assisted Sliding-Mode Control for Networked State-Saturated Systems over Hidden Markov Fading Channels

National Natural Science Foundation of China under Grants 61903143, 61933007, 61873058, 61873148, 61673174 and 61773162; Research Fund for the Taishan Scholar Project of Shandong Province of China; Shanghai Sailing Program of China under Grant 19YF1412100; 111 Project of China under Grant B17017; Royal Society of the U.K.; Alexander von Humboldt Foundation of Germany