Robust Performance Analysis for Time-Varying Multi-Agent Systems with Stochastic Packet Loss

Recently, a scalable approach to system analysis and controller synthesis for homogeneous multi-agent systems with Bernoulli distributed packet loss has been proposed. As a key result of that line of work, it was shown how to obtain upper bounds on the $H_2$-norm that are robust with respect to uncertain interconnection topologies. The main contribution of the current paper is to show that the same upper bounds hold not only for uncertain but also time-varying topologies that are superimposed with the stochastic packet loss. Because the results are formulated in terms of linear matrix inequalities that are independent of the number of agents, multi-agent systems of any size can be analysed efficiently. The applicability of the approach is demonstrated on a numerical first-order consensus example, on which the obtained upper bounds are compared to estimates from Monte-Carlo simulations.Comment: 8 pages, 4 figures. Extended version of a paper to be published at IFAC World Congress 202

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

A Scalable Approach for Analysing Multi-Agent Systems with Heterogeneous Stochastic Packet Loss

An important aspect in jointly analysing networked control systems and their communication is to model the networking in a sufficiently rich but at the same time mathematically tractable way. As such, this paper improves on a recently proposed scalable approach for analysing multi-agent systems with stochastic packet loss by allowing for heterogeneous transmission probabilities and temporal correlation in the communication model. The key idea is to consider the transmission probabilities as uncertain, which facilitates the use of tools from robust control. Due to being formulated in terms of linear matrix inequalities that grow linearly with the number of agents, the result is applicable to very large multi-agent systems, which is demonstrated by numerical simulations with up to 10000 agents.Comment: 8 pages, 3 figure

Robust Controller for Delays and Packet Dropout Avoidance in Solar-Power Wireless Network

Solar Wireless Networked Control Systems (SWNCS) are a style of distributed control systems where sensors, actuators, and controllers are interconnected via a wireless communication network. This system setup has the benefit of low cost, flexibility, low weight, no wiring and simplicity of system diagnoses and maintenance. However, it also unavoidably calls some wireless network time delays and packet dropout into the design procedure. Solar lighting system offers a clean environment, therefore able to continue for a long period. SWNCS also offers multi Service infrastructure solution for both developed and undeveloped countries. The system provides wireless controller lighting, wireless communications network (WI-FI/WIMAX), CCTV surveillance, and wireless sensor for weather measurement which are all powered by solar energy

A Decomposition Approach to Multi-Agent Systems with Bernoulli Packet Loss

In this paper, we extend the decomposable systems framework to multi-agent systems with Bernoulli distributed packet loss with uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance - which are expressed in the form of linear matrix inequalities - scale linearly with increased network size and thus allow to analyse even very large-scale multi-agent systems. A numerical example demonstrates the potential of the approach by application to a first-order consensus problem.Comment: 11 pages, 4 figure

H1 and H2 control design for polytopic continuous-time Markov jump linear systems with uncertain transition rates.

This paper investigates the problems of H1 and H2 state feedback control design for continuous-time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi-simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter-dependent Lyapunov matrices to certify the mean square closed-loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with H1 and H2 state feedback control in both mode-independent and modedependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system

Networked Control System Design and Parameter Estimation

Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6). Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of H₂ and H∞ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed H₂/H∞ control problem is solved under the framework of LMIs. To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system. Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The l₂-l∞ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques. Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities. Finally, several open problems are listed as the future research directions

Control of Impulsive Renewal Systems: Application to Direct Design in Networked Control

Abstract — We consider the control of impulsive systems with jumps triggered by a renewal process, that is, the intervals between jumps are independent and identically distributed. The control action and output measurement are assumed to take place only at jump times. Necessary and sufficient conditions, in the form of LMIs, are given for mean square stabilizability and detectability for the class of systems considered. An infinite horizon quadratic optimal control problem is solved, under appropriate stabilizability and detectability properties. The class of impulsive renewal systems is shown to be especially suited to model networked control systems utilizing CSMA-type protocols, with stochastic intervals between transmissions and packet drops. In this setting, the analysis and synthesis tools mentioned above are used to (i) prove that for an emulationbased design, stability of the closed-loop is preserved if the distribution of the intervals between transmissions assigns high probability to fast sampling (ii) illustrate through a benchmark example the potential advantages of controller direct-design over an emulation-based design. I

Fault Compensation Controller for Markovian Jump Linear Systems

In this paper, we tackle the fault-compensation controller in the context of Marko- vian Jump Linear Systems (MJLS). More specifically, we propose the design of H∞ Fault- Compensation Controllers under the MJLS formulation, which is provided in terms of linear matrices inequalities optimization problems. These particular controllers have as the main motivation the network communication loss which is inherent to any automation process. We present a numerical example of a coupled tank system, where a Monte Carlo simulation illustrates the feasibility of the proposed solution. The results show that the proposed approach is indeed a valuable alternative to compensate for the fault occurrence