9 research outputs found
A Survey on Reachable Set Techniques for Fault Recoverability Assessment
The development of any fault-tolerant control solution is based on the strong assumption that fault situations can be accommodated. This paper provides a survey of four reachable set techniques to assess the fault recoverability property for constrained linear time invariant (LTI) systems by means of ellipsoid, zonotope, polytope and support function representations. These techniques are next applied to an angular velocity spacecraft model. A discussion is finally made to assess the computational complexity for the four algorithms
Interval predictors for a class of uncertain discrete-time systems
This work presents set-valued algorithms to compute tight interval predictions of the state trajectories for a class of uncertain dynamical systems, where the dynamics is described as a sum of a linear and a nonlinear term. Based on interval analysis and the analytic expression of the state response of discrete-time linear systems, non-conservative numerical schemes are proposed. Moreover, under some stability conditions, the convergence of the width of the predicted state enclosures is proved. The performance of the proposed set-valued algorithms is illustrated through two numerical examples, and the results are compared to that obtained with another method selected from the literature
Sensitivity analysis of uncertain dynamic systems using set-valued integration
We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators
Avoiding geometric intersection operations in reachability analysis of hybrid systems
Although a growing number of dynamical systems studied in various fields are hybrid in nature, the verification of prop-erties, such as stability, safety, etc., is still a challenging problem. Reachability analysis is one of the promising meth-ods for hybrid system verification, which together with all other verification techniques faces the challenge of making the analysis scale with respect to the number of continuous state variables. The bottleneck of many reachability analysis techniques for hybrid systems is the geometrically computed intersection with guard sets. In this work, we replace the in-tersection operation by a nonlinear mapping onto the guard, which is not only numerically stable, but also scalable, mak-ing it possible to verify systems which were previously out of reach. The approach can be applied to the fairly common class of hybrid systems with piecewise continuous solutions, guard sets modeled as halfspaces, and urgent semantics, i.e. discrete transitions are immediately taken when enabled by guard sets. We demonstrate the usefulness of the new ap-proach by a mechanical system with backlash which has 101 continuous state variables
Distributed estimation techniques forcyber-physical systems
Nowadays, with the increasing use of wireless networks, embedded devices and agents with processing and sensing capabilities, the development of distributed estimation techniques has become vital to monitor important variables of the system that are not directly available. Numerous distributed estimation techniques have been proposed in the literature according to the model of the system, noises and disturbances.
One of the main objectives of this thesis is to search all those works that deal with distributed estimation techniques applied to cyber-physical systems, system of systems and heterogeneous systems, through using systematic review methodology. Even though systematic reviews are not the common way to survey a topic in the control community, they provide a rigorous, robust and objective formula that should not be ignored. The presented systematic review incorporates and adapts the
guidelines recommended in other disciplines to the field of automation and control and presents a brief description of the different phases that constitute a systematic review.
Undertaking the systematic review many gaps were discovered: it deserves to be remarked that some estimators are not applied to cyber-physical systems, such as sliding mode observers or set-membership observers. Subsequently, one of these particular techniques was chosen, set-membership estimator, to develop new applications for cyber-physical systems. This introduces the other objectives of the thesis, i.e. to present two novel formulations of distributed set-membership
estimators. Both estimators use a multi-hop decomposition, so the dynamics of the system is rewritten to present a cascaded implementation of the distributed set-membership observer, decoupling the influence of the non-observable modes to the observable ones. So each agent must find a different set for each sub-space, instead of a unique set for all the states. Two different approaches have been used to address the same problem, that is, to design a guaranteed distributed estimation method for linear full-coupled systems affected by bounded disturbances, to be implemented in a set of distributed agents that need to communicate and collaborate to achieve this goal
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Formal verification of analog and mixed signal circuits using deductive and bounded approaches
This thesis presents novel formal verification techniques to verify the important property of inevitability of states in analog and mixed signal (AMS) circuits. Two techniques to verify the inevitability of phase locking in a Charge Pump Phase Lock Loop (PLL) circuit are presented: mixed deductivebounded and deductive-only verification approaches. The deductive-bounded approach uses Lyapunov-like certificates with bounded advection of sets to verify the inevitability of phase locking. The deductive-only technique uses a combination of Lyapunov and Escape certificates to verify the inevitability property. Both deductive-only and deductive-bounded verification approaches involve positivity/negativity checks of polynomials over semi-algebraic sets, which both belong to the NP-hard set of problems. The Sum of Squares (SOS) programming technique is used to transform the positivity tests of polynomials to the feasibility of semi-definite programs. The efficacy of the approach is demonstrated by verifying the inevitability of phase locking for a third and fourth order CP PLL. Similarly, the inevitability of oscillation in ring oscillators (ROs) is verified using a numeric-symbolic deductive approach. The global inevitability (of oscillation) property is specified as a conjunction of several sub-properties that are verified via different Lyapunov-like certificates in different subsets of the state space. The construction of these certificates is posed as the verification of First Order Formulas (FOFs) having Universal-Existential quantifiers. A tractable numeric-symbolic approach, based on SOS programming and Quantifier Elimination (QE), is used to verify these FOFs. The approach is applied to the verification of inevitability of oscillation in ROs with odd and even topologies.
Furthermore, frequency domain properties specification and verification for analog oscillators is presented. The behaviour of an oscillator in the frequency domain is specified, while it operates in close proximity to the desired limit cycle, employing finite Fourier series representation of a periodic signal. To be sufficiently robust enough against parameter variations, robustness of parameters is introduced in these specifications. These frequency domain properties are verified using a mixed time-frequency domain technique based on Satisfiability Modulo Ordinary Differential Equation (SMODE). The efficacy of the technique is demonstrated for the benchmark voltage controlled and tunnel diode oscillators
Caractérisations et performances des assemblages collés époxyde-amine/aluminium
La caractĂ©risation et lâĂ©valuation des propriĂ©tĂ©s physiques, chimiques, physico-chimiques et mĂ©caniques sont un point important dans la comprĂ©hension du comportement des assemblages collĂ©s polymĂšre/substrat. La spectroscopie diĂ©lectrique est une mĂ©thode de caractĂ©risation efficace permettant dâĂ©tudier la dynamique molĂ©culaire, et permettre aussi un suivi in situ de joints collĂ©s. La modĂ©lisation mathĂ©matique de rĂ©sultats expĂ©rimentaux par la mĂ©thode de lâanalyse par intervalle permet de sâaffranchir de nombreux dĂ©fauts de logiciels utilisĂ©s couramment (erreur expĂ©rimentale prise en compte dans les calculs du modĂšle, permet dâaccepter ou de rejeter un modĂšle, âŠ). Il a Ă©tĂ© dĂ©montrĂ© quâen prĂ©sence dâun substrat mĂ©tallique, une compĂ©tition avait lieu entre la rĂ©action de polymĂ©risation et des rĂ©actions entre les monomĂšres et les substrats mĂ©talliques, menant Ă une interphase (i.e. interface dâĂ©paisseur non nulle) ayant des propriĂ©tĂ©s diffĂ©rentes des propriĂ©tĂ©s du mĂȘme polymĂšre en volume. Ces propriĂ©tĂ©s influent sur lâadhĂ©rence entre le polymĂšre Ă©poxydeamine et le substrat dâaluminium. LâadhĂ©rence sera caractĂ©risĂ©e par un test normĂ© et reliĂ©e aux propriĂ©tĂ©s de lâinterphase par diverses techniques. Des vieillissements de systĂšmes DGEBAanime/ aluminium ont Ă©tĂ© effectuĂ©s. Durant ces vieillissements, des tests destructifs et non destructifs ont Ă©tĂ© effectuĂ©s afin dâavoir un suivi sur les propriĂ©tĂ©s des interphases et interfaces de ces joints collĂ©s. Les rĂ©sultats obtenus ont Ă©tĂ© mis en corrĂ©lation afin de pouvoir ĂȘtre capable par lâutilisation de tests non destructifs in situ, de pouvoir prĂ©venir une rupture Ă lâinterphase/interface entre lâadhĂ©sif et le substra