Backstepping PDE Design: A Convex Optimization Approach

Abstract\u2014Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sumof- Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs

Structural and analytical characterization by scanning transmission electron microscopy of silicon-based nanostructures

A few recent applications of scanning transmission electron microscopy (STEM) methods to problems of interest for nanoelectronics are reported. They include nanometer-scaled dopant profiles by Z-contrast and strain mapping by convergent beam diffraction

Model-Based Fault Detection and Estimation for Linear Time Invariant and Piecewise Affine Systems by Using Quadratic Boundedness

Quadratic boundedness is a notion of stability that is adopted to investigate the design of observers for dynamic systems subject to bounded disturbances. We will show how to exploit such observers for the purpose of fault detection. Toward this end, first of all we present the naive application of quadratic boundedness to construct state observers for linear time-invariant systems with state augmentation, i.e., where additional variables may be introduced to account for the occurrence of a fault. Then a Luenberger observer is designed to estimate the augmented state variable of the system in such a way to detect the fault by using a convenient threshold selection. Finally, such an approach is extended to piecewise affine systems by presenting a hybrid Luenberger observer and its related design based on quadratic boundedness. The design of all the observers for both linear time-invariant and piecewise affine systems can be done by using linear matrix inequalities. Simulation results are provided to show the effectiveness of the proposed approach

State Estimation Using a Network of Distributed Observers With Unknown Inputs

State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer has access to only local output measurements that may not be sufficient on their own to reconstruct the entire system’s state. Existing results in the literature on distributed state estimation assume either that the system does not have inputs, or that all the system’s inputs are globally known to all the observers. Accordingly, we address this gap by proposing a distributed observer capable of estimating the overall system’s state in the presence of inputs, while each observer only has limited local information on inputs and outputs. We provide a design method that guarantees convergence of the estimation errors to zero under joint detectability conditions. This design suits undirected communication graphs that may have switching topologies and also applies to strongly connected directed graphs.We also give existence conditions that are consistent with existing results on unknown input observers. Finally, simulation results verify the effectiveness of the proposed estimation scheme for various scenarios

Sensor fault-tolerant state estimation by networks of distributed observers

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system’s observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system’s state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme

Traffic-light control in urban environment exploiting drivers' reaction to the expected red lights duration

Traffic congestion in urban environment is one of the most critical issue for drivers and city planners for both environment and efficiency reasons. Traffic lights are one of the main tools used to regulate traffic by diverting the drivers between different paths. Rational drivers, in turn, react to the traffic light duration by evaluating their options and, if necessary, by changing direction in order to reach their destination quicker. In this paper, we introduce a macroscopic traffic model for urban intersections that incorporates this rational behavior of the drivers. Then, we exploit it to show that, by providing additional information about the expected redtime duration to the drivers, one can decrease the amount of congestion in the network and the overall length of the queues at the intersections. Additionally, we develop a control policy for the traffic lights that exploits the reaction of the drivers in order to divert them to a different route to further increase the performances. These claims are supported by extensive numerical simulations

Non-Asymptotic Kernel-based Parametric Estimation of Continuous-time Linear Systems

In this paper, a novel framework to address the problem of parametric estimation for continuous-time linear time-invariant dynamic systems is dealt with. The proposed methodology entails the design of suitable kernels of non-anticipative linear integral operators thus obtaining estimators showing, in the ideal case, \u201cnon-asymptotic\u201d (i.e., \u201cfinite-time\u201d) convergence. The analysis of the properties of the kernels guaranteeing such a convergence behaviour is addressed and a novel class of admissible kernel functions is introduced. The operators induced by the proposed kernels admit implementable (i.e., finite-dimensional and internally stable) state-space realizations. Extensive numerical results are reported to show the effectiveness of the proposed methodology. Comparisons with some existing continuous-time estimators are addressed as well and insights on the possible bias affecting the estimates are provided

A Distributed Approach for the Detection of Covert Attacks in Interconnected Systems with Stochastic Uncertainties

The design of a distributed architecture for the detection of covert attacks in interconnected Cyber-Physical Systems is addressed in this paper, in the presence of stochastic uncertainties. By exploiting communication between neighbors, the proposed scheme allows for the detection of covert attacks that are locally stealthy. The proposed methodology adopts a decentralized filter, jointly estimating the local state and the aggregate effect of the physical interconnections, and uses the communicated estimates to obtain an attack-sensitive residual. We derive some theoretical detection properties for the proposed architecture, and present numerical simulations

Switching-based Sinusoidal Disturbance Rejection for Uncertain Stable Linear Systems

The problem of rejection of sinusoidal disturbances with known frequencies acting on an unknown singleinput single-output linear system is addressed in this note. We present a new approach that does not require knowledge of the frequency response of the transfer function over the frequency of interest. The proposed methodology reposes upon the combination of the classic feedforward control algorithm and logic-based switching. The use of three different switching logics is proposed in this paper, namely: pre-routed, dwell-time and hysteresis switching. A comparative evaluation of the three switching strategies is performed via a simulation study

Traffic-light control in urban environment exploiting drivers’ reaction to the expected red lights duration

Traffic congestion in urban environment is one of the most critical issue for drivers and city planners for both environment and efficiency reasons. Traffic lights are one of the main tools used to regulate traffic by diverting the drivers between different paths. Rational drivers, in turn, react to the traffic light duration by evaluating their options and, if necessary, by changing direction in order to reach their destination quicker. In this paper, we introduce a macroscopic traffic model for urban intersections that incorporates this rational behavior of the drivers. Then, we exploit it to show that, by providing additional information about the expected red-time duration to the drivers, one can decrease the amount of congestion in the network and the overall length of the queues at the intersections. Additionally, we develop a control policy for the traffic lights that exploits the reaction of the drivers in order to divert them to a different route to further increase the performances. These claims are supported by extensive numerical simulations