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1. Adaptive RKHS-based functional estimation of structurally perturbed second order infinite dimensional systems

   https://doi.org/10.1109/CDC51059.2022.9992577  

   Demetriou, Michael A. (December 2022, 2022 IEEE 61st Conference on Decision and Control (CDC))

   . (Ed.)

   This paper proposes a new approach for the adaptive functional estimation of second order infinite dimensional systems with structured perturbations. First, the proposed observer is formulated in the natural second order setting thus ensuring the time derivative of the estimated position is the estimated velocity, and therefore called natural adaptive observer. Assuming that the system does not yield a positive real system when placed in first order form, then the next step in deriving parameter adaptive laws is to assume a form of input-output collocation. Finally, to estimate structured perturbations taking the form of functions of the position and/or velocity outputs, the parameter space is not identified by a finite dimensional Euclidean space but instead is considered in a Reproducing Kernel Hilbert Space. Such a setting allows one not to be restricted by a priori assumptions on the dimension of the parameter spaces. Convergence of the position and velocity errors in their respective norms is established via the use of a parameter-dependent Lyapunov function, specifically formulated for second order infinite dimensional systems that include appropriately defined norms of the functional errors in the reproducing kernel Hilbert spaces. Boundedness of the functional estimates immediately follow and via an appropriate definition of a persistence of excitation condition for functional estimation, a functional convergence follows. When the system is governed by vector second order dynamics, all abstract spaces for the state evolution collapse to a Euclidean space and the natural adaptive observer results simplify. Numerical results of a second order PDE and a multi-degree of freedom finite dimensional mechanical system are presented. 

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2. Efficient and Adaptive Decentralized Sparse Gaussian Process Regression for Environmental Sampling Using Autonomous Vehicles

   Norton, Tanner A. (June 2022, BYU Scholars Archive)

   In this thesis, I present a decentralized sparse Gaussian process regression (DSGPR) model with event-triggered, adaptive inducing points. This DSGPR model brings the advantages of sparse Gaussian process regression to a decentralized implementation. Being decentralized and sparse provides advantages that are ideal for multi-agent systems (MASs) performing environmental modeling. In this case, MASs need to model large amounts of information while having potential intermittent communication connections. Additionally, the model needs to correctly perform uncertainty propagation between autonomous agents and ensure high accuracy on the prediction. For the model to meet these requirements, a bounded and efficient real-time sparse Gaussian process regression (SGPR) model is needed. I improve real-time SGPR models in these regards by introducing an adaptation of the mean shift and fixed-width clustering algorithms called radial clustering. Radial clustering enables real-time SGPR models to have an adaptive number of inducing points through an efficient inducing point selection process. I show how this clustering approach scales better than other seminal Gaussian process regression (GPR) and SGPR models for real-time purposes while attaining similar prediction accuracy and uncertainty reduction performance. Furthermore, this thesis addresses common issues inherent in decentralized frameworks such as high computation costs, inter-agent message bandwidth restrictions, and data fusion integrity. These challenges are addressed in part through performing maximum consensus between local agent models which enables the MAS to gain the advantages of decentralization while keeping data fusion integrity. The inter-agent communication restrictions are addressed through the contribution of two message passing heuristics called the covariance reduction heuristic and the Bhattacharyya distance heuristic. These heuristics enable user to reduce message passing frequency and message size through the Bhattacharyya distance and properties of spatial kernels. The entire DSGPR framework is evaluated on multiple simulated random vector fields. The results show that this framework effectively estimates vector fields using multiple autonomous agents. This vector field is assumed to be a wind field; however, this framework may be applied to the estimation of other scalar or vector fields (e.g., fluids, magnetic fields, electricity, etc.). Keywords: Sparse Gaussian process regression, clustering, event-triggered, decentralized, sensor fusion, uncertainty propagation, inducing points 

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3. Cooperative Filtering and Parameter Identification for Advection–Diffusion Processes Using a Mobile Sensor Network

   https://doi.org/10.1109/TCST.2022.3183585  

   You, Jie; Zhang, Ziqiao; Zhang, Fumin; Wu, Wencen (June 2022, IEEE Transactions on Control Systems Technology)

   This article presents an online parameter identification scheme for advection-diffusion processes using data collected by a mobile sensor network. The advection-diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in the field values can be estimated. This leads to a co-design scheme for state estimation and parameter identification for advection-diffusion processes that is different from comparable schemes using sensors installed at fixed spatial locations. Using state estimates from the constrained cooperative Kalman filter, a recursive least-square (RLS) algorithm is designed to estimate unknown model parameters of the advection-diffusion processes. Theoretical justifications are provided for the convergence of the proposed cooperative Kalman filter by deriving a set of sufficient conditions regarding the formation shape and the motion of the mobile sensor network. Simulation and experimental results show satisfactory performance and demonstrate the robustness of the algorithm under realistic uncertainties and disturbances. 

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4. Learning-Based Adaptive Optimal Output Regulation of Discrete-Time Linear Systems

   https://doi.org/10.1016/j.ifacol.2023.10.912  

   Chakraborty, Sayan; Gao, Weinan; Cui, Leilei; Lewis, Frank L; Jiang, Zhong-Ping (October 2023, IFAC-PapersOnLine)

   In this paper, we address the problem of model-free optimal output regulation of discrete-time systems that aims at achieving asymptotic tracking and disturbance rejection when we have no exact knowledge of the system parameters. Insights from reinforcement learning and adaptive dynamic programming are used to solve this problem. An interesting discovery is that the model-free discrete-time output regulation differs from the continuous-time counterpart in terms of the persistent excitation condition required to ensure the uniqueness and convergence of the policy iteration. In this work, it is shown that this persistent excitation condition must be carefully established in order to ensure the uniqueness and convergence properties of the policy iteration. 

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5. Sensing-motion co-planning for reconstructing a spatially distributed field using a mobile sensor network

   https://doi.org/10.1109/CDC.2017.8264114  

   You, Jie; Wu, Wencen (December 2017, 56th IEEE Conference on Decision and Control)

   We investigate the problem of simultaneous parameter identification and mapping of a spatially distributed field using a mobile sensor network. We first develop a parametrized model that represents the spatially distributed field. Based on the model, a recursive least squares algorithm is developed to achieve online parameter identification. Next, we design a global state observer, which uses the estimated parameters, together with data collected by the mobile sensor network, to real-timely reconstruct the whole spatial-temporal varying field. Since the performance of the parameter identification and map reconstruction algorithms depends on the trajectories of the mobile sensors, we further develop a Lyapunov redesign based online trajectory planning algorithm for the mobile sensor network so that the mobile sensors can use local real-time information to guide them to move along information-rich paths that can improve the performance of the parameter identification and map construction. Lastly, a cooperative filtering scheme is developed to provide the state estimates of the spatially distributed field, which enables the recursive least squares method. To test the proposed algorithms in realistic scenarios, we first build a CO2 diffusion field in a lab and construct a sensor network to measure the field concentration over time. We then validate the algorithms in the reconstructed CO2 field in simulation. Simulation results demonstrate the efficiency of the proposed method. 

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