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Description
The goal of this thesis research is to contribute to the design of set-valued methods, i.e., algorithms that leverage a set-theoretic framework that can provide a powerful means for control designs for general classes of uncertain nonlinear dynamical systems, and in particular, to develop set-valued algorithms for constrained reachability problems and estimation.I propose novel fixed-order hyperball-valued observers for different classes of nonlinear systems, including Linear Parameter Varying, Lipschitz continuous and Decremental Quadratic Constrained nonlinearities, with unknown inputs that simultaneously find bounded sets of states and unknown inputs that contain the true states and inputs and are compatible with the measurement/outputs. In addition, I provide sufficient conditions for the existence and stability of the estimates, the convergence of the estimation errors, and the optimality of the observers.
Moreover, I design state and unknown input observers, as well as mode detectors for hidden mode, switched linear and nonlinear systems with bounded-norm noise and unknown inputs. To address this, I propose a multiple-model approach to obtain a bank of mode-matched set-valued observers in combination with a novel mode observer, based on elimination. My mode elimination approach uses the upper bound of the norm of to-be-designed residual signals to remove inconsistent modes from the bank of observers. I also provide sufficient conditions for mode detectability.
Furthermore, I address the problem of designing interval observers for partially unknown nonlinear systems, using affine abstractions, nonlinear decomposition functions, and a data-driven function over-approximation approach to over-estimate the unknown dynamic model. The proposed observer recursively computes the correct interval estimates. Then, using observed measurement signals, the observer iteratively shrinks the intervals. Moreover, the observer updates the over-approximation model
of the unknown dynamics.
Finally, I propose a tractable family of remainder-from decomposition functions for
a broad range of dynamical systems. Moreover, I introduce a set-inversion algorithm that along with the proposed decomposition functions have several applications, e.g., in the approximation of the reachable sets for bounded-error, constrained, continuous, and/or discrete-time systems, as well as in guaranteed state estimation. Leveraging mixed-monotonicity, I provide novel set-theoretic approaches to address the problem of polytope-valued state estimation in bounded-error discrete-time nonlinear systems, subject to nonlinear observations/constraints.
ContributorsKhajenejad, Mohammad (Author) / Zheng Yong, Sze S.Z.Y (Thesis advisor) / Nedich, Angelia A.N (Committee member) / Reffett, Kevin K.R (Committee member) / M. Berman, Spring S.M.B (Committee member) / Fainekos, Georgios G.F (Committee member) / Lee, Hyunglae H.L (Committee member) / Arizona State University (Publisher)
Created2021
Description
The objective of this thesis is to propose two novel interval observer designs for different classes of linear and hybrid systems with nonlinear observations. The first part of the thesis presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations. The observer is constructed using mixed-monotone decompositions, which ensures correctness and positivity without additional constraints/assumptions. The proposed design also involves additional degrees of freedom that may improve the performance of the observer design. The proposed observer is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. The observer gains are computed using mixed-integer (linear) programs. The second part of the thesis addresses the problem of designing a novel asymptotically stable interval estimator design for hybrid systems with nonlinear dynamics and observations under the assumption of known jump times. The proposed architecture leverages mixed-monotone decompositions to construct a hybrid interval observer that is guaranteed to frame the true states. Moreover, using common Lyapunov analysis and the positive/cooperative property of the error dynamics, two approaches were proposed for constructing the observer gains to achieve uniform asymptotic stability of the error system based on mixed-integer semidefinite and linear programs, and additional degrees of freedom are incorporated to provide potential advantages similar to coordinate transformations. The effectiveness of both observer designs is demonstrated through simulation examples.
ContributorsDaddala, Sai Praveen Praveen (Author) / Yong, Sze Zheng (Thesis advisor) / Tsakalis, Konstantinos (Thesis advisor) / Lee, Hyunglae (Committee member) / Arizona State University (Publisher)
Created2023