Matching Items (1)
Filtering by
- All Subjects: Nonlinear systems
- Creators: M. Berman, Spring S.M.B
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