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Title:The constrained discrete-time state-dependent Riccati equation technique for uncertain nonlinear systems
Author(s):Chang, Insu
Director of Research:Bentsman, Joseph
Doctoral Committee Chair(s):Bentsman, Joseph
Doctoral Committee Member(s):Namachchivaya, Navaratnam Sri; Voulgaris, Petros G.; Alleyne, Andrew G.
Department / Program:Aerospace Engineering
Discipline:Aerospace Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Nonlinear control
Riccati equations
Discrete-time systems
Nonlinear analysis
Optimal control
Robust control
Uncertain dynamic systems
Target tracking
Kalman filters
Recursive estimation
Optimal estimation
Nonlinear analysis
Tuning algorithm
Particle swarm optimization
gain scheduling
Lookup table
Feedback linearization
open-loop control
Power balance
Spacecraft autonomy
Track-type tractor
Wheel loader
Abstract:The objective of the thesis is to introduce a relatively general nonlinear controller/estimator synthesis framework using a special type of the state-dependent Riccati equation technique. The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided. Stability of the D-SDRE feedback system is established using Lyapunov stability approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller. Stability condition of the CD-SDRE controller is analyzed by using a switched system. The use of CD-SDRE scheme in the presence of constraints is then systematically demonstrated by applying this scheme to problems of spacecraft formation orbit reconfiguration under limited performance on thrusters. Simulation results demonstrate the efficacy and reliability of the proposed CD-SDRE. The CD-SDRE technique is further investigated in a case where there are uncertainties in nonlinear systems to be controlled. First, the system stability under each of the controllers in the robust CD-SDRE technique is separately established. The stability of the closed-loop system under the robust CD-SDRE controller is then proven based on the stability of each control system comprising switching configuration. A high fidelity dynamical model of spacecraft attitude motion in 3-dimensional space is derived with a partially filled fuel tank, assumed to have the first fuel slosh mode. The proposed robust CD-SDRE controller is then applied to the spacecraft attitude control system to stabilize its motion in the presence of uncertainties characterized by the first fuel slosh mode. The performance of the robust CD-SDRE technique is discussed. Subsequently, filtering techniques are investigated by using the D-SDRE technique. Detailed derivation of the D-SDRE-based filter (D-SDREF) is provided under the assumption of Gaussian noises and the stability condition of the error signal between the measured signal and the estimated signals is proven to be input-to-state stable. For the non-Gaussian distributed noises, we propose a filter by combining the D-SDREF and the particle filter (PF), named the combined D-SDRE/PF. Two algorithms for the filtering techniques are provided. Several filtering techniques are compared with challenging numerical examples to show the reliability and efficacy of the proposed D-SDREF and the combined D-SDRE/PF.
Issue Date:2015-12-10
Rights Information:Copyright 2016 Insu Chang
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05

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