Browsing by Subject "System Identification"
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Item First-Order Algorithms for Unconstrained/Constrained Dynamic Games and Identification of Linear Dynamic Systems with Multiplicative Noise(2021-02) Di, BoleiThe thesis consists of two parts or works. The first part focuses on numerical methods for computing the Nash equilibria of unconstrained and constrained dynamics games, and the second one studies linear system identification with multiplicative noise. We approach both topics from the angles of optimal control and optimization theory.Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems, etc. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. We focus on the state space formulation of dynamic games. Extra constraints that limit the space of actions based on the current state and other players’ actions at each step, make the distinction between our unconstrained and constrained dynamic games. As in the single-agent case, only specific dynamic games can be solved exactly, so approximation algorithms are required. We focus on iterative numerical methods for finding the Nash equilibria of constrained/unconstrained full-information non-zero-sum dynamic games. We make a clear distinction between open-loop Nash equilibrium (OLNE) and feedback Nash equilibrium (FNE), which are very different in the structures. Therefore, we need different numerical methods. In the unconstrained case, we show how the stagewise Newton method, the approximated Bellman recursion (ABR), and the popular differential dynamic programming (DDP) originated from single-agent optimization or optimal control, can be adapted to the multi-player dynamic games. While the Newton step method works for OLNE, the other methods are related to FNE. We show that Newton’s step can be solved in a computationally efficient manner and inherits its original quadratic convergence rate to open-loop Nash equilibria and that the ABR and DDP methods are very similar and can be used to find local feedback O(ε2)-Nash equilibria. For the constrained case, we show how to extend the projected gradient and Douglas- Rachford (DR) splitting methods that originated from constrained optimization and variational inequalities to solve the OLNEs. The resulting algorithms converge locally to open-loop Nash equilibria (OLNE) at linear rates. Furthermore, we extend the approximated Bellman recursion we proposed for the unconstrained dynamic games method to find local FNE for constrained dynamic games. In the case of linear dynamics and polyhedral constraints, we show that this local feedback policy is a local approximated feedback Nash equilibrium (FNE). All of our methods exploit the temporal structure of a dynamic system and therefore have a linear complexity with respect to the number of stages, which is a major improvement on the previously existing methods. Linear systems with multiplicative noise (LSMN) have been approached from robust control, filtering and optimal control, system identification, and reinforcement learning since LSMN’s early emergence in the 1960s. We focus on the improvement of system identification methods for LSMN by offering an algorithm based on least-squares estimation, which estimates both the first and second moments of the system parameters, and offers a probability bound on the estimates. Our proposed method can be applied to a more general problem formulation than the existing ones. We further develop an online scheme for estimation and a robust control scheme based on the estimation and bound. Overall, the thesis is focusing on proposing novel numerical algorithms for control/game problems that have not been satisfactorily solved. The effectiveness of the proposed algorithms in terms of their scope, convergence, and complexity is analyzed. Inspirations of these new numerical algorithms typically came from existing methods for optimization, optimal control, and variational inequality problems. For each topic we focus on, the problem formulation, proposed algorithms, and analysis of the algorithms are the three major components.Item Integration of environment sensing and control functions for Robust Rotorcraft UAV (RUAV) guidance.(2012-05) Tehrani, Navid DadkhahUnmanned Air Vehicles (UAVs) have started supplanting manned aircraft in a broad range of tasks. Vehicles such as miniature rotorcrafts with broad maneuvering range and small size can enter remote locations that are hard to reach using other air and ground vehicles. Developing a guidance system which enables a Rotorcraft UAV (RUAV) to perform such tasks involves combing key elements from robotics motion planning, control system design, trajectory optimization as well as dynamics modeling. The focus of this thesis is to integrate a guidance system for a small-scale rotorcraft to enable a high level of performance and situational awareness. We cover large aspects of the system integration including modeling, control system design, environment sensing as well as motion planning in the presence of uncertainty. The system integration in this thesis is performed around a Blade-CX2 miniature coaxial helicopter. The first part of the thesis focuses on the development of the parameterized model for the Blade-CX2 helicopter with an emphasis on the coaxial rotor configuration. The model explicitly accounts for the dynamics of lower rotor and uses an implicit lumped parameter model for the upper rotor and stabilizer-bar. The parameterized model was identified using frequency domain system identification. In the second part of the thesis, we use the identified model to design a control law for the Blade-CX2 helicopter. The control augmentation for the Blade-CX2 helicopter was based on a nested attitude-velocity loop control architecture and was designed following classical loop-shaping and dynamic inversion techniques. A path following layer wrapped around the velocity control system enables the rotorcraft to follow reference trajectories specified by a sequence of waypoints and velocity vectors. Such reference paths are common in autonomous guidance systems. Finally, the third part of the thesis addresses the problem of autonomous navigation through a partially known or unknown 3D cluttered environment. The proposed multi-layer hierarchical guidance framework is based on optimal control principles and relies on the interaction of several subsystems such as environment sensing and mapping, Cost-to-Go (CTG) function update, reactive planning and Receding Horizon (RH) optimization. It is also tightly integrated with the path following controller.Item Long-Term Vibration Monitoring of the I-35W St. Anthony Falls Bridge(2017-05) Gaebler, KarlVibration based structural health monitoring has become more common in recent years as the required data acquisition and analysis systems become more affordable to deploy. It has been proposed that by monitoring changes in the dynamic signature of a structure, primarily the natural frequency, one can detect damage. This approach to damage detection is made difficult by the fact that environmental factors, such as temperature, have been shown to cause variation in the dynamic signature in a structure, effectively masking those changes due to damage. Another parameter, such as displacement estimates, may be better suited for damage detection, however and effective and accurate routine for such estimates is required. A monitoring system on the I-35W St. Anthony Falls Bridge, which crosses the Mississippi River in Minneapolis, MN, has been collecting vibration and temperature data since the structures opening in 2008. This provides a uniquely large data set, in a climate that sees extreme variation in temperature, to test the relationship between the dynamic signature of a concrete structure and temperature. A system identification routine utilizing NExT-ERA/DC is proposed to effectively analyze this large data set, and the relationship between structural temperature and natural frequency is investigated, and a displacement estimation technique is proposed.Item Non-Parametric Estimation of Uncertain Closed-Loop Multivariate Frequency Response for Stability Assurance(2022-03) Regan, ChristopherSystem identification of closed-loop, multivariate systems presents a complex challenge; the use case for this study is on estimation for the purpose of stability margin assurance. Assessing both the nominal, or "best", estimated stability margins and the uncertainty range of those estimates are critical. This challenge is addressed by subjecting the system to multisine excitations and evaluating the response at both the excited frequencies and a set of null frequencies that are interleaved with the excited frequencies. This unique form of frequency separation allows for isolation of the response due to disturbances; which provides a critical source of estimation uncertainty. Additional sources of uncertainty, arising from response variations with time and spectral leakage, are combined to form a total estimated uncertainty. The impact of nonlinearities in the response are addressed, along with a particular approach to identification of nonlinearities. System stability assessment is performed, that directly accounts for estimation uncertainty. The approach to system estimation and stability assessment requires minimal prior knowledge and relies on only in situ data; the result is an independent assurance of system stability.Item Thor Flight 25(2011-10-05) Taylor, BrianItem Thor Flight 36(2012-04-20) Taylor, BrianItem Thor Flight 37(2012-04-20) Taylor, BrianItem Thor Flight 38(2012-04-20) Taylor, BrianItem Thor Flight 39(2012-04-20) Taylor, BrianItem Thor Flight 40(2012-04-20) Taylor, BrianItem Thor Flight 41(2012-05-09) Taylor, BrianItem Thor Flight 44(2012-05-21) Taylor, BrianItem Thor Flight 45(2012-05-21) Taylor, Brian