Graduation Year

2020

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mechanical Engineering

Major Professor

Tansel Yucelen, Ph.D.

Committee Member

Jonathan A. Muse, Ph.D.

Committee Member

Rajiv Dubey, Ph.D.

Committee Member

Kyle Reed, Ph.D.

Committee Member

Yasin Yilmaz, Ph.D.

Keywords

distributed control, model reference adaptive control, multiagent systems, stability and performance guarantees

Abstract

In adaptive control of physical systems, it is well-known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed-loop system trajectories. Motivated by this standpoint, this dissertation presents novel model reference and distributed adaptive control architectures with stability and performance guarantees for uncertain sole and multiagent dynamical systems with unmodeled and/or actuator dynamics.

Specifically, model reference and distributed adaptive control architectures are powerful theoretical tools for both sole and multiagent systems, where they have the capability to suppress the effect of exogenous disturbances and system uncertainties for achieving a desired level of closed-loop system response. However, the closed-loop system stability with these methods can be challenged for a wide array of applications that involve unmodeled dynamics (e.g., rigid body systems coupled with flexible appendages, airplanes with high aspect ratio wings, high speed vehicles with rigid body and flexible dynamics coupling, and flexible dynamics as in lightweight agents and/or flexible appendages as in freight carrying operations), actuator dynamics (e.g., cooperation of low and high speed autonomous vehicles and nonidentical agent actuation

capabilities), and system uncertainties (e.g., unknown parameters in dynamics due to modelling errors and/or structural damage due to adverse conditions).

The challenges associated with the system uncertainties and unmodeled dynamics are first addressed using six novel approaches that determine and relax the stability limits (e.g., conditions and trade-offs) as well as the improve transient performance. In particular, it is known that a closed-loop dynamical system subject to an adaptive controller remains stable either if there does not exist significant unmodeled dynamics or the effect of system uncertainties is negligible. This implies that these controllers cannot tolerate large system uncertainties even when the unmodeled dynamics satisfy a set of limits. The first approach is predicated on a novel model reference adaptive control architecture that is augmented with an adaptive robustifying term. Unlike standard adaptive controllers, the proposed architecture allows the closed-loop

dynamical system to remain stable in the presence of large system uncertainties when the unmodeled system dynamics satisfy a set of conditions. The second, third, fourth, fifth, and sixth approaches of this dissertation are the generalizations of the first one. These approaches respectively consider an experimental verification, a theoretical extension to a class of nonlinear unmodeled dynamics, an architecture to achieve a guaranteed performance, a theoretical extension for dynamical systems with unstructured uncertainties, and an asymptotic decoupling approach for the problem of presence of unmodeled dynamics in the dynamical system. In particular, the second approach presents an experimental result for the purpose of demonstrating the efficacy of the first approach, where a benchmark mechanical system setup is used involving an inverted

pendulum on a cart coupled with another cart through a spring in the presence of unknown frictions. The third approach presents an extension of the first approach to a wider class of unmodeled dynamics involving nonlinear functions. Moreover, the fourth approach presents a direct uncertainty minimization framework with the added term in the control signal and the update law, which is developed through a gradient descent procedure with a new cost function involving a cost function gain, in order to minimize the effect of both system uncertainties and unmodeled dynamics on the closed-loop system response. The fifth approach presents stability conditions of model reference adaptive control architectures in the presence of unstructured system uncertainties subject to (residual) approximating errors satisfying the linear growth inequality and

unmodeled dynamics. Note that the fourth and fifth approaches are also experimentally validated on the benchmark mechanical system setup. Finally, the last approach presents a new framework guaranteeing asymptotic convergence between the trajectories of an uncertain dynamical system and a given reference model without relying on any measurements from the coupled dynamics.

The challenges associated with the uncertain dynamical systems in the presence of both unmodeled and actuator dynamics are second addressed using four novel approaches that determine and relax the stability limits. Specifically, model reference adaptive control architectures with standard, hedging-based (that alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of actuator dynamics), and expanded reference models (uses a reference model predicated on the weight estimation and a copy of the actuator dynamics) are analyzed for this class of uncertain dynamical systems and sufficient stability conditions are developed. A robustifying term is then synthesized for the latter architecture and to analytically show that this term can allow for a relaxed sufficient stability condition.

The challenges associated with the uncertain multiagent systems in the presence of unmeasurable unmodeled dynamics are third addressed using a novel distributed adaptive architecture. Specifically, standard distributed adaptive control method with system uncertainties and coupled dynamics in a leader-follower setting is analyzed, where local stability conditions are developed. An additional feedback term within the control signal of each agent is also proposed for relaxing the local stability conditions.

The challenges associated with the uncertain multiagent systems in the presence of heterogeneous actuator dynamics are finally addressed using novel distributed adaptive architectures. First, a distributed adaptive control architecture in a leader-follower setting for the class of both scalar and high-order multiagent systems is proposed. The proposed architectures use a hedging method for ensuring correct adaptation in the presence of heterogeneous actuator dynamics of these agents. Second, sufficient stability conditions are showed, where evaluation of these conditions with respect to a given graph topology allows stability verification of the controlled multiagent system.

To summarize, verifiable model reference adaptive control architectures for both sole and multiagent systems are introduced in this dissertation, where the stability limits of these architectures in the presence of unmodeled and actuator dynamics as well as system uncertainties are shown. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. For bridging the gap between theory and practice, several simulation and experimental results are also presented.

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