Baris Taner

ORCID Identifier(s)

0000-0003-2942-2269

Graduation Semester and Year

2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Aerospace Engineering

Department

Mechanical and Aerospace Engineering

First Advisor

Kamesh Subbarao

Abstract

Cooperative systems, like any other dynamic systems, suffer in performance because of uncertainty yet there is an added layer of uncertainty due to the communication among agents. Therefore, analytic solution to these problems are hard if not impossible. With the advancements in the linear and non-linear methods, i.e. linear matrix inequalities (LMI) and non-linear transformations, robust performance analysis and controller synthesis for cooperative systems can be reformulated as optimization problems with LMI constraints as has been done in the last two decades. Another aspect of the problem becomes visible as the cooperative system grows larger and that necessitates faster solution methodologies to solve the aforementioned problem. Based on this context, the general objectives of this research are to develop computationally efficient analysis and synthesis methods for cooperative systems with uncertainties, which are •Develop computationally efficient linear parameter varying (LPV) and Linear Time Invariant (LTI) synthesis framework and regarding tailored optimization techniques for cooperative systems, which suffer performance because of uncertainties. - develop computationally efficient linear parameter varying controller synthesis method that accommodates uncertainty analysis in a distributed fashion and provide a framework to synthesize a robust cooperative system starting from a single agent - develop a robust cooperative system synthesis method that consider uncertainty analysis in edge weight synthesis - develop a cooperative system synthesis method that is formulated in distributed fashion to improve computational efficiency and suitable for distributed optimization. - develop implementation strategies for cooperative synthesis methods to state of the art applications. • develop computationally efficient linear parameter varying controller synthesis method that accommodates uncertainty analysis in a distributed fashion and provide a framework to synthesize a robust cooperative system starting from a single agent, • develop a cooperative system synthesis method that consider uncertainties, • develop a cooperative system synthesis method that is formulated in distributed fashion to improve computational efficiency and suitable for distributed optimization. The methods developed in this dissertation are verified using numerical simulations using the short-period dynamics of an aircraft as an application to benchmark the computational efficiency of the LMI-based methods. On top of that, the cooperative synthesis methodology is implemented on a cooperative docking application and a bipedal locomotion application through Model Predictive Control (MPC). This dissertation develops a framework for a systematic design of robust controllers to guarantee desired output performance for an interconnected group of multi-input-multi-output dynamic systems. The framework enables the design of a robust Linear Parameter Varying (LPV) controller for all individual vehicles and the interconnected group to account for uncertainties associated with the individual vehicles and the interconnections. In this dissertation, the robust controller design methodology for the individual and cooperative systems is implemented in a nested manner to enhance performance. The application of the nested robust controller is distributed wherein well-known robust performance analysis is adopted and modified. The controller synthesis methodology is developed on top of the same performance condition. Nested robust LPV controllers are synthesized for agents of the cooperative system. Then the cooperative system of these agents is interconnected using a connection topology that suffers time delays. A cooperative controller is designed using two methods described in this work in a nested fashion. Robustness against given uncertainties is studied with an integral quadratic constraint (IQC) framework. A benchmark is drawn by comparing conventional lumped and the developed distributed method in terms of time efficiency. Improving the robust performance of a cooperative system using cooperative controllers is a method. However, it increases the complexity of the synthesis due to the added states, and as the number of systems grows higher, the problem becomes intractable. A solution to this is to synthesize a cooperative system to improve its robust performance. Therefore the next problem studied in this work is implementing a non-linear programming method to synthesize edge weights of an adjacency matrix for a cooperative system using bi-linear matrix inequalities, which suffer uncertainties. First, convex-concave decompositions are used on the bi-linear matrix inequality constraints for nominal $H_{\infty}$ synthesis. Then this method is improved to consider uncertainties using the IQC framework. Agents composing the cooperative system are represented as a linear time-invariant single input, single output systems, which share their output information to achieve consensus. The topology of the cooperative system is predefined, and edge weights are defined as functions of a variable. Following a synthesis strategy that brings the best local robust performance of a cooperative system without adding the complexity of controllers is valuable, as, without loss of generality, these controllers have at least as many states as the agent. However, more efficient ways exist to extract the best local performance than synthesizing a cooperative system in lumped fashion. A more efficient way is to introduce distributed synthesis methodologies. Based on this context, this work further studies a distributed edge weight synthesis of a cooperative system for a fixed topology to improve $H_{\infty}$ performance, considering that disturbances are injected at interconnection channels. Performance metrics for lumped and distributed methods are common; therefore, constraints related to performance for both methods are similar. However, the connection between agents of the cooperative system is defined in a distributed fashion in terms of additional synthesis constraints, which constructs the optimization problem. Then this problem is cast into a linear matrix inequality problem by replacing the original cooperative system with an equivalent ideal cooperative system. Derivations of the method rely on the dissipative system framework. The proposed method provides an upper bound for the induced $\mathcal{L}_{2}$ norm of the original lumped cooperative system while reducing the computation time. A comparison of computation time illustrates the advantage of the proposed method against the lumped counterpart. As presented above, the implementation strategy for cooperative synthesis ideology is presented in terms of a fast-slow MPC. The MPC is built with task prioritization to perform docking maneuvers on cooperative systems. The studied method allows agents and a single agent to perform a docking maneuver. In addition, agents give different priorities to a specific subset of shared states. In this way, overall degrees of freedom to achieve the docking task are distributed among various subsets of the task space. Fast-slow model predictive control strategy uses non-linear and linear model predictive control formulations such that docking is handled as a non-linear problem until agents are close enough, where direct transcription is calculated using the Euler discretization method. During this phase generated trajectory is tracked with a linear model predictive control. Then linear model predictive control performs the sensitive close proximity motion to finish docking. The proposed strategy is illustrated in a case study, where quadcopter docks on a non-holonomic rover using a leader-follower topology. Finally, this dissertation presents a graph theoretic modeling and trajectory optimization technique for a biped robot named ASLB. This method utilizes a cooperative control framework to divide the state propagation and trajectory optimization of the lumped multi-body model of the robot into cooperative multi-bodies. The non-linear robot model is linearized at the current state, and states are propagated using the discrete newton Euler method. In addition, robot dynamics, contact location kinematics, and external forces are represented with respect to the body frame. This allows the cooperative quadratic optimization method to handle trajectory optimization for ASLB, a highly non-linear system with large degrees of freedom.

Keywords

Robust control, Cooperative control, H-infinity synthesis, Sequential programing, Linear Matrix inequalities, Bilinear matrix inequalities, Model predictive control, Cooperative docking, Online trajectory generation, Graph theoretic bipedal modeling

Disciplines

Aerospace Engineering | Engineering | Mechanical Engineering

Comments

Degree granted by The University of Texas at Arlington

Download

Share

COinS