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<p>Robotic platforms have several characteristics such as speed and precision that make them enticing for use in medical procedures. Companies such as Intuitive Medical and Titan Medical have taken advantage of these features to introduce surgical robots for minimally invasive procedures. Such robots aim to reduce procedure and patient recovery times. Current technology requires platforms to be master-slave manipulators controlled by a surgeon, effectively converting the robot into an expensive surgical tool. Research into the interaction between robotic platforms and deformable objects such as human tissue is necessary in the development of autonomous and semi-autonomous surgical systems. This thesis investigates a class of robust linear controllers based on a worst case performance measure known as the $H_{\infty}$ norm, for the purpose of performing so called Indirect Deformable Object Manipulation (IDOM). This task allows positional regulation of regions of interest in a deformable object without directly interacting with them, enabling tasks such as stabilization of tumors during biopsies or automatic suturing. A complete approach to generating linear $H_{\infty}$ based controllers is presented, from derivation of a plant model to the actual synthesis of the controller. The introduction of model uncertainty requires $\mu$ synthesis techniques, which extend $H_{\infty}$ designs to produce highly robust controller solutions. In addition to $H_{\infty}$ and $\mu$ synthesis designs, the thesis presents an approach to design an optimal PID controller with gains that minimize the $H_{\infty}$ norm of a weighted plant. The three control approaches are simulated performing set point regulation in $\text{MATLAB}^{TM}$'s $simulink$. Simulations included disturbance inputs and noises to test stability and robustness of the approaches. $H_{\infty}$ controllers had the best robust performance of the controllers simulated, although all controllers simulated were stable. The $H_{\infty}$ and PID controllers were validated in an experimental setting, with experiments performed on two different deformable synthetic materials. It was found that $H_{\infty}$ techniques were highly robust and provided good tracking performance for a material that behaved in a relatively elastic manner, but failed to track well when applied to a highly nonlinear rubber compound. PID based control was outperformed by $H_{\infty}$ control in experiments performed on the elastic material, but proved to be superior when faced with the nonlinear material. These experimental findings are discussed and a linear $H_{\infty}$ control design approach is proposed.</p> / Master of Applied Science (MASc)

The focus of this dissertation is on developing novel methods and extending existing ones to improve the security and reliability of fixed-wing unmanned aircraft systems (UAS). Specifically, we focus on three strands of work: i) designing UAS controllers with performance guarantees using the robust control framework, ii) developing tools for detection and mitigation of physical-layer security threats in UAS, and iii) extending tools from compositional verification to design and verify complex systems such as UAS. Under the first category, we use the robust H-infinity control approach to design a linear parameter-varying (LPV) path-following controller for a fixed-wing UAS that enables the aircraft to follow any arbitrary planar curvature-bounded path under significant environmental disturbances. Three other typical path-following controllers, namely, a linear time-invariant H-infinity controller, a nonlinear rate-tracking controller, and a PID controller, are also designed. We study the relative merits and limitations of each approach and demonstrate through extensive simulations and flight tests that the LPV controller has the most consistent position tracking performance for a wide array of geometric paths. Next, convex synthesis conditions are developed for control of distributed systems with uncertain initial conditions, whereby independent norm constraints are placed on the disturbance input and the uncertain initial state. Using this approach, we design a distributed controller for a network of three fixed-wing UAS and demonstrate the improvement in the transient response of the network when switching between different trajectories. Pertaining to the second strand of this dissertation, we develop tools for detection and mitigation of security threats to the sensors and actuators of UAS. First, a probabilistic framework that employs tools from statistical analysis to detect sensor attacks on UAS is proposed. By incorporating knowledge about the physical system and using a Bayesian network, the proposed approach minimizes the false alarm rates, which is a major challenge for UAS that operate in dynamic and uncertain environments. Next, the security vulnerabilities of existing UAS actuators are identified and three different methods of differing complexity and effectiveness are proposed to detect and mitigate the security threats. While two of these methods involve developing algorithms and do not require any hardware modification, the third method entails hardware modifications to the actuators to make them resilient to malicious attacks. The three methods are compared in terms of different attributes such as computational demand and detection latency. As for the third strand of this dissertation, tools from formal methods such as compositional verification are used to design an unmanned multi-aircraft system that is deployed in a geofencing application, where the design objective is to guarantee a critical global system property. Verifying such a property for the multi-aircraft system using monolithic (system-level) verification techniques is a challenging task due to the complexity of the components and the interactions among them. To overcome these challenges, we design the components of the multi-aircraft system to have a modular architecture, thereby enabling the use of component-based reasoning to simplify the task of verifying the global system property. For component properties that can be formally verified, we employ results from Euclidean geometry and formal methods to prove those properties. For properties that are difficult to be formally verified, we rely on Monte Carlo simulations. We demonstrate how compositional reasoning is effective in reducing the use of simulations/tests needed in the verification process, thereby increasing the reliability of the unmanned multi-aircraft system. / Doctor of Philosophy / Given the safety-critical nature of many unmanned aircraft systems (UAS), it is crucial for stake holders to ensure that UAS when deployed behave as intended despite atmospheric disturbances, system uncertainties, and malicious adversaries. To this end, this dissertation deals with developing novel methods and extending existing ones to improve the security and reliability of fixed-wing UAS. Specifically, we focus on three key areas: i) designing UAS controllers with performance guarantees, ii) developing tools for detection and mitigation of security threats to sensors and actuators of UAS, and iii) extending tools from compositional verification to design and verify complex systems such as UAS. Pertaining to the first area, we design controllers for UAS that would enable the aircraft to follow any arbitrary planar curvature-bounded path under significant atmospheric disturbances. Four different controllers of differing complexity and effectiveness are designed, and their relative merits and limitations are demonstrated through extensive simulations and flight tests. Next, we develop control design tools to improve the transient response of multi-mission UAS networks. Using these tools, we design a controller for a network of three fixed-wing UAS and demonstrate the improvement in the transient response of the network when switching between different trajectories. As for the contributions in the second area, we develop tools for detection and mitigation of security threats to the sensors and actuators of UAS. First, we propose a framework for detecting sensor attacks on UAS. By judiciously using knowledge about the physical system and techniques from statistical analysis, the framework minimizes the false alarm rates, which is a major challenge in designing attack detection systems for UAS. Then, we focus on another important attack surface of the UAS, namely, the actuators. Here, we identify the security vulnerabilities of existing UAS actuators and propose three different methods to detect and mitigate the security threats. The three methods are compared in terms of different attributes such as computational demand, detection latency, need for hardware modifications, etc. In regard to the contributions in the third area, tools from compositional verification are used to design an unmanned multi-aircraft system that is tasked to track and compromise an aerial encroacher, wherein the multi-aircraft system is required to satisfy a global system property pertaining to collision avoidance and close tracking. A common approach to verifying global properties of systems is monolithic verification where the whole system is analyzed. However, such an approach becomes intractable for complex systems like the multi-aircraft system considered in this work. We overcome this difficulty by employing the compositional verification approach, whereby the problem of verifying the global system property is reduced to a problem of reasoning about the system’s components. That being said, even formally verifying some component properties can be a formidable task; in such cases, one has to rely on Monte Carlo simulations. By suitably designing the components of the multi-aircraft system to have a modular architecture, we show how one can perform focused component-level simulations rather than conduct simulations on the whole system, thereby limiting the use of simulations during the verification process and, as a result, increasing the reliability of the system.

The main contributions of this work are applications of robust control and analysis methods to complex engineering systems, namely, small fixed-wing unmanned aircraft systems (UAS). Multiple path-following controllers for a small fixed-wing Telemaster UAS are presented, including a linear parameter-varying (LPV) controller scheduled over path curvature. The controllers are synthesized based on a lumped path-following and UAS dynamic system, effectively combining the six degree-of-freedom aircraft dynamics with established parallel transport frame virtual vehicle dynamics. The robustness and performance of these controllers are tested in a rigorous MATLAB simulation environment that includes steady winds, turbulence, measurement noise, and delays. After being synthesized off-line, the controllers allow the aircraft to follow prescribed geometrically defined paths bounded by a maximum curvature. The controllers presented within are found to be robust to the disturbances and uncertainties in the simulation environment. A robust analysis framework for mathematical validation of flight control systems is also presented. The framework is specifically developed for the complete uncertainty characterization, quantification, and analysis of small fixed-wing UAS. The analytical approach presented within is based on integral quadratic constraint (IQC) analysis methods and uses linear fractional transformations (LFTs) on uncertainties to represent system models. The IQC approach can handle a wide range of uncertainties, including static and dynamic, linear time-invariant and linear time-varying perturbations. While IQC-based uncertainty analysis has a sound theoretical foundation, it has thus far mostly been applied to academic examples, and there are major challenges when it comes to applying this approach to complex engineering systems, such as UAS. The difficulty mainly lies in appropriately characterizing and quantifying the uncertainties such that the resulting uncertain model is representative of the physical system without being overly conservative, and the associated computational problem is tractable. These challenges are addressed by applying IQC-based analysis tools to analyze the robustness of the Telemaster UAS flight control system. Specifically, uncertainties are characterized and quantified based on mathematical models and flight test data obtained in house for the Telemaster platform and custom autopilot. IQC-based analysis is performed on several time-invariant H∞ controllers along with various sets of uncertainties aimed at providing valuable information for use in controller analysis, controller synthesis, and comparison of multiple controllers. The proposed framework is also transferable to other fixed-wing UAS platforms, effectively taking IQC-based analysis beyond academic examples to practical application in UAS control design and airworthiness certification. IQC-based analysis problems are traditionally solved using convex optimization techniques, which can be slow and memory intensive for large problems. An oracle for discrete-time IQC analysis problems is presented to facilitate the use of a cutting plane algorithm in lieu of convex optimization in order to solve large uncertainty analysis problems relatively quickly, and with reasonable computational effort. The oracle is reformulated to a skew-Hamiltonian/Hamiltonian eigenvalue problem in order to improve the robustness of eigenvalue calculations by eliminating unnecessary matrix multiplications and inverses. Furthermore, fast, structure exploiting eigensolvers can be employed with the skew-Hamiltonian/Hamiltonian oracle to accurately determine critical frequencies when solving IQC problems. Applicable solution algorithms utilizing the IQC oracle are briefly presented, and an example shows that these algorithms can solve large problems significantly faster than convex optimization techniques. Finally, a large complex engineering system is analyzed using the oracle and a cutting-plane algorithm. Analysis of the same system using the same computer hardware failed when employing convex optimization techniques. / Ph. D.

<p dir="ltr">The automotive industry has incorporated controls since the 1970s, starting with the pioneering application of an air-to-fuel ratio feedback control carburetor. Over time, significant advancements have been made in control strategies to meet industry standards for reduced fuel consumption, exhaust emissions, and enhanced safety. This thesis focuses on the implementation of advanced control strategies in heavy-duty diesel powertrains and their advantages over traditional control methods commonly employed in the automotive industry.</p><p dir="ltr">The initial part of the thesis demonstrates the utilization of model predictive control (MPC) to generate an optimized velocity profile for class 8 trucks. These velocity profiles are designed to minimize fuel consumption along a given route with known grade conditions, while adhering to the time constraints comparable to those of standard commercial cruise controllers. This methodology is further expanded to include the platooning of two trucks, with the rear truck following a desired gap (variable or fixed), resulting in additional fuel savings throughout the designated route. Through collaborative efforts involving Cummins, Peloton Technology, and Purdue University, these control strategies were implemented and validated through simulation, hardware-in-the-loop testing, and ultimately, in demonstration vehicles.</p><p dir="ltr">MPC is highly effective for vehicle-level controls due to the accurate plant model used for optimization. However, when it comes to engine controls, the plant model becomes highly nonlinear and loses accuracy when linearized [20]. To address this issue, robust control techniques are introduced to account for the inherent inaccuracies in the plant model, which can be represented as uncertainties.</p><p dir="ltr">The second study showcases the application of robust controllers in diesel engine operations, focusing on a 4.5L John Deere diesel engine equipped with an electrified intake boosting system. The intake boosting system is selectively activated during transient operations to mitigate drops in the air-to-fuel ratio (AFR), which can result in smoke emissions. Initially, a two-degree-of-freedom robustsingle-input single-output (SISO) eBooster controller is synthesized to control the eBooster during load transients. Although the robust SISO controller yields improvements, the eBooster alone does not encompass all factors affecting the gas exchange process. Other actuators, such as the exhaust throttle and EGR valve, need to be considered to enhance the air handling system. To achieve this, a robust model-basedmultiple-input multiple-output (MIMO) controller is developed to regulate the desired AFR, engine speed, and diluent air ratio (DAR) using various air handling actuators and fueling strategies. The robust MIMO controller is synthesized based on a physics-based mean value engine model, which has been calibrated to accurately reflect high-fidelity engine simulation software. The robust SISO and MIMO controllers are implemented in simulation using the high-fidelity engine simulation software. Following the simulation, the controllers are validated through experimental testing conducted in an engine dynamometer at University of Wisconsin. Results from these controllers are compared against a non-eBoosted engine, which serves as the baseline. While both the SISO and MIMO controllers show improvements in AFR (Air-Fuel Ratio), DAR (Diluent Air Ratio), and engine speed recovery during the load transients, the robust MIMO controller outperforms them by demonstrating the best overall engine performance. This superiority is attributed to its comprehensive understanding of the coupling between each actuator input and the model output. When the MIMO controller operates alongside the electrified intake boosting system, the engine exhibits remarkable enhancements. Not only does it recover back to a steady state 70% faster than the baseline, but it also reduces engine speed droop by 45%. Consequently, the engine's ability to accept load torque increases significantly.</p><p dir="ltr">As a result, a single robust MIMO controller can efficiently perform the same task instead of employing multiple PIDs or look-up tables for each actuator.</p>