<p>Automated Vehicle Path Following Control (PFC) is an advanced control system that can regulate the vehicle into a collision-free region in the presence of other objects on the road. Common collision avoidance functions, such as forward collision warning and automatic emergency braking, have recently been developed and equipped on production vehicles. However, it is impossible to develop a perfectly precise vehicle model when the vehicle is driving. The most PFC did not consider uncertainties in the vehicle model, external disturbances, and parameter variations at the same time. To address the issues associated with this important feature and function in autonomous driving, a new vehicle PFC is proposed using a robust model predictive control (MPC) design technique based on matrix inequality and the theoretical approach of the hybrid $\&$ switched system. The proposed methodology requires a combination of continuous and discrete states, e.g. regulating the continuous states of the AV (e.g., velocity and yaw angle) and discrete switching of the control strategy that affects the dynamic behaviors of the AV under different driving speeds. Firstly, considering bounded model uncertainties, norm-bounded external disturbances, the system states and control matrices are modified. In addition, the vehicle time-varying longitudinal speed is considered, and a vehicle lateral dynamic model based on Linear Parameter Varying (LPV) is established by utilizing a polytope with finite vertices. Then the Min-Max robust MPC state feedback control law is obtained at every timestamp by solving a set of matrix inequalities which are derived from Lyapunov stability and the minimization of the worst-case in infinite-horizon quadratic objective function. Compared to adaptive MPC, nonlinear MPC, and cascade LPV control, the proposed robust LPV MPC shows improved tracing accuracy along vehicle lateral dynamics. Finally, the state feedback switched LPV control theory with separate Lyapunov functions under both arbitrary switching and average-dwell-time (ADT) switching conditions are studied and applied to cover the path following control in full speed range. Numerical examples, tracking effectiveness, and convergence analysis are provided to demonstrate and ensure the control effectiveness and strong robustness of the proposed algorithms.</p>

付記する学位プログラム名: デザイン学大学院連携プログラム / 京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21761号 / 工博第4578号 / 新制||工||1713(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 教授 泉田 啓, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

Path-following is a primary task for most marine, air or space crafts, especially during autonomous operations. Research on autonomous underwater vehicles (AUV) has received large interests in the last few decades with research incentives emerging from the safe, cost-effective and practical solutions provided by their applications such as search and rescue, inspection and monitoring of pipe-lines ans sub-sea structures. This thesis presents a novel guidance system based on the popular line-of-sight (LOS) guidance law for path-following (PF) of underwater vehicles (UVs) subject to environmental disturbances. Mathematical modeling and dynamics of (UVs) is presented first. This is followed by a comprehensive literature review on guidance-based path-following control of marine vehicles, which includes revised definitions of the track-errors and more detailed illustrations of the general PF problem. A number of advances on relative equations of motion are made, which include an improved understanding of the fluid FLOW frame and expression of its motion states, an analytic method of modeling the signs of forces and moments and the proofs of passivity and boundedness of relative UV systems in 3-D. The revision in the relative equations of motion include the concept of state relativity, which is an improved understanding of relativity of motion states expressed in reference frames and is also useful in incorporating environmental disturbances. In addition, the concept of drift rate is introduced along with a revision on the angles of motion in 3-D. A switching mechanism was developed to overcome a drawback of a LOS guidance law, and the linear and nonlinear stability results of the LOS guidance laws have been provided, where distinctions are made between straight and curved PF cases. The guidance system employs the unique formulation and solution of the speed allocation problem of allocating a desired speed vector into x and y components, and the course control that employs the slip angle for desired heading for disturbance rejection. The guidance system and particularly the general course control problem has been extended to 3-D with the new definition of vertical-slip angle. The overall guidance system employing the revised relative system model, course control and speed allocation has performed well during path-following under strong ocean current and/or wave disturbances and measurement noises in both 2-D and 3-D scenarios. In 2-D and 3-D 4 degrees-of-freedom models (DOF), the common sway-underactuated and fully actuated cases are considered, and in 3-D 5-DOF model, sway and heave underactuated and fully actuated cases are considered. Stability results of the LOS guidance laws include the semi-global exponential stability (SGES) of the switching LOS guidance and enclosure-based LOS guidance for straight and curved paths, and SGES of the loolahead-based LOS guidance laws for curved paths. Feedback sliding mode and PID controllers are applied during PF providing a comparison between them, and simulations are carried out in MatLab.

This dissertation advances tools for robust control and analysis of complex nonlinear dynamical systems. Specifically, it leverages standard synthesis and robustness analysis techniques developed for linear systems and provides additional results to design robust controllers for nonlinear systems over the considered operating envelopes. To facilitate the application of these linear techniques, nonlinear systems are represented as uncertain linear models. A significant contribution of this dissertation is the development of data-driven approaches to generate these uncertain linear models, which capture the behavior of nonlinear systems reasonably well over the considered operating envelopes without being overly conservative. We propose two approaches where a nominal linear time-invariant (LTI) approximation of a nonlinear system is first obtained using traditional linearization techniques, and data-driven methods are then applied to model the discrepancies arising from this simplification. In the first approach, the discrepancies are modeled using polynomials, resulting in an improved linear parameter-varying (LPV) approximation that can be expressed as a linear fractional transformation (LFT) on uncertainties. The second approach utilizes coprime factorization and a data-driven lifting technique to approximate the nonlinear discrepancy model with an LTI state-space system in a higher-dimensional state space. Additionally, a purely data-driven modeling approach is proposed for nonlinear systems with uncertain initial conditions. In this approach, a deep learning framework is developed to approximate nonlinear dynamical systems with LPV state-space models in higher-dimensional spaces while simultaneously characterizing the uncertain initial states within the lifted state space. Another contribution is the development of a systematic method for identifying critical attack points in cyber-physical systems using integral quadratic constraints (IQCs). IQC analysis is also used in developing a framework focused on the design and analysis of robust path-following controllers for an autonomous underwater vehicle (AUV). In this framework, the AUV is modeled as an LFT on uncertainties and is affected by exogenous inputs such as measurement noise and ocean currents. A tuning routine is developed for robust control design, using the robust performance level derived from IQC analysis to guide the tuning process. This framework is applied to design \( H_\infty \), \( H_2 \), and LPV controllers for the AUV, with the results validated through extensive nonlinear simulations and underwater experiments. Finally, this dissertation presents novel controller synthesis and IQC analysis techniques for LPV systems with uncertain initial conditions. These methods, combined with the lifting-based LPV modeling approach, enable the design of static, nonstationary LPV controllers for nonlinear systems in a higher-dimensional space. When interpreted in the original state space, these controllers become nonlinear with explicit dependence on both the scheduling parameters and time. Through examples, it is demonstrated that these controllers outperform those designed using nominal linearized models. / Doctor of Philosophy / This dissertation focuses on robust control design and analysis for complex nonlinear dynamical systems using well-established methods developed for linear systems. These methods are relatively easier to implement than their counterparts for nonlinear systems and can provide both stability and performance guarantees. A major contribution of this dissertation is the development of data-driven approaches to generate linear approximations of nonlinear systems that are valid over larger operating envelopes compared to those obtained through traditional linearization techniques. Another contribution is the development of a systematic method for identifying critical attack points in cyber-physical systems using robust control tools. Robust control methods are also used in developing a framework focused on the design and analysis of robust path-following controllers for an autonomous underwater vehicle (AUV). In this framework, the AUV is modeled as an uncertain linear system and is affected by external inputs such as measurement noise and ocean currents. A tuning routine is developed to automate the control design process, and the framework is validated through extensive nonlinear simulations and underwater experiments. Finally, this dissertation presents novel controller synthesis and analysis techniques for linear systems with uncertain initial conditions. These methods, combined with a data-driven modeling approach, enable the design of nonlinear controllers that are demonstrated to outperform those designed using nominal linearized models.