The Maneuvering Problem

The main contributions of this thesis is based on a new control problem statement called The Maneuvering Problem. This involves a desired path for the output of the system to follow and a speed assignment setting the desired motion along the path. This separation of tasks implies, on the one hand, that the design of the path and the desired motion along the path can be approached individually. On the other hand, this also introduces more flexibility in the development of the control law, since the desired motion along the path can be shaped by state feedback. The main theoretical aspects are discussed in Chapters 2, 3, and 4. The Maneuvering Problem statement is presented in Chapter 2. A few application examples show how their respective control objectives can be conveniently set up as maneuvering problems by constructing a parametrized path and a speed assignment along the path. The last section of this chapter shows further that the problem statement implies the existence of a forward invariant manifold of the state space, represented by a desired noncompact set, to which all solutions must converge. Chapter 3 presents a constructive control design solving the maneuvering problem. A feedback linearizable system is, for clarity of presentation, used in this section, and most of the involved theoretical aspects concerning the control objective with design are addressed. First the static part of the control law is developed, solving essentially the geometric part of the problem. Then the loop is closed by the design of an update law that shapes the motion along the path. The last section of Chapter 3 considers further one of the proposed update laws and show that this incorporates a gradient optimization algorithm that will improve transient performance in the system. Uncertain systems are addressed in Chapter 4, and constructive designs based on ISS backstepping, adaptive backstepping, and sliding-mode are proposed for solving the maneuvering problem. In the backstepping designs, n design steps are first performed to derive the static part of the control law. Then the dynamic update law is constructed to bridge the path following objective with the speed assignment. In the sliding-mode design, a maneuvering control law is first designed for the nominal part of the plant, and then traditional techniques are used to deal with the uncertain part and develop the overall control law. Chapters 5 and 6 present applications of the theory, where the former chapter considers ships and the latter considers formation control. In Chapter 5, a fully actuated ship model is used, and specific maneuvering control laws are constructed based on adaptive backstepping, sliding-mode, and nonlinear PID techniques. Experimental results, using the model ship CyberShip II, are reported for each design. Experiments of both success and failure are discussed. Chapter 6 proposes a maneuvering setup and design for formation control of r vessels. Two formation control designs are proposed. The first develops decentralized control laws and a centralized dynamic guidance law, which includes the dynamic update law, to solve the problem. In the second design, the guidance law is further decentralized in order to reduce communication demand. Emphasis has been put on making the thesis coherent, starting with motivation and examples in the introduction, leading to the problem statement and its implications in Chapter 2, designs and analysis in Chapters 3 and 4, and finally applications with experimental results in Chapters 5 and 6. Moreover, Appendix A provides necessary background material on control theory, with emphasis on set-stability, and Appendix B reports an extensive work on modeling, system identification, and adaptive maneuvering with experiments performed for CyberShip II.