Hybrid Set-theoretic Approaches for Constrained Control and Estimation with Applications to Autonomous Sailing Boats

Set-theoretic or set-membership methods generally refer to all the set-membership techniques theoretically based on some properties of subsets of the state space. On the one hand, sets are a pertinent language and formulation to specify uncertainties, constraints, estimation errors, design specifications and system performances for control systems. On the other hand, sets also play an active role in the solutions of the problems due to their specific mathematical formats and the associated set-theoretic methods. For example, branch-and-bound of an admissible domain can lead to the global minimum or maximum of a non-convex optimization problem and a Lyapunov function for guaranteeing the stability of a system may be synthesized from positively invariant sub-level sets.

Various types of sets such as intervals, ellipsoids, zonotopes and polytopes have been extensively studied in the literature and each individual type of set has its own advantages and disadvantages in the context of problem formulation and solving. Making full use of the specific advantages provided by each set-membership tool, this research project aims to develop hybrid set-theoretic approaches that can integrate all set-membership tools as well as their specific advantages. For instance, the idea of bisecting an interval has been introduced to bisect a zonotope and a polytope can be represented as the intersection of zonotopes for enabling exact polytopic set computation via zonotopic set computation. The developed hybrid set-theoretic methods and algorithms are to used for solving constrained control and estimation issues encountered in various kinds of control systems with improved accuracy and/or efficiency such as the search of a robust control invariant set via the bisection of zonotopes or even polytopes and guaranteed state estimation via exact polytopic set computation for nonlinear discrete-time systems. These developed hybrid set-theoretic methods and algorithms are also to be used for reachability analysis and fault detection of piecewise affine and hybrid systems. Finally, these theoretical progresses on constrained control and estimation via the developed hybrid set-theoretic approaches are to be applied to solve path planning, obstacle avoidance, control and estimation issues of autonomous sailing boats under complex marine environments where set-based solutions are more pertinent than point-based solutions.

The proposed research project addresses both theoretical and application aspects of control engineering and thus the project will have a significant impact both in academia and industry.

The developed hybrid set-membership toolbox and algorithms will bring new incentive and vision into this promising research field of set-theoretic methods for control. Researchers in this domain will be able to introduce the developed hybrid set-membership tools into their own research topics so as to obtain renewed solutions with improved accuracy and/or efficiency. Moreover, the hybrid approach of this project will also encourage interdisciplinary collaboration and bring together researchers with various expertise and background.

The application aspect of this research project will also impact the development of autonomous sailing technologies for surveying, surveillance and reconnaissance. The project will pioneer in the engineering applications of set-theoretic methods for control as the developed control and estimation algorithms will be tested on an autonomous sailing boat. Such technologies would be beneficial to local companies in marine sector such as MSubs Ltd for enriching their research horizon and technology expertise.

The proposed research project can also generate impact for the people involved and the society around as well. The project will be an ideal platform to train young researchers, undergraduates and postgraduates to enhance their engineering skills and employability. The project will have the potential to be engaged with the public in university open days, Tomorrow's Engineers Week and other engineering outreach activities. The potential host of the World Robotic Sailing Championship and International Robotic Sailing Conference (WRSC/IRSC) in Plymouth as an outcome of this proposed project will generate further public interests and wider socioeconomic impact for the South West region of the UK.