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

Lead Research Organisation: Plymouth University
Department Name: Sch of Engineering


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.

Planned Impact

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.


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Description From the perspective of control theory, this project has proposed novel set-membership methods for dealing with uncertainty in engineering systems.

From the perspective of marine robotics, this project has developed novel algorithms for position keeping of autonomous sailboats.

From the perspective of new research questions, this project has opened research topics on platooning and reinforcement learning control of autonomous sailboats.
Exploitation Route The novel set-membership methods developed from the project can be used by other researchers in this domain. The contributions to existing and new questions on autonomous sailing technologies will also generate wider interest from other researchers. All the technologies involved are helpful to address nowadays environmental challenges and ocean exploration needs.
Sectors Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Energy,Environment

Description Along with a seed fund project from the Royal Academy of Engineering, the developed autonomous sailing technologies from this project has generated wider interest from Malaysian collaborators. Under the support of another project funded by the University of Plymouth Internal Global Challenges Research Fund, the PI and the Malaysian collaborators have developed capacity and capability to monitor coastal marine environments such as water quality for sustainable development in Penang Island, Malaysia. The developed system has been used at Penang Island, Malaysia for the purpose of environmental monitoring and ecological conservation.
First Year Of Impact 2022
Sector Aerospace, Defence and Marine,Agriculture, Food and Drink,Digital/Communication/Information Technologies (including Software),Education,Energy,Environment
Impact Types Cultural,Societal,Policy & public services

Description Royal Academy of Engineering Frontiers of Engineering for Development Seed Fund 2018
Amount £20,000 (GBP)
Organisation Royal Academy of Engineering 
Sector Charity/Non Profit
Country United Kingdom
Start 01/2018 
End 01/2019
Description University of Plymouth Internal Global Challenges Research Fund
Amount £26,280 (GBP)
Organisation University of Plymouth 
Sector Academic/University
Country United Kingdom
Start 02/2019 
End 02/2021
Description Collaboration with Associate Professor Julien Alexandre dit Sandretto 
Organisation ENSTA ParisTech (École Nationale Supérieure de Techniques Avancées)
Country France 
Sector Academic/University 
PI Contribution Train summer internship students from Associate Professor Julien Alexandre dit Sandretto's institute and contribute to joint paper publication
Collaborator Contribution Contribute to joint paper publication
Impact Alexandre dit Sandretto, Julien & Wan, Jian. (2018). Reachability Analysis of Nonlinear ODEs Using Polytopic Based Validated Runge-Kutta: 12th International Conference, RP 2018, Marseille, France, September 24-26, 2018, Proceedings. 10.1007/978-3-030-00250-3-1.
Start Year 2018
Description Collaboration with Professor Luc Jaulin 
Organisation National Institute of Advanced Technologies of Brittany
Country France 
Sector Academic/University 
PI Contribution Train summer internship students from Professor Luc Jaulin's institute and contribute to joint paper publication
Collaborator Contribution Provide robotic research platforms and contribute to PhD student supervision and joint paper publication
Impact Viel, Christophe & Vautier, Ulysse & Wan, Jian & Jaulin, Luc. (2018). Position keeping control of an autonomous sailboat. IFAC-PapersOnLine. 51. 14-19. 10.1016/j.ifacol.2018.09.462.
Start Year 2017