Cooperative Control of Multiple Autonomous Vehicles Based on Viability Theory

UoM administered thesis: Phd

  • Authors:
  • Bowen Peng


Self-organization and emergence are properties of a group of many living beings that dynamically modify network's organization with complete autonomy. The proposed multi-agent system (MAS) adaptively reorganize its structure to fit unforeseen heterogeneous environment without any initial knowledge. The problem lies in how to design such a realistic cooperative control system in engineering application. This thesis is going to deliver a numerical method in solving cooperative control problems for constrained nonlinear MAS. This study relates to interval methods and viability theory. As numerical solutions for either functions or inequalities can be sets of real numbers, when implementing algorithms via digital computers, explicit solutions can not be obtained due to uncertainty in the numerical model, computational error of digital computer, etc. By digital computation, many values become intervals such that some functions and inequalities are formed as inclusion functions. Therefore, it is crucial to find reliable algorithms for digital computers to handle practical engineering problems. All the possible solutions must be taken into account, and they are gathered together to form solution regions represented by sets. Interval methods are the mathematical tools to find out such sets according to known inclusion functions. In detail, interval methods are the numerical algorithms that can be realized by programming with relatively less computational burden compared to conventional computation ways, and it works out a general solution for uncertain models with inputs. A novel algorithm is proposed that characterizes the robust capture basin and the discriminating kernel for constrained nonlinear systems with uncertainties based on viability theory. For nonlinear systems with constrained inputs and bounded uncertainties, the viability kernel is the largest set of states possessing a possibility to be viable in a set, and the capture basin is the largest set of states possessing a possibility to reach a target in a finite time, and keeping viable in a set before reaching the target. However, in viability theory, both control and uncertainty in a parameterized system are considered as parameters. The discriminating kernel and the proposed robust capture basin link viability theory with robust control, which take both control and uncertainties into account. For the constrained uncertain nonlinear systems, the discriminating kernel is the largest set of states that is robust invariant in a set with proper control, and the robust capture basin is the largest set of states reaching their target in finite time with proper control despite of uncertainties, and keeping viable in a set before reaching the target. Furthermore, all the states are mapped to optimal regulatory control such that the systems are regulated by a regulation map. To compute the robust capture basin and the discriminating kernel, interval methods are adopted to provide guaranteed solutions. The proposed algorithms in this thesis approximate an outer approximation of the minimum reachable target and inner approximations of the robust capture basin and the discriminating kernel in a guaranteed way. An optimal distributed control protocol is designed for constrained multi-vehicle systems with an unknown switching communication graph. The optimal distributed control problem is formulated to differential graphical games, and the Pareto optimum to multi-player games is sought based on the viability theory and reinforcement learning techniques. The feasible learning region is characterized for the reinforcement learner by computing the capture basin. In addition, the approximation of the capture basin provides the learner with prior knowledge. Unlike the existing works that employ the viability theory to solve control problems with only one agent and differential games with only two players, the viability theory, in this thesis, is utilized to solve multi-agent control problems and multi-player differential games. The distributed control law is composed of two parts: the approximation of the capture basin and reinforcement learning, which are computed off-line and on-line respectively. The convergence properties of the parameters' estimation errors in reinforcement learning are proved, and the convergence of the control policy to the Pareto optimum of the differential graphical game is discussed. The guaranteed approximation results of the capture basin are provided, and the simulation results of the differential graphical game are provided for multi-vehicle systems with the proposed distributed control policy.


Original languageEnglish
Awarding Institution
Award date1 Aug 2020