Approximate Optimal Enclosing Control for UAVs With Performance Guarantees: A Prescribed-Time Learning Solution

This paper presents a prescribed time learning-based near optimal enclosing controller to ensure that unmanned aerial vehicles (UAVs) encircle around the specified target with prescribed performance constraints and minimum cost efforts. First, a basic enclosing controller is established to achieve the enclosing error stabilization and stable circumnavigation around a given target. Second, a new prescribed time behavior envelope that eliminates the availability on initial error is proposed. To render the satisfaction of performance constraints and optimal enclosing actions, a transformed enclosing error is obtained by enforcing state conversion on original error. Then, aiming at stabilizing the enclosing error to a prescribed accuracy within a prescribed time, a prescribed time learning-based near optimal enclosing controller under a critic-only adaptive dynamic programming (ADP) is explored, approximating the solution of a novel Hamilton-Jacobi-Bellman (HJB) equation via pursuing the minimum cost associated with transformed errors. Especially, a novel prescribed time learning rule driven by weight errors is elaborated by revisiting real-time and historical information, such that the convergence of weights is only determined by a user-defined time constant. The prominent merit is that the optimal enclosing with performance guarantees can be achieved by a prescribed time ADP. Lyapunov stability demonstrates that involved error variables are ultimately limited and resultant controller satisfies optimality. Finally, simulations verify the values and superiority of the proposed methodology.