(Georgia Institute of Technology, 2012-12)
Wardi, Yorai Y.; Egerstedt, Magnus B.; Twu, Philip Y.
This paper describes an adaptive-precision algorithm for solving a general optimal mode-scheduling problem in switched-mode dynamical systems. The problem is complicated by the fact that the controlled variable has discrete and continuous components, namely the sequence of modes and the switching times between them. Recently we developed a gradient-descent algorithm whose salient feature is that its descent at a given iteration is independent of the length (number of modes) of the schedule, hence it is suitable to situations where the schedule-lengths at successive iterations grow unboundedly. The computation of the descent direction requires grid-based approximations to solve differential equations as well as minimize certain functions on uncountable sets. However, the algorithm’s convergence analysis assumes exact computations, and it breaks down when approximations are used, because the descent directions are discontinuous in the problem parameters. The purpose of the present paper is to overcome this theoretical gap and its computational implications by developing an implementable, adaptive-precision algorithm that controls the approximation levels by balancing precision with computational workloads. Its asymptotic convergence is proved, and simulation results are provided to support the theoretical developments.
(Georgia Institute of Technology, 2010-12)
Wardi, Yorai Y.; Egerstedt, Magnus B.; Twu, Philip Y.
This paper considers a real-time algorithm for performance optimization of switched-mode hybrid dynamical systems. The controlled parameter consists of the switching times between the modes, and the cost criterion has the form of the integral of a performance function defined on the system's state trajectory. The dynamic response functions (state equations) associated with the modes are not known in advance; rather, at each time t, they are estimated for all future times s ≥ t. A first-order algorithm is proposed and its behavior is analyzed in terms of its convergence rate. Finally, an example of a mobile robot tracking a moving target while avoiding obstacles is presented.