This paper presents a new numerical method for treating the problem of optimal control when there are hard bounds on the control variables (e.g., limit switches on a linear drive, current limits to motor input, etc.) and/or on the state/output variables (e.g., obstacle avoidance). This is accomplished by means of a new approach for discretizing the optimal control problem, while introducing regularization terms to reduce the solution space to smooth functions. Further, by introducing a consistent discretization of the state-space equations with arbitrary boundary conditions, the problem is cast as a problem of quadratic programming, whereby (hard) bounds can be put on any of the state-space variables (i.e., input or output). The method is demonstrated on the example of a pendulum on a cart. Bounded optimal control solutions are computed for two examples: Velocity bounds are placed on the cart in the classic optimal control problem; a variation of trajectory tracking where instead of specifying a single valued path, the bounds of the trajectory of the pendulum bob are specified, and the required input to keep the bob within these bounds during its motion is computed.
|Titel||2023 12th Mediterranean Conference on Embedded Computing (MECO)|
|Herausgeber (Verlag)||Publ by IEEE|
|Publikationsstatus||Veröffentlicht - 6 Juni 2023|
|Veranstaltung||12th Mediterranean Conference on Embedded Computing - Budva, Montenegro|
Dauer: 6 Juni 2023 → 10 Juni 2023
|Konferenz||12th Mediterranean Conference on Embedded Computing|
|Zeitraum||6/06/23 → 10/06/23|