On Closed-loop Lyapunov Stability with Minimum-time MPC Feedback Laws for Discrete-time Systems

Sutherland, Richard L.; Kolmanovsky, Ilya; Girard, Anouck; Leve, Frederick A.; Petersen, Christopher

doi:10.1109/cdc40024.2019.9029869

Cited by 8 publications

(1 citation statement)

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“…More recent approaches realize time-optimal feedback control in the framework of predictive control. General analyses and theoretical results for time-optimal feedback control of nonlinear discrete time systems are presented in [10], [11]. For continuous-time systems, direct methods for the underlying optimal control problems are usually preferred to indirect methods based on larger convergence regions and their suitability for real-time optimization.…”

Section: Introductionmentioning

confidence: 99%

Time-optimal control with direct collocation and variable discretization

Rösmann,

Makarow,

Bertram

2020

Preprint

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This paper deals with time-optimal control of nonlinear continuous-time systems based on direct collocation. The underlying discretization grid is variable in time, as the time intervals are subject to optimization. This technique differs from approaches that are usually based on a time transformation. Hermite-Simpson collocation is selected as common representative in the field of optimal control and trajectory optimization. Hereby, quadratic splines approximate the system dynamics. Several splines of different order are suitable for the control parameterization. A comparative analysis reveals that increasing the degrees of freedom in control, e.g. quadratic splines, is not suitable for time-optimal control problems due to constraint violation and inherent oscillations. However, choosing constant or linear control splines points out to be very effective. A major advantage is that the implicit solution of the system dynamics is suited for stiff systems and often requires smaller grid sizes in practice.

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Section: Introductionmentioning

confidence: 99%