Stabilization System Quality in Synthesized Optimal Control

Abstract

Stability is crucial for practical implementation of computed optimal controls onboard, as it compensates for discrepancies that arises, as a result, of
objectively existing differences in the models used during control design and the real objects. The synthesized control approach solves optimal control problems by strategically placing stable equilibrium points in state space, activated at equal time intervals. However, stability alone proves insufficient for maintaining optimal performance; equilibrium points must also exhibit specified quality characteristics to minimize sensitivity to external disturbances and model uncertainties.
Stable equilibria can be classified as aperiodic or oscillatory. Near oscillatory points, the system's differential equations fail to ensure strict contractivity in state space mappings, potentially causing unpredictable error growth between the actual object state and its model-based estimate. Thus, oscillatory equilibria are undesirable for control synthesis.
This paper imposes additional quality requirements on the stabilization dynamics approaching equilibrium points namely to the object’s movement to the stability point. A numerical approximation method is proposed for synthesizing stabilization systems meeting these criteria. Optimal trajectories are first generated around the target equilibrium for various initial conditions via optimal control solutions. Symbolic machine learning then serves as a universal function approximator, trained on these supervised trajectories to minimize approximation error across the trajectory set.
A computational experiment demonstrates stabilization synthesis for a dif-ferential-drive mobile robot using symbolic regression, a form of evolution-ary machine learning. Results confirm that high quality stabilization system is little sensitive to disturbances.