Scalable iterative Gramian synthesis for control-affine systems
This work provides a practical computational pathway for applying rigorous nonlinear synthesis theory to high-dimensional control applications, addressing a key scalability bottleneck.
The paper presents a scalable implementation of nonlinear Gramian-based control synthesis for control-affine systems, achieving rapid convergence and high precision. It demonstrates efficacy on five canonical systems and 100-dimensional recurrent neural network models, showing that convergence depends on intrinsic system properties rather than dimensionality.
This article presents a scalable implementation of nonlinear Gramian-based control synthesis for control-affine systems, including a minimum energy control construction. These synthesis advances are achieved by addressing key computational bottlenecks inherent to iterative synthesis map formulations, yielding a computational scheme that exhibits rapid convergence and high-precision. The efficacy of this synthesis framework is demonstrated across five canonical nonlinear control systems and 100-dimensional recurrent neural network models, including underactuated systems. Empirical scaling results further indicate that convergence is primarily governed by intrinsic system properties, such as nonlinearity and controllability, rather than by state-space dimensionality. This work provides a practical, scalable computational pathway for translating rigorous nonlinear synthesis theory into high-dimensional control applications.