Novel algorithms leveraging the pontryagin minimum principle improve optimal control in nonlinear systems, suggesting enhanced solutions for complex dynamics.
In this article, novel adaptive iterative algorithms based on Pontryagin minimum principle are provided for finite-horizon optimal control of nonlinear systems with constrained inputs. The technique of concurrent learning is used to identify the unknown drift dynamics and input dynamics. Adaptive iterative algorithms are proposed to find the optimal control solution. The new algorithms are fundamentally different from existing infinite-horizon algorithms, in the sense that they overcome the technical obstacle to address the time-varying behaviour of Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Simulation examples on motor system and time-varying memristive circuit system are provided for effectiveness verification.
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Zhang et al. (2025) studied this question.
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