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Optimal Control Unifying Harmonic Control: Convergence Proof and Simulations

This work presents a comprehensive analysis demonstrating that harmonic control is a specific instance of optimal control. We address an optimal control problem influenced by isotropic noise, allowing the noise level to approach infinity. Through rigorous convergence proofs and relevant simulations, we provide insights into the relationship between these two control methods and their implications for trajectory planning. Our findings highlight the versatility of optimal control in scenarios with varying noise levels.

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Optimal Control Unifying Harmonic Control: Convergence Proof and Simulations

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  1. Optimal control subsumes harmonic control Amine Boumaza and Bruno ScherrerLORIA Campus Scientifique B.P. 239 54506 Vandoeuvre-les-Nancy, France Email: boumaza@loria.fr, scherrer@loria.fr • Trajectory planning can be done with optimal control or harmonic control • We show that harmonic control is a specific case of optimal control • We consider an optimal control problem with isotropic noise and make the noise level tend to infinity • Convergence proof, Simulations Optimal control with a slight noise

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