NAVIGATION
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Given a policy γ∈ΓA\gamma\in\Gamma_{A}γ∈ΓA with the objective of minimizing J∞(X,γ)=lim supN→∞1NExγ[∑k=0N−1c(Xk,Uk)]J_{\infty}(X,\gamma) =\limsup_{ N \to \infty } \frac{1}{N} E_{x}^{\gamma}\left[ \sum_{k=0}^{N-1}c(X_{k},U_{k}) \right]J∞(X,γ)=N→∞limsupN1Exγ[k=0∑N−1c(Xk,Uk)]this is known as the Average Cost Optimal Control problem.