Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

Sudeep Kundu () and Karl Kunisch ()
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Sudeep Kundu: University of Graz
Karl Kunisch: University of Graz

Computational Optimization and Applications, 2024, vol. 87, issue 3, No 5, 785-809

Abstract: Abstract Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Keywords: Optimal feedback control; $${\mathcal {H}}_2$$ H 2 control synthesis; Hamilton–Jacobi–Bellman equations; Policy iteration; Upwind scheme; 49J20; 49L20; 49N35; 93B52 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-021-00278-3

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