An iterative computational scheme for solving the coupled Hamilton–Jacobi–Isaacs equations in nonzero-sum differential games of affine nonlinear systems

M. D. S. Aliyu ()
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M. D. S. Aliyu: King Faisal University

Decisions in Economics and Finance, 2017, vol. 40, issue 1, No 1, 30 pages

Abstract: Abstract In this paper, we present iterative or successive approximation methods for solving the coupled Hamilton–Jacobi–Isaacs equations (HJIEs) arising in nonzero-sum differential game for affine nonlinear systems. We particularly consider the ones arising in mixed $${\mathcal H}_{2}/{\mathcal H}_{\infty }$$ H 2 / H ∞ control. However, the approach is perfectly general and can be applied to any others including those arising in the N-player case. The convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the utility of the method. The results are also specialized to the coupled algebraic Riccati equations arising typically in mixed $${\mathcal H}_{2}/{\mathcal H}_{\infty }$$ H 2 / H ∞ linear control. In this case, a bound within which the optimal solution lies is established. Finally, based on the iterative approach developed, a local existence result for the solution of the coupled-HJIEs is also established.

Keywords: Differential games; Coupled Hamilton–Jacobi–Isaacs equations; Vector identity; Successive approximation method; Bounded continuous functions; Convergence; Coupled algebraic Riccati equations; C7; G1; M2; P0 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10203-017-0184-x

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