A transformation approach for solving the Hamilton-Jacobi-Bellman equation in \({\mathcal H}_2\) deterministic and stochastic optimal control of affine nonlinear systems.

DOI10.1016/S0005-1098(03)00080-3zbMath1045.93046OpenAlexW2093459505MaRDI QIDQ1398404

M. D. S. Aliyu

Publication date: 29 July 2003

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0005-1098(03)00080-3

zbMATH Keywords

Hamilton-Jacobi-Bellman equationnonlinear systemsLyapunov equationviscosity solutionstochastic controlalgebraic-differential inequalities

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Transformations (93B17) Optimal stochastic control (93E20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items

Robust \(H_\infty\) filtering for nonlinear discrete-time stochastic systems, Derivatives pricing with market impact and limit order book, An iterative computational scheme for solving the coupled Hamilton-Jacobi-Isaacs equations in nonzero-sum differential games of affine nonlinear systems, Optimal residual evaluation for nonlinear systems using post-filter and threshold, Iterative computational approach to the solution of the Hamilton-Jacobi-Bellman-Isaacs equation in nonlinear optimal control, A stochastic optimal regulator for a class of nonlinear systems, An improved iterative computational approach to the solution of the Hamilton–Jacobi equation in optimal control problems of affine nonlinear systems with application

Cites Work

• Robustness of nonlinear state feedback. A survey
• Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation
• An approach for solving the Hamilton-Jacobi-Isaacs equation (HJIE) in nonlinear \(\mathcal H_{\infty}\) control
• L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control
• Normalized coprime factorizations and balancing for unstable nonlinear systems
• Nonlinear H/sub ∞/ control: a J-dissipative approach
• Output-feedback stochastic nonlinear stabilization
• Worst case analysis of nonlinear systems
• J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems
• The class of stabilizing nonlinear plant controller pairs
• Optimal Regulation of Nonlinear Dynamical Systems
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item