Differential games, finite-time partial-state stabilisation of nonlinear dynamical systems, and optimal robust control

Two-player zero-sum differential games are addressed within the framework of state-feedback finite-time partial-state stabilisation of nonlinear dynamical systems. Specifically, finite-time partial-state stability of the closed-loop system is guaranteed by means of a Lyapunov function, which we prov...

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Bibliographic Details
Published in:International journal of control 2017-09, Vol.90 (9), p.1861-1878
Main Author: L'Afflitto, Andrea
Format: Article
Language:English
Subjects:
Control systems
Controllers
Differential equations
Differential games
disturbance rejection
Disturbances
Dynamic stability
Dynamical systems
Economic models
Feedback
Feedback control
finite-time stability
Functionals
Hamilton-Jacobi-Isaacs theory
Nonlinear dynamics
optimal control theory
Optimization
Partial differential equations
partial stability
partial-state stabilisation
Robust control
Saddle points (game theory)
Two-player zero-sum differential games
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Summary:Two-player zero-sum differential games are addressed within the framework of state-feedback finite-time partial-state stabilisation of nonlinear dynamical systems. Specifically, finite-time partial-state stability of the closed-loop system is guaranteed by means of a Lyapunov function, which we prove to be the value of the game. This Lyapunov function verifies a partial differential equation that corresponds to a steady-state form of the Hamilton-Jacobi-Isaacs equation, and hence guarantees both finite-time stability with respect to part of the system state and the existence of a saddle point for the system's performance measure. Connections to optimal regulation for nonlinear dynamical systems with nonlinear-nonquadratic cost functionals in the presence of exogenous disturbances and parameter uncertainties are also provided. Furthermore, we develop feedback controllers for affine nonlinear systems extending an inverse optimality framework tailored to the finite-time partial-state stabilisation problem. Finally, two illustrative numerical examples show the applicability of the results proven.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2016.1226518