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Open AccessJournal ArticleDOI

L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control

A.J. van der Schaft
- 01 Jun 1992 - 
- Vol. 37, Iss: 6, pp 770-784
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TLDR
In this article, the results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field.
Abstract
Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H/sub infinity / control, namely the state feedback H/sub infinity / optimal control problem. Furthermore, the relation with H/sub infinity / control of the linearized system is dealt with. >

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Citations
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Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem

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Reinforcement Learning and Feedback Control: Using Natural Decision Methods to Design Optimal Adaptive Controllers

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Survey Constructive nonlinear control: a historical perspective

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Online actor critic algorithm to solve the continuous-time infinite horizon optimal control problem

TL;DR: This paper presents an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks, and calls this ‘synchronous’ policy iteration.
References
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Book

Mathematical Methods of Classical Mechanics

TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Journal ArticleDOI

State-space solutions to standard H/sub 2/ and H/sub infinity / control problems

TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Book

Dynamic Noncooperative Game Theory

TL;DR: In this paper, the authors present a general formulation of non-cooperative finite games: N-Person nonzero-sum games, Pursuit-Evasion games, and Stackelberg Equilibria of infinite dynamic games.
Journal ArticleDOI

Dissipative dynamical systems part I: General theory

TL;DR: In this paper, a general theory of dissipative dynamical systems is presented, where dissipativeness is defined in terms of an inequality involving the storage function and the supply function, which is bounded from below by the available storage and from above by the required supply.
Proceedings ArticleDOI

State-space solutions to standard H 2 and H ∞ control problems

TL;DR: In this article, simple state-space formulas are presented for a controller solving a standard H∞-problem, where the controller has the same state-dimension as the plant, its computation involves only two Riccati equations, and it has a separation structure reminiscent of classical LQG theory.
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