# A dynamic game approximation for a linear regulator problem with a log-barrier state constraint

@inproceedings{Dower2016ADG, title={A dynamic game approximation for a linear regulator problem with a log-barrier state constraint}, author={Peter M. Dower and William M. McEneaney and Michael Cantoni}, year={2016} }

An exact supremum-of-quadratics representation for log-barrier functions is developed for, and subsequently applied in, a state-constrained linear regulator problem. By approximating this representation, it is shown that this regulator problem can be approximated by an unconstrained linear quadratic dynamic game. It is anticipated that this game approximation may facilitate the computation of approximate solutions to such state-constrained regulator problems.

## 6 Citations

A game representation for state constrained linear regulator problems

- Mathematics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

It is shown that any linear regulator problem constrained by such a convex barrier-type constraint can be equivalently formulated as an unconstrained two player linear quadratic game.

An approximating game for a continuous-time state-constrained linear regulator problem

- Mathematics2016 Australian Control Conference (AuCC)
- 2016

A supremum-of-quadratics representation for convex barrier functions is used to approximate a continuous-time state-constrained linear regulator problem as a two-player dynamic game. State feedback…

Game representations for state constrained continuous time linear regulator problems

- Mathematics
- 2019

A supremum-of-quadratics representation for convex barrier-type constraints is developed and applied within the context of a class of continuous time state constrained linear regulator problems.…

State constrained optimal control of linear time-varying systems

- Mathematics2017 IEEE 56th Annual Conference on Decision and Control (CDC)
- 2017

A state constrained optimal control problem subject to continuous-time linear time-varying dynamics is decomposed into a family of linear quadratic regulator (LQR) problems via convex duality and a…

Optimal control synthesis for the constrained bilinear biquadratic regulator problem

- Computer Science, MathematicsOptim. Lett.
- 2018

In this paper, a single input continuous time constrained linear quadratic regulator problem, is defined and fully solved and Krotov’s method is used to solve it.

Neural network architectures using min plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs

- Computer ScienceArXiv
- 2021

This work provides the mathematical analysis for the two abstract neural network architectures which respectively represent the value function and the state feedback characterisation of the optimal control for certain class of high dimensional optimal control problems.

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