Efficient Computational Methods for Worst-Case Analysis and Optimal Control of Nonlinear Dynamical Systems

A max-plus primal space fundamental solution for a class of differential Riccati equations

PM Dower, H Zhang

2017-09-01

A class of differential Riccati equations (DREs) is considered for which the evolution of any solution can be identified with the ..

Staticization, its dynamic program and solution propagation

WM McEneaney, PM Dower

2017-07-01

Stationary-action formulations of dynamical systems are considered. Use of stationary-action formulations allows one to generate f..

Relationships between Subclasses of Integral Input-to-State Stability

CM Kellett, PM Dower, H Ito

2017-05-01

A certain "qualitative equivalence" has been recently demonstrated between integral input-to-state stability (iISS) and a nonlinea..

A reduced complexity min-plus method for synchronisation of qubits

Z Miao, PM Dower

2017-03-01

Solutions to optimal control problems can be obtained via grid-based dynamic programming iterations. However, such an approach is ..

A max-plus based fundamental solution for a class of discrete time linear regulator problems

H Zhang, PM Dower

2015-04-15

Efficient Riccati equation based techniques for the approximate solution of discrete time linear regulator problems are restricted..

Max-plus fundamental solution semigroups for a class of difference Riccati equations

H Zhang, PM Dower

2015-02-01

Recently, a max-plus dual space fundamental solution semigroup for a class of difference Riccati equations (DREs) has been develop..

A max-plus dual space fundamental solution semigroup for operator differential Riccati equations

PM DOWER, WM McEneaney

2014-01-01

Analysis of difference Riccati equations via a new max-plus based fundamental solution

H Zhang, PM DOWER

2014-01-01

A new non-iterative solution for a class of difference Riccati equations

H Zhang, PM DOWER

2014-01-01

Recently, two non-iterative solutions for difference Riccati equations (DREs) have been developed employing max-plus primal and du..

Nonlinear systems with nonlinear L2-gain

PM DOWER, CM Kellett

2014-01-01

Nonlinear <inf>2</inf>-gain is a robust stability property whereby the <inf>2</inf>-norm of the state trajectory is bounded above ..

Stability of (integral) input-to-state stable interconnected nonlinear systems via qualitative equivalences

CM Kellett, PM Dower

2013-12-01

The input-to-state stability (ISS) framework has proven successful for analysing interconnections of ISS and integral ISS systems...

Performance bounds for nonlinear systems with a nonlinear L 2-gain property

H Zhang, PM Dower

2012-09-01

Nonlinear L <inf>2</inf>-gain is a finite gain concept that generalises the notion of conventional (linear) finite L <inf>2</inf>-..

An approximation arising in max-plus based optimal stopping

PM Dower

2012-01-01

An algorithm is developed for computing a key approximation required in the implementation of a max-plus eigenvector method for th..

An explicit solution to a class of constrained optimal control problems

H Zhang, PM Dower

2012-01-01

Optimal control problems that admit closed form solutions are rare so that numerical methods have to be used to obtain an approxim..

A weak L2-gain property for nonlinear systems

PM Dower, CM Kellett, H Zhang

2012-01-01

Nonlinear L<inf>2</inf>-gain is a generalization of the conventional (linear) notion of L<inf>2</inf>-gain in which the linear sca..

Tight comparison function bounds for nonlinear systems with a nonlinear L2-gain property

PM Dower, H Zhang

2012-01-01

Nonlinear L<inf>2</inf>-gain is a finite gain concept that generalizes the notion of conventional linear L<inf>2</inf>-gain via th..