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Representation of linear PDEs with spatial integral terms as Partial Integral Equations
Sachin Shivakumar, Amritam Das, Matthew Peet
In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial int…
Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems
Muhammad Umar B. Niazi, John Cao, Xudong Sun +2
Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where…
Dual Representations and -Optimal Control of Partial Differential Equations
Sachin Shivakumar, Amritam Das, Matthew Peet
We consider $\hinf$-optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While…
Extension of the Partial Integral Equation Representation to GPDE Input-Output Systems
Sachin Shivakumar, Amritam Das, Siep Weiland +1
It has been shown that the existence of a Partial Integral Equation (PIE) representation of a Partial Differential Equation (PDE) simplifies many numerical aspects of analysis, sim…