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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…
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…
Computational stability analysis of PDEs with integral terms using the PIE framework
Sachin Shivakumar, Matthew Peet
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and th…
Efficient Data Structures for Exploiting Sparsity and Structure in Representation of Polynomial Optimization Problems: Implementation in SOSTOOLS
Declan Jagt, Sachin Shivakumar, Peter Seiler +1
We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables are polynomial i…