72 research outputs found
On the Newton-Kleinman method for strongly stabilizable infinite-dimensional systems
We consider the Newton–Kleinman method for strongly stabilizable infinite-dimensional systems. Under certain assumptions, the maximal self-adjoint solution to the associated control algebraic Riccati equation is constructed. The constructed solution is also the maximal solution to the corresponding control algebraic Riccati inequality
Interconnection structures in physical systems: a mathematical formulation
The power-conserving structure of a physical system is known as interconnection structure. This paper presents a mathematical formulation of the interconnection structure in Hilbert spaces. Some properties of interconnection structures are pointed out and their three natural representations are treated. The developed theory is illustrated on two examples: electrical circuit and one-dimensional transmission lin
Optimal time-domain moment matching with partial placement of poles and zeros
In this paper we consider a minimal, linear, time-invariant (LTI) system of order n, large. Our goal is to compute an approximation of order ν < n that simultaneously matches ν moments, has ℓ poles and k zeros fixed, with ℓ + k < ν, and achieves minimal H2 norm of the approximation error. For this, in the family of ν order parametrized models that match ν moments we impose ℓ+k linear constraints yielding a subfamily of models with ℓ poles and k zeros imposed. Then, in the subfamily of ν order models matching ν moments, with ℓ poles and k zeros imposed we propose an optimization problem that provides the model yielding the minimal H2-norm of the approximation error. We analyze the first-order optimality conditions of this optimization problem and compute explicitly the gradient of the objective function in terms of the controllability and the observability Gramians of the error system. We then propose a gradient method that finds the (optimal) stable model, with fixed ℓ poles and k zeros
Model reduction with pole-zero placement and high order moment matching
In this paper, we compute a low order approximation of a system of large
order that matches moments of order of the transfer function,
at interpolation points, has poles and zeros fixed and also
matches moments of order , where is the
multiplicity of the -th interpolation point. We derive explicit linear
systems in the free parameters to simultaneously achieve the required pole-zero
placement and match the desired high order moments. We compute the closed form
of the free parameters that meet the constraints, as the solution of a
order linear system. Furthermore, for data-driven model reduction, we
generalize the construction of the Loewner matrices to include the data and the
imposed pole and higher order moment constraints. The resulting approximations
achieve a trade-off between the good norm approximation and the preservation of
the dynamics of the original system in a region of interest.Comment: 7 page
- …