Orest V. Iftime

System theoretic properties of a class of spatially invariant systems

In this paper we develop new readily testable criteria for system theoretic properties such as stability, controllability, observability, stabilizability and detectability for a class of spatially invariant systems. Our approach uses the well-established theory developed to solve infinite-dimensional systems. The theoretical results are illustrated by several examples.

Optimal control of switched distributed parameter systems with spatially scheduled actuators

In many areas of control there are gaps between the existing theory and applications. This is more so in hybrid infinite dimensional systems and in particular hybrid systems in which both the actuator and the controller are switched. The main objective of this paper is to start filling in one of these gaps. We present a theoretical formulation and provide methodologies for implementing optimal and switching policies of spatially scheduled actuators for a class of distributed parameter systems (DPS). The optimization method employed is based on finite horizon LQR optimal control. Well posedness and optimality, pertaining to the switching policies of spatially scheduled actuators, are presented and proven. Tutorial examples motivated by thermal manufacturing applications along with extensive simulation results of the proposed actuator-plus-controller switching scheme are presented.

Finite horizon optimal control of switched distributed parameter systems with moving actuators

The objective of this work is to provide a theoretical formulation for optimal switching of a moving (or scanning) actuator for distributed parameter systems. The proposed hybrid controller switches both the location and control signal of the plant at the beginning of a time interval and remains unchanged over the duration of the time interval. This is repeated for different time intervals. The method employed is based on LQR optimal control. First, a set of admissible locations for which the moving actuator can reside at throughout the duration of a given time interval is considered. Guiding the moving actuator at these a priori selected positions at different time intervals is made possible by solving a double optimization problem. Further, an optimal set of admissible locations at which the moving actuator can reside at throughout the duration of a given time interval is chosen. A numerical example with simulation results is presented.

A comparison between LQR control for a long string of SISO systems and LQR control of the infinite spatially invariant version

In this paper we consider a long string of SISO systems which in the limit becomes a scalar infinite spatially invariant system. We compare the LQR control for long-but-finite strings with the LQR control for the corresponding infinite strings. We give analytical and numerical examples where these are quite different and we investigate the cause. In addition, we obtain sufficient conditions for the LQR solutions to be similar as the length of the string increases.

A representation of all solutions of the control algebraic Riccati equation for infinite-dimensional systems

We obtain a representation of all self-adjoint solutions of the control algebraic Riccati equation associated to the infinite-dimensional state linear system Σ(A,B,C) under the following assumptions: A generates a C 0-group, the system is output stabilizable, strongly detectable and the dual Riccati equation has an invertible self-adjoint non-negative solution.

System theoretic properties of platoon-type systems

This paper presents readily checkable criteria for several system theoretic properties (stability, approximate and exact controllability, exponential stabilizability) for a particular class of infinite-dimensional systems, the platoon-type systems. These systems are used for modeling infinite platoons of vehicles which have spatially invariant dynamics. Several examples are presented to illustrate the theory.

Interconnection of Dirac structures via kernel/image representation

Dirac structures are used to mathematically formalize the power-conserving interconnection structure of physical systems. For finite-dimensional systems several representations are available and it is known that the composition (or interconnection) of two Dirac structures is again a Dirac structure. It is also known that for infinite-dimensional systems the composition of two Dirac structures may not be a Dirac structure. In this paper, the theory of linear relations is used in the first instance to provide different representations of infinite dimensional Dirac structures (on Hilbert spaces): an orthogonal decomposition, a scattering representation, a constructive kernel representation and an image representation. Some links between scattering and kernel/image representations of Dirac structures are also discussed. The Hilbert space setting is large enough from the point of view of the applications. Further, necessary and sufficient conditions (in terms of the scattering representation and in terms of kernel/image representations) for preserving the Dirac structure on Hilbert spaces under the composition (interconnection) are also presented. Complete proofs and illustrative example(s) will be included in a follow up paper.

Tools for analysis of Dirac Structures on Banach Spaces

Power-conserving and Dirac structures are known as an approach to mathematical modeling of physical engineering systems. In this paper connections between Dirac structures and well known tools from standard functional analysis are presented. The analysis can be seen as a possible starting framework towards the study of compositional properties of Dirac structures.

Moment matching with prescribed poles and zeros for infinite-dimensional systems

In this paper we approach the problem of moment matching for a class of infinite-dimensional systems, based on the unique solution of an operator Sylvester equation. It results in a class of parameterized, finite-dimensional, reduced order models that match a set of prescribed moments of the given system. We show that, by properly choosing the free parameters, additional constraints are met, e.g., pole placement, preservation of zeros. To illustrate the proposed method, we apply it to the heat equation with mixed boundary conditions. We obtain a second order reduced model which approximates the original systems better (in terms of the infinity norm of the approximation error) than the fourth order reduced model obtained by modal truncation.

Sub-optimal Hankel norm approximation problem: a frequency domain approach

We obtain a simple solution for the sub-optimal Hankel norm approximation problem for the Wiener class of matrix-valued functions. The approach is via J-spectral factorization and frequency-domain techniques.