Lassi PaunonenTampere University | UTA · Department of Mathematics and Statistics
Lassi Paunonen
PhD
About
87
Publications
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662
Citations
Introduction
Current main research interests:
- Nonuniform stability of semigroups
- Perturbation theory for semigroups
- Robust control of linear infinite-dimensional systems
Additional affiliations
July 2016 - present
Position
- Professor (Assistant)
Description
- Leader of the Systems Theory Research Group.
Publications
Publications (87)
In this paper we study the robustness properties of strong and polynomial stability of semigroups of operators. We show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator. The presented results apply to general polynomially stable semigroups and bo...
In this paper, we consider robust output regulation and the internal model principle for infinite-dimensional linear systems. We concentrate on a problem where the control law is required to be robust with respect to a restricted class of perturbations. We show that depending on the class of admissible perturbations, it is often possible to constru...
In this paper we consider robust output regulation of distributed parameter systems and the internal model principle. The main purpose is to generalize the internal model principle by Francis and Wonham for infinite-dimensional systems and clarify the relationships between different generalizations of the internal model. We also construct a signal...
![A steady-state solution (wss1,wss2,Tss)\documentclass[12pt]{minimal}...](publication/356884994/figure/fig4/AS:1168142587953152@1655518304054/A-steady-state-solution-wss1-wss2-Tssdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The initial state (v0,θ0)\documentclass[12pt]{minimal}...](publication/356884994/figure/fig5/AS:1168142587961353@1655518304157/The-initial-state-v0-th0documentclass12ptminimal-usepackageamsmath_Q320.jpg)
We study a temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models for actuation and sensing dynamics; thus, the complete model dynamics are governed by an ODE–PDE–ODE cascade....
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are memory-efficient to train, process time series naturally, and incorporate knowledge of physical systems into deep learning (D...
We consider a PDE-ODE model of a flexible satellite that is composed of two identical flexible solar panels and a center rigid body. We prove that the satellite model is exponentially stable in the sense that the energy of the solutions decays to zero exponentially. In addition, we construct two internal model based controllers, a passive controlle...
In this paper we study robust output tracking and disturbance rejection of linear partial differential equation (PDE) models. We focus on demonstrating how the abstract internal model based controller design methods developed for "regular linear systems" are applied in controller design for concrete PDE systems. We show that when implemented for PD...
In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation w...
This study proposes an adaptive subsystem-based control (SBC) for systematic and straightforward nonlinear control of nth-order strict-feedback form (SFF) systems. By decomposing the SFF system to subsystems, a generic term (namely stability connector) can be created to address dynamic interactions between the subsystems. This 1) enables modular co...
A mixed lattice group is a generalization of a lattice ordered group. The theory of mixed lattice semigroups dates back to the 1970s, but the corresponding theory for groups and vector spaces has been relatively unexplored. In this paper we investigate the basic structure of mixed lattice groups, and study how some of the fundamental concepts in Ri...
We consider output tracking for a class of viscous nonlinear fluid flows including the incompressible 2D Navier–Stokes equations. The fluid is subject to in-domain inputs and disturbances. We construct an error feedback controller which guarantees approximate local velocity output tracking for a class of reference outputs. The control solution cove...
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are memory-efficient to train, process time-series naturally and incorporate knowledge of physical systems into deep learning mod...
In this paper, we incorporate velocity observer design into the virtual decomposition control (VDC) strategy of an n-DoF open chain robotic manipulator. Descending from the VDC strategy, the proposed design is based on decomposing the n-DoF manipulator into subsystems, i.e., rigid links and joints, for which the decentralized controller-observer im...
We study output tracking and disturbance rejection for an Euler-Bernoulli beam with Kelvin-Voigt damping. The system has distributed control and pointwise observation. As our main result we design a finite-dimensional low-order internal model based controller that is based on a spectral Galerkin method and model reduction by Balanced Truncation. Th...
This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port-Hamiltonian systems including second order models such as the Euler-Bernoulli beam. The control design is achieved using the internal model principle and the stability analysis using a Lyapunov approach. Contrary to existing works o...
We study the asymptotic behaviour of solutions to a one-dimensional coupled wave-heat system with Coleman-Gurtin thermal law. As our main results, we represent the system as a feedback interconnection between the wave part and the Coleman-Gurtin part and, using the asymptotic theory of $C_0$-semigroups, we show that the associated semigroup in the...
We study temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models for actuation and sensing dynamics, thus the complete model dynamics are governed by an ODE-PDE-ODE system. As...
Mathematical modeling of biological neuronal networks is important in order to increase understanding of the brain and develop systems capable of brain-like learning. While mathematical analysis of these comprehensive, stochastic, and complex models is intractable, and their numerical simulation is very resource intensive, mean-field modeling is an...
We consider robust output regulation of a partial differential equation model describing temperature evolution in a room. More precisely, we examine a two-dimensional room model with the velocity field and temperature evolution governed by the incompressible steady state Navier-Stokes and advection-diffusion equations, respectively, which coupled t...
We study the well-posedness and asymptotic behaviour of selected PDE–PDE and PDE–ODE systems on one-dimensional spatial domains, namely a boundary coupled wave–heat system and a wave equation with a dynamic boundary condition. We prove well-posedness of the models and derive rational decay rates for the energy using an approach where the coupled sy...
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely monotonic we obtain a drastically simplified condition which ensures boundedness of the associates semigroup. If th...
We study the robust output regulation problem for linear distributed parameter systems in the situation where the frequencies of the exogeneous signals are unknown and need to be estimated based on the reference signal. We present a generalisation of the internal model principle for time-dependent controllers whose parameters converge asymptoticall...
In this paper, we incorporate velocity observer design into the virtual decomposition control (VDC) strategy of an $n$-DoF open chain robotic manipulator. Descending from the VDC strategy, the proposed design is based on decomposing the $n$-DoF manipulator into subsystems, i.e., rigid links and joints, for which the controller-observer implementati...
In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster's equation, and a wave equation w...
We consider a PDE-ODE model of a satellite and robust output regulation of the corresponding model. The satellite is composed of two flexible solar panels and a rigid center body. Exponential stability of the model is proved using passivity and resolvent estimates in the port-Hamiltonian framework. In addition, we construct a simple low-gain contro...
In this study mathematical model order reduction is applied to a nonlinear model of a network of biophysically realistic heterogeneous neurons. The neuron model describes a pyramidal cell in the hippocampal CA3 area of the brain and includes a state-triggered jump condition. The network displays synchronized firing of action potentials (spikes), a...
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely monotonic we obtain a drastically simplified condition which ensures boundedness of the associates semigroup. If th...
We study the well-posedness and asymptotic behaviour of selected PDE-PDE and PDE-ODE systems on one-dimensional spatial domains, namely a boundary coupled wave-heat system and a wave equation with a dynamic boundary condition. We prove well-posedness of the models and derive rational decay rates for the energy using an approach where the coupled sy...
We investigate the stability properties of strongly continuous semigroups generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a contraction semigroup and $B$ is a possibly unbounded operator. Such systems arise naturally in the study of hyperbolic partial differential equations with damping on the boundary or inside the spat...
Electronic coupling between adjacent molecules is one of the key parameters determining the charge transfer (CT) rates in the bulk heterojunction (BHJ) polymer solar cells (PSC). We calculate theoretically electronic couplings for exciton dissociation (ED) and charge recombination (CR) processes at local poly(thiophene-co-quinoxaline) (TQ) and PC71...
We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show that robust output tracking and disturbance rejection for our class of systems can be achieved using a finite-dimensional controller and present algorithms for constructio...
The current trend in computational neuroscience is to incorporate multiple physical levels of the brain into mathematical models. Such comprehensive models with accurate system dynamics are necessary in order to increase understanding of different mechanisms in the
brain. Mathematical analysis of these models is intractable, hence numerical method...
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finite-dimensional reduced order controllers. The controller design is then used f...
This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port-Hamiltonian systems including second order models such as the Euler-Bernoulli beam. The control design is achieved using the internal model principle and the stability analysis using a Lyapunov approach. Contrary to existing works o...
This document contains the mathematical introduction to RORPack - a Python software library for robust output tracking and disturbance rejection for linear PDE systems. The RORPack library is open-source and freely available at https://github.com/lassipau/rorpack/ The package contains functionality for automated construction of robust internal mode...
Multi-scale models in neuroscience typically integrate detailed biophysical and neurobiological phenomena from molecular level up to network and system levels. These models are very challenging to simulate. Model Order Reduction (MOR) is an established method in engineering sciences, such as control theory, for improving computational efficiency of...
We consider a partial differential equation model widely used for counter-flow heat exchangers and the related robust output regulation problem with boundary control and boundary observation. We show that the control system is an exponentially stable regular linear system, which enables us to use a specific known controller design to robustly regul...
![Fig. 2. The state profile of the heat equation for t ∈ [0, 15].](profile/Lassi-Paunonen/publication/335371227/figure/fig2/AS:827580504633346@1574321976865/The-state-profile-of-the-heat-equation-for-t-0-15_Q320.jpg)
We extend the internal model principle for boundary control system to cover robust tracking of sinusoidal reference signals with polynomial coefficients. The internal model principle is presented in the form of both the internal model structure and the (G-conditions. A controller structure will be presented and its internal model properties will be...
We study robust output regulation for linear parabolic control systems. As our main results we show that robust output tracking and disturbance rejection for this class of PDE models can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller...
Multi-scale models in neuroscience typically integrate detailed biophysical and neurobiological phenomena from molecular level up to network and system levels. These models are very challenging to simulate. Model Order Reduction (MOR) is an established method in engineering sciences, such as control theory, for improving computational efficiency of...
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence....
We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of $C_0$-semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that the energy of classical solutions decays like $t^{-2/3}$ as $t\to\infty$. This rate is moreover shown to be shar...
We consider robust output regulation of passive infinite-dimensional linear port-Hamiltonian systems. As the main result, we present a Lyapunov-based proof to show that a passive internal model based low-gain controller solves the control problem for stable port-Hamiltonian systems. The theoretic results are used to construct a controller controlle...
![Figure 1. Output profile for the controlled wave equation for t ∈ [0, 15].](profile/Mikael-Kurula/publication/321571256/figure/fig1/AS:631648076980242@1527608045974/Output-profile-for-the-controlled-wave-equation-for-t-0-15_Q320.jpg)
We extend the internal model principle for systems with boundary control and boundary observation, and construct a robust controller for this class of systems. However, as a consequence of the internal model principle, any robust controller for a plant with infinite-dimensional output space necessarily has infinite-dimensional state space. We proce...
In this study a nonlinear mathematical model of plasticity in the brain is reduced using the Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method. Such methods are remarkably useful for connecting reduced small scale models via the inputs and outputs to form optimally performing large scale models. Novel results were obtained...
![Figure 1. Regulation error on t ? [0, 20].](profile/Lassi-Paunonen/publication/318029162/figure/fig1/AS:665186146975746@1535604144705/Regulation-error-on-t-0-20_Q320.jpg)
We will give general sufficient conditions under which a controller achieves robust regulation for a boundary control and observation system. Utilizing these conditions we construct a minimal order robust controller for an arbitrary order impedance passive linear port-Hamiltonian system. The theoretical results are illustrated with a numerical exam...
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the stability results to the construction of passive error feedback controllers for robust output tracking and disturbanc...
This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications. For this class of systems we analyse in detail the...
The internal model principle states that all robustly regulating controllers must contain a suitably reduplicated internal model of the signal to be regulated. Using frequency domain methods, we show that the number of the copies may be reduced if the class of perturbations in the problem is restricted. We present a two step design procedure for a...
We study a simple one-dimensional coupled wave-heat system and obtain a sharp
estimate for the rate of energy decay of classical solutions. Our approach is
based on the asymptotic theory of $C_0$-semigroups and in particular on a
result due to Borichev and Tomilov (Math. Ann., 2010), which reduces the
problem of estimating the rate of energy decay...
We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A feedforward control law and a discrete-time dynamic error feedback controller for output tracking and disturbance...
We use frequency domain methods to study robust output regulation of a stable plant in a situation where the controller is only required to be robust with respect to a predefined class of perturbations. We present a characterization for the solvability of the control problem and design a minimal order controller that achieves robustness with respec...
We present a method for obtaining robust control over a first-order port-Hamiltonian system. The presented method is especially designed for controlling impedance energy-preserving port-Hamiltonian systems. By combining the stabilization results of port-Hamiltonian systems and the theory of robust output regulation for exponentially stable systems,...
We present a non-technical overview of the results obtained by the authors (2015) concerning the so-called robot rendezvous problem studied by Feintuch and Francis (2012). In particular, we present a necessary and sufficient condition for convergence of the solution in terms of Ces\`aro convergence of the translates $S^k x_0$, $k\ge0$, of the seque...
We construct two error feedback controllers for robust output tracking and disturbance rejection of a regular linear system with nonsmooth reference and disturbance signals. We show that for sufficiently smooth signals the output converges to the reference at a rate that depends on the behaviour of the transfer function of the plant on the imaginar...
This paper investigates the asymptotic behaviour of solutions to certain
infinite systems of ordinary differential equations. In particular, we use
results from ergodic theory and the asymptotic theory of $C_0$-semigroups to
obtain a characterisation, in terms of convergence of certain Ces\`aro
averages, of those initial values which lead to conver...
We study the robustness properties of strong stability of a strongly continuous semigroup on a Hilbert space. We concentrate on a situation where the generator of the unperturbed semigroup has a finite spectral point on the imaginary axis and the resolvent operator is polynomially bounded elsewhere on the imaginary axis. As our main result we prese...
We introduce the concept of polynomial input-output stability for infinite-dimensional linear systems. We show that this stability type corresponds exactly to the recent notion of P-stability in the frequency domain. In addition, we show that on a Hilbert space a regular linear system whose system operator generates a polynomially stable semigroup...
We present three dynamic error feedback controllers for robust output
regulation of regular linear systems. These controllers are (i) a minimal order
robust controller for exponentially stable systems (ii) an observer-based
robust controller and (iii) a new internal model based robust controller
structure. In addition, we present two controllers th...
In this technical note we study robust output tracking for autonomous linear systems. We introduce a new approach to designing robust controllers using a recent observation that a full internal model is not always necessary for robustness. Especially this may be the case if the control law is only required to be robust with respect to a specific pr...
In this paper we employ a new controller structure in solving the robust output regulation problem for a linear distributed parameter system with finite or infinite-dimensional exosystems. In the case of an infinite-dimensional exosystem we also present additional conditions for achieving polynomial or logarithmic nonuniform decay rates for the clo...
In this paper, we study the robust output regulation problem for distributed parameter systems with infinite-dimensional exosystems. The main purpose of this paper is to demonstrate the several advantages of using a controller that achieves polynomial closed-loop stability, instead of a one stabilizing the closed-loop system strongly. In particular...
In this paper the theory of robust output regulation of distributed parameter
systems with infinite-dimensional exosystems is extended for plants with
unbounded control and observation. As the main result, we present the internal
model principle for linear infinite-dimensional systems with unbounded input
and output operators. We do this for two di...
In this technical note we study the role of the exosystem in the theory of output regulation for linear infinite-dimensional systems. The main result of this technical note shows that a stabilizing autonomous controller that achieves output tracking of an almost periodic reference signal is also capable of tracking any signal generated by a full ex...
In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points. We characterize class...
In this paper, we consider robust output regulation of distributed parameter systems with infinite-dimensional exosystems capable of generating polynomially growing signals. We design an observer-based error feedback controller solving the control problem. The controller is chosen in such a way that it incorporates an internal model of the infinite...
In this paper we consider the theory of robust out-put regulation for distributed parameter systems with infinite-dimensional exosystems. The main purpose of the paper is to extend selected results of the existing state space theory to allow plants with unbounded control and observation operators. In particular, we show that under suitable assumpti...
In this paper we study the stability properties of strongly continuous
semigroups generated by block operator matrices. We consider triangular and
full operator matrices whose diagonal operator blocks generate polynomially
stable semigroups. As our main results, we present conditions under which also
the semigroup generated by the operator matrix i...
In this paper we present Lyapunov based proofs for the well-known Arendt–Batty–Lyubich–Vũ Theorem for strongly continuous and discrete semigroups. We also study the spectral properties of the limit isometric groups used in the proofs.
In this paper we study robust output regulation for distributed parameter systems. In particular we are interested in the internal model principle, which can be used in characterizing controllers that achieve robust output tracking and disturbance rejection for a linear system. We show that if we do not require robustness with respect to arbitrary...
In this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator. In addition, we also improve recent perturbation results for bounded finite rank perturbations. The results are illustrated with two examples. In the...
In this paper we study the asymptotic output tracking for distributed parameter systems with general infinite-dimensional exosystems. We present conditions for the solvability of the problem and construct the appropriate open loop control law using the states of the system and the exosystem. In particular the results do not assume the exosystem to...
In this paper the output regulation of a linear distributed parameter system with a non-autonomous periodic exosystem is considered. It is shown that the solvability of the output regulation problem can be characterized by the solvability of a certain constrained infinite-dimensional Sylvester differential equation. Conditions are given for the exi...
In this paper robust output regulation of distributed parameter systems with infinite-dimensional exosystems is discussed. We divide the problem into two parts, namely robust stabilization and robust regulation, and focus on the latter. Our aim is to give a unified treatment of the problem in time and frequency domains by using blocking zeros.
In this paper we study output regulation of distributed parameter systems with infinite-dimensional exosystems. The purpose of the paper is to find simple and minimal conditions on the signal generator under which the solvability of the output regulation problem can be characterized by the solvability of the regulator equations. We also study the p...
In this paper the solvability of the infinite-dimensional Sylvester differential equation is considered.Th is is an operator differential equation on a Banach space.Con ditions for the existence of a unique classical solution to the equation are presented.In addition, a periodic version of the equation is studied and conditions for the existence of...
In this paper we consider bounded and relatively bounded finite rank perturbations of a Riesz-spectral operator generating a polynomially stable semigroup of linear operators on a Hilbert space. We concentrate on a commonly encountered situation where the spectrum of the unperturbed operator is contained in the open left half-plane of the complex p...
In this paper we study certain infinite-dimensional Sylvester equations. The equations are closely related to robust output regulation of infinite-dimensional systems. If the signal generator is finite-dimensional or has discrete spectrum and a complete set of orthonormal eigenvectors, there are some known sufficient conditions for the decomposing...
In this paper we study the decomposing of certain infinite-dimensional Sylvester equations. This property of the equations is closely related to robust output regulation of infinite-dimensional systems. When the signal generator has discrete spectrum and a complete set of orthonormal eigenvectors, some sufficient conditions for the decomposing of t...
Projects
Projects (4)
Computational neuroscience relies heavily on simulation studies to understand the brain. This project aims at discovering mathematical methods for reducing computational time of nonlinear models used in the field of computational neuroscience. Such methods should not simplify, instead they should approximate. The methods will be released as open source implementations and their integration into neuronal simulators and neuromorphic hardware is studied.
Public description:
One of the important results of classical systems theory is the (finite-dimensional) Internal Model Principle. It states that a feedback controller stabilizing the closed-loop system is robust if and only if it incorporates a copy of exogenous reference signals. This result is used to design control systems, but it can also be seen as a guideline for understanding how nature has implemented this principle to accomplish robust regulation. The aim of the research is to develop the theory of robust regulation for infinite-dimensional systems. The extension of the theory is crucial since many important processes, such as diffusion, heat transfer and vibration, are infinite-dimensional. Applications include control of heat diffusion, vibrations, and flexible structures.