arXiv subjects

Jukka-Pekka Humaloja

Publications and source records attributed to Jukka-Pekka Humaloja.

17 recordsLinked to original sources

arXiv2026

Active Disturbance Rejection for Boundary Control Systems

We consider stabilisation of abstract boundary control systems and controlled partial differential equations with general unknown input disturbances and unmodeled nonlinearities at the input. We utilise the active disturbance rejection control approach to design a controller which rejects the input disturbance and achieves stability and external well-posedness of the closed-loop system for a class of boundary control systems with collocated inputs and outputs. We apply our main results to design controllers for one-dimensional wave and heat equations.

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arXiv2026

Observer Design for a Class of ODE -- Continuum-PDE Cascade Systems Inspired by a Control-Theoretic Model of Large-Scale Arterial Networks of Blood Flow

We develop a backstepping-based observer design for a class of ODE - continuum-PDE cascade systems, which can be viewed as the limit, of a finite collection of ODE - $2 \times 2$ hyperbolic systems, as the number of individual PDE system components tends to infinity. The large-scale collection of ODE - $2 \times 2$ hyperbolic systems is motivated by a dynamic model that we present, of a network of peripheral arteries, to which central (aortic) blood flow/pressure enters. We address a case in which average (boundary) measurements, over the ensemble dimension, are available, which is motivated by the availability of non-invasive, peripheral flow/pressure measurements. Exponential stability of the estimation error system is shown by proving well-posedness of the kernel equations and constructing a Lyapunov functional. We also establish that part of the backstepping kernels derived coincide with the solution of a Sylvester equation. We then apply the continuum-based observer for state estimation of the large-scale counterpart and, in particular, of the blood flow system, introducing an approach for optimal construction of continuum approximations. We also introduce an implementation method, adopting a spectral-based approach for computing the observer dynamics, which we illustrate in an academic, numerical simulation example. Furthermore, we illustrate the design in the problem of central flow/pressure estimation using realistic parameters and flow/pressure waveforms.

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arXiv2026

Micro-Macro Backstepping Control of Large-Scale Hyperbolic Systems (Extended Version)

We introduce a control design and analysis framework for micro-macro, boundary control of large-scale, $n+m$ hyperbolic PDE systems. Specifically, we develop feedback laws for stabilization of hyperbolic systems at the micro level (i.e., of the large-scale system) that employ a) measurements obtained from the $n+m$ system (i.e., at micro level) and kernels constructed based on an $\infty+\infty$ continuum system counterpart (i.e., at macro level), or b) kernels and measurements both stemming from a continuum counterpart, or c) averaged-continuum kernels/measurements. We also address (d)) stabilization of the continuum (macro) system, employing continuum kernels and measurements. Towards addressing d) we derive in a constructive manner an $\infty+\infty$ continuum approximation of $n+m$ hyperbolic systems and establish that its solutions approximate, for large $n$ and $m$, the solutions of the $n+m$ system. We then construct a feedback law for stabilization of the $\infty+\infty$ system via introduction of a continuum-PDE backstepping transformation. We establish well-posedness of the resulting 4-D kernel equations and prove closed-loop stability via construction of a novel Lyapunov functional. Furthermore, under control configuration a) we establish that the closed-loop system is exponentially stable provided that $n$ and $m$ are large, by proving that the exact, stabilizing $n+m$ control kernels can be accurately approximated by the continuum kernels. While under control configurations b) and c), we establish closed-loop stability capitalizing on the established solutions' and kernels' approximation properties via employment of infinite-dimensional ISS arguments. We provide two numerical simulation examples to illustrate the effectiveness and potential limitations of our design approach.

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arXiv2025

Model Reference-Based Control with Guaranteed Predefined Performance for Uncertain Strict-Feedback Systems

To address the complexities posed by time- and state-varying uncertainties and the computation of analytic derivatives in strict-feedback form (SFF) systems, this study introduces a novel model reference-based control (MRBC) framework which applies locally to each subsystem (SS), to ensure output tracking performance within the specified transient and steady-state response criteria. This framework includes 1) novel homogeneous adaptive estimators (HAEs) designed to match the uncertain nonlinear SFF system to a reference model, enabling easier analysis and control design at the level, and 2) model-based homogeneous adaptive controllers enhanced by logarithmic barrier Lyapunov functions (HAC-BLFs), intended to control the reference model provided by HAEs in each SS, while ensuring the prescribed tracking responses under control amplitude saturation. The inherently robust MRBC achieves uniformly exponential stability using a generic stability connector term, which addresses dynamic interactions between the adjacent SSs. The parameter sensitivities of HAEs and HAC-BLFs in the MRBC framework are analyzed, focusing on the system's robustness and responsiveness. The proposed MRBC framework is experimentally validated through several scenarios involving an electromechanical linear actuator system with an uncertain SFF, subjected loading disturbance forces challenging 0-95% of its capacity.

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arXiv2025

Observer-Based Output-Feedback Backstepping Stabilization of Continua of Hyperbolic PDEs and Application to Large-Scale $n+m$ Coupled Hyperbolic PDEs

We develop a non-collocated, observer-based output-feedback law for a class of continua of linear hyperbolic PDE systems, which are viewed as the continuum version of $n+m$, general heterodirectional hyperbolic systems as $n\to\infty$. The design relies on the introduction of a novel, continuum PDE backstepping transformation, which enables the construction of a Lyapunov functional for the estimation error system. Stability under the observer-based output-feedback law is established by using the Lyapunov functional construction for the estimation error system and proving well-posedness of the complete closed-loop system, which allows utilization of the separation principle. Motivated by the fact that the continuum-based designs may provide computationally tractable control laws for large-scale, $n+m$ systems, we then utilize the control/observer kernels and the observer constructed for the continuum system to introduce an output-feedback control design for the original $n+m$ system. We establish exponential stability of the resulting closed-loop system, which consists of a mixed $n+m$-continuum PDE system (comprising the plant-observer dynamics), introducing a virtual continuum system with resets, which enables utilization of the continuum approximation property of the solutions of the $n+m$ system by its continuum counterpart (for large $n$). We illustrate the potential computational complexity/flexibility benefits of our approach via a numerical example of stabilization of a large-scale $n+m$ system, for which we employ the continuum observer-based controller, while the continuum-based stabilizing control/observer kernels can be computed in closed form.

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arXiv2024

On Computation of Approximate Solutions to Large-Scale Backstepping Kernel Equations via Continuum Approximation

We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system counterpart (with computational complexity that does not grow with the number of state components of the large-scale system). In the first method, we provide explicit formulae for the solution to the continuum kernels PDEs, employing a (triple) power series representation of the continuum kernel and establishing its convergence properties. In this case, we also provide means for reducing computational complexity by properly truncating the power series (in the powers of the ensemble variable). In the second method, we identify a class of systems for which the solution to the continuum (and hence, also an approximate solution to the respective large-scale) kernel equations can be constructed in closed form. We also present numerical examples to illustrate computational efficiency/accuracy of the approaches, as well as to validate the stabilization properties of the approximate control kernels, constructed based on the continuum.

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arXiv2024

Stabilization of a Class of Large-Scale Systems of Linear Hyperbolic PDEs via Continuum Approximation of Exact Backstepping Kernels

We establish that stabilization of a class of linear, hyperbolic partial differential equations (PDEs) with a large (nevertheless finite) number of components, can be achieved via employment of a backstepping-based control law, which is constructed for stabilization of a continuum version (i.e., as the number of components tends to infinity) of the PDE system. This is achieved by proving that the exact backstepping kernels, constructed for stabilization of the large-scale system, can be approximated (in certain sense such that exponential stability is preserved) by the backstepping kernels constructed for stabilization of a continuum version (essentially an infinite ensemble) of the original PDE system. The proof relies on construction of a convergent sequence of backstepping kernels that is defined such that each kernel matches the exact backstepping kernels (derived based on the original, large-scale system), in a piecewise constant manner with respect to an ensemble variable; while showing that they satisfy the continuum backstepping kernel equations. We present a numerical example that reveals that complexity of computation of stabilizing backstepping kernels may not scale with the number of components of the PDE state, when the kernels are constructed on the basis of the continuum version, in contrast to the case in which they are constructed on the basis of the original, large-scale system. In addition, we formally establish the connection between the solutions to the large-scale system and its continuum counterpart. Thus, this approach can be useful for design of computationally tractable, stabilizing backstepping-based control laws for large-scale PDE systems.

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arXiv2024

Backstepping Control of Continua of Linear Hyperbolic PDEs and Application to Stabilization of Large-Scale $n+m$ Coupled Hyperbolic PDE Systems

We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of $m$ leftward transporting PDEs. The key analysis challenge of the design is to establish well-posedness of the resulting ensemble of kernel equations, since they evolve on a prismatic (3-D) domain and inherit the potential discontinuities of the kernels for the case of $n+m$ hyperbolic systems. We resolve this challenge generalizing the well-posedness analysis of Hu, Di Meglio, Vazquez, and Krstic to continua of general, heterodirectional hyperbolic PDE systems, while also constructing a proper Lyapunov functional. Since the motivation for addressing such PDE systems continua comes from the objective to develop computationally tractable control designs for large-scale PDE systems, we then introduce a methodology for stabilization of general $n+m$ hyperbolic systems, constructing stabilizing backstepping control kernels based on the continuum kernels derived from the continuum system counterpart. This control design procedure is enabled by establishing that, as $n$ grows, the continuum backstepping control kernels can approximate (in certain sense) the exact kernels, and thus, they remain stabilizing (as formally proven). This approach guarantees that complexity of computation of stabilizing kernels does not grow with the number $n$ of PDE systems components. We further establish that the solutions to the $n+m$ PDE system converge, as $n\to\infty$, to the solutions of the corresponding continuum PDE system. We also provide a numerical example in which the continuum kernels can be obtained in closed form (in contrast to the large-scale kernels), thus resulting in minimum complexity of control kernels computation, which illustrates the potential computational benefits of our approach.

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arXiv2024

Region-free explicit model predictive control for linear systems on Hilbert spaces

We extend discrete-time explicit model predictive control (MPC) rigorously to linear distributed parameter systems. After formulating an MPC framework and giving a relevant KKT theorem, we realize fast regionless explicit MPC by using the dual active set method QPKWIK. A Timoshenko beam with input and state constraints is used to demonstrate the efficacy of the design at controlling a continuous-time hyperbolic PDE with constraints, using a discrete-time explicit MPC controller.

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arXiv2023

Robust Controllers for a Flexible Satellite Model

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 controller and an observer based controller, such that the linear and angular velocities of the center rigid body converge to the given sinusoidal signals asymptotically. A numerical simulation is presented to compare the performances of the two controllers.

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arXiv2022

On Robust Regulation of PDEs: from Abstract Methods to PDE Controllers

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" can be utilised in controller design for concrete PDE systems. We show that when implemented for PDE systems, the abstract control design methods lead in a natural way to controllers with "PDE parts". Moreover, we formulate the controller construction in a way which utilises minimal knowledge of the abstract system representation and is instead solely based on natural properties of the original PDE. We also discuss computation and approximation of the controller parameters, and illustrate the results with an example on control design for a boundary controlled diffusion equation.

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arXiv2021

Subsystem-Based Control with Modularity for Strict-Feedback Form Nonlinear Systems

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 control design with global asymptotic stability, 2) such that both the control design and the stability analysis can be performed locally at a subsystem level, 3) while avoiding an excessive growth of the control design complexity when the system order n increases. The latter property makes the method suitable especially for high-dimensional systems. We also design a smooth projection function for addressing system parametric uncertainties. Numerical simulations demonstrate the efficiency of the method.

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arXiv2021

Decentralized Observer Design for Virtual Decomposition Control

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 implementation can be done locally. Similar to VDC, the combined controller-observer design is passivity-based, and we show that it achieves semiglobal exponential convergence of the tracking error. The convergence analysis is carried out using Lyapunov functions based on the observer and controller error dynamics. The proposed design is demonstrated in a simulation study of a 2-DoF open chain robotic manipulator in the vertical plane.

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arXiv2020

The interval turnpike property for adjoints

In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.

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arXiv2020

Model Predictive Control for Regular Linear Systems

The present work extends known finite-dimensional constrained optimal control realizations to the realm of well-posed regular linear infinite-dimensional systems modelled by partial differential equations. The structure-preserving Cayley-Tustin transformation is utilized to approximate the continuous-time system by a discrete-time model representation without using any spatial discretization or model reduction. The discrete-time model is utilized in the design of model predictive controller accounting for optimality, stabilization, and input and output/state constraints in an explicit way. The proposed model predictive controller is dual-mode in the sense that predictive controller steers the state to a set where exponentially stabilizing unconstrained feedback can be utilized without violating the constraints. The construction of the model predictive controller leads to a finite-dimensional constrained quadratic optimization problem easily solvable by standard numerical methods. Two representative examples of partial differential equations are considered.

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arXiv2018

Approximate robust output regulation of boundary control systems

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 proceed to formulate the approximate robust output regulation problem and present a finite-dimensional controller structure to solve it. Our main motivating example is a wave equation on a bounded multidimensional spatial domain with force control and velocity observation at the boundary. In order to illustrate the theoretical results, we construct an approximate robust controller for the wave equation on an annular domain and demonstrate its performance with numerical simulations.

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arXiv2017

Robust Regulation of Infinite-Dimensional Port-Hamiltonian Systems

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 example where we implement a controller for a one-dimensional Euler-Bernoulli beam with boundary controls and boundary observations.

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