Publications
17 results found
Simard JD, Astolfi A, 2024, On the construction and parameterization of interpolants in the Loewner framework, Automatica, Vol: 159, ISSN: 0005-1098
We develop a general method for the construction of interpolants in the Loewner framework for nonlinear differential–algebraic systems. The approach involves building a family of systems preserving the properties of Loewner equivalence and matching of tangential data functions. It is shown that under mild conditions this family of systems parameterizes all interpolants of sufficiently large dimension matching the tangential data while possessing tangential generalized controllability and observability functions with full column and row rank Jacobians. As a result, this family of systems provides all possible degrees of freedom that an interpolant can have. The results are also discussed in the linear setting and, when taken in combination with existing results, provide a broader framework for the construction of linear interpolating systems.
Moreschini A, Simard JD, Astolfi A, 2023, Model Reduction for Linear Port-Hamiltonian Systems in the Loewner Framework, Pages: 9493-9498
The problem of model order reduction with assignment and preservation of port-Hamiltonian structure in the reduced order model is tackled in the Loewner framework. Given a set of right-tangential interpolation data, the (subset of) left-tangential interpolation data that allow for the construction of an interpolant possessing port-Hamiltonian structure is characterized. Conditions under which an interpolant retains the underlying port-Hamiltonian structure of the system generating the data are given by requiring a particular structure of the generalized observability matrix.
Simard JD, Cheng X, Moreschini A, 2023, Interpolants With Second-Order Structure in the Loewner Framework, Pages: 4278-4283
We consider the problem of assigning a particular structure to interpolants constructed in the Loewner framework. Specifically, a dynamically extended family of interpolants matching sets of right and left tangential data is used to parameterize a family of systems matching the tangential data while also possessing a specific second-order structure. At the cost of adding states to the interpolant, the approach does not require the addition of any strict conditions on the structure of the tangential data. Conditions are stated under which, if satisfied, the interpolant corresponds to a system with physical meaning, and an illustrative example is provided.
Simard J, 2023, Interpolation and model reduction of nonlinear systems in the Loewner framework
Simard JD, Moreschini A, 2023, Enforcing Stability of Linear Interpolants in the Loewner Framework, IEEE Control Systems Letters, Vol: 7, Pages: 3537-3542
This letter considers the problem of constructing exponentially stable interpolants in the Loewner framework for linear systems of differential-algebraic equations. A designer must solve the static output feedback problem to construct a stable interpolant of minimal order without compromising the interpolation conditions. Yet, this problem is not always solvable even for controllable and observable systems. We provide a motivating example where sets of tangential interpolation data are given for which it is impossible to construct a stable interpolant of minimal order. Following this, two new parameterized families of interpolants are given, which embed an observer with state-feedback into the interpolant. Hence, with the cost of some additional states, the existence of a stable interpolant is guaranteed with standard controllability and observability conditions. Finally, the results are demonstrated by using these new families to construct stable interpolants of the tangential data given in the motivating example.
Simard JD, Moreschini A, Astolfi A, 2023, Moment Matching for Nonlinear Systems of Second-Order Equations, Pages: 4978-4983, ISSN: 0743-1546
In this paper we consider the problem of constructing nonlinear systems of second-order equations that achieve moment matching. In particular, necessary and sufficient conditions are given for which a system of second-order equations achieves moment matching, and a family of systems of second-order equations achieving moment matching is directly constructed by extracting it, via particular choices of the free mappings, from a parameterization of all systems achieving moment matching. The results are specialized for the scenario in which the signal generator is a linear system. Finally, the results of the paper are demonstrated by constructing reduced order models of a two link robotic manipulator in the second-order equation form.
Moreschini A, Simard JD, Astolfi A, 2023, Model Reduction in the Loewner Framework for Second-Order Network Systems On Graphs, Pages: 6713-6718, ISSN: 0743-1546
This paper studies the model reduction problem in the Loewner framework for second-order network systems evolving on graphs. The selection of particular sets of tangential interpolation data allows constructing reduced order models which interpolate the underlying network system while preserving the second-order structure of the system. The conditions that the tangential interpolation data must satisfy are established on the basis of the block structure of the Loewner matrices. We use this result to link the Loewner matrices to the cluster matrix gained by partitioning the graph associated with the underlying model. Finally, we provide an illustrative example to validate the obtained results.
Simard JD, Moreschini A, Astolfi A, 2023, Parameterization of All Moment Matching Interpolants, European Control Conference (ECC), Publisher: IEEE
Simard JD, Astolfi A, 2022, Regularization of Underconstrained Interpolants in the Loewner Framework, European Control Conference (ECC), Publisher: IEEE, Pages: 1684-1689
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- Citations: 2
Simard JD, Astolfi A, 2022, Loewner Functions for a Class of Nonlinear Differential-Algebraic Systems, IEEE 61st Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6542-6547, ISSN: 0743-1546
Simard JD, Astolfi A, 2021, Nonlinear model reduction in the loewner framework, IEEE Transactions on Automatic Control, Vol: 66, Pages: 5711-5726, ISSN: 0018-9286
We introduce a novel method of model reduction for nonlinear systems by extending the Loewner framework developed for linear time-invariant systems. This objective is achieved by defining Loewner functions obtained by utilizing a state-space interpretation of the Loewner matrices. A Loewner equivalent model using these functions is derived. This allows constructing reduced order models achieving interpolation in the Loewner sense.
Astolfi A, Scarciotti G, Simard J, et al., 2021, Model reduction by moment matching: beyond linearity a review of the last 10 years, 2020 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE
We present a review of some recent contributions to the theory and application of nonlinear model order reduction by moment matching. The tutorial paper is organized in four parts: 1) Moments of Nonlinear Systems; 2) Playing with Moments: Time-Delay, Hybrid, Stochastic, Data-Driven and Beyond; 3) The Loewner Framework; 4) Applications to Optimal Control and Wave Energy Conversion.
Simard JD, Astolfi A, 2021, Loewner Functions and Model Order Reduction for Nonlinear Input-Affine Descriptor Systems, 60th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6887-6894, ISSN: 0743-1546
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- Citations: 3
Simard JD, Astolfi A, 2020, Online Estimation of the Loewner Matrices, 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3425-3430, ISSN: 0743-1546
Simard JD, Astolfi A, 2020, Loewner Functions for Linear Time-Varying Systems with Applications to Model Reduction, 21st IFAC World Congress on Automatic Control - Meeting Societal Challenges, Publisher: ELSEVIER, Pages: 5623-5628, ISSN: 2405-8963
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- Citations: 6
Simard JD, Nielsen C, Miller DE, 2019, Periodic adaptive stabilization of rapidly time-varying linear systems, Mathematics of Control, Signals, and Systems, Vol: 31, ISSN: 0932-4194
Adaptive control deals with systems that have unknown and/or time-varying parameters. Most techniques are proven for the case in which any time variation is slow, with results for systems with fast time variations limited to those for which the time variation is of a known form or for which the plant has stable zero dynamics. In this paper, a new adaptive controller design methodology is proposed in which the time variation can be rapid and the plant may have unstable zero dynamics. Under the structural assumptions that the plant is relative degree one and that the plant uncertainty is a single scalar variable, as well as some mild regularity assumptions, it is proven that the closed-loop system is exponentially stable under fast parameter variations with persistent jumps. The proposed controller is nonlinear and periodic, and in each period the parameter is estimated and an appropriate stabilizing control signal is applied.
Simard JD, Astolfi A, 2019, An Interconnection-Based Interpretation of the Loewner Matrices, 58th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 7788-7793, ISSN: 0743-1546
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- Citations: 7
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