Ilya Kolmanovsky’s research while affiliated with University of Michigan and other places


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Publications (602)


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EnsureDualFeasibility(x,v,d,r,μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document})
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Inexact log-domain interior-point methods for quadratic programming
  • Article
  • Publisher preview available

September 2024

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9 Reads

Computational Optimization and Applications

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Ilya Kolmanovsky

This paper introduces a framework for implementing log-domain interior-point methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent towards centered points if the residual of the inexact Newton step satisfies a set of termination criteria. Three inexact LDIPM implementations based on the conjugate gradient (CG) method are developed using this framework. In a set of computational experiments, the inexact LDIPMs demonstrate a 24–72% reduction in the total number of CG iterations required for termination relative to implementations with a fixed termination tolerance. This translates into an important computation time reduction in applications such as real-time optimization and model predictive control.

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On Complexity Bounds for theMaximal Admissible Set of Linear Time-Invariant Systems

September 2024

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7 Reads

IEEE Transactions on Automatic Control

Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for discrete-time, linear, time-invariant, stable, observable systems with polytopic constraints, this set is a polytope described by a finite number of inequalities (i.e., has finite complexity). However, it is not possible to know the number of inequalities a priori from problem data. To address this gap, this contribution presents two computationally efficient methods to obtain upper bounds on the complexity of the MAS. The first method is algebraic and is based on matrix power series, while the second is geometric and is based on Lyapunov analysis. The two methods are rigorously introduced, a detailed numerical comparison between the two is provided, and an extension to systems with constant inputs is presented.


Regret Analysis of Shrinking Horizon Model Predictive Control

August 2024

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5 Reads

Journal of Dynamic Systems Measurement and Control

This paper analyzes the suboptimal implementation of Shrinking Horizon Model Predictive Control (SHMPC) when a fixed number of solver iterations and a warm-start are utilized at each time step to solve the underlying Optimal Control Problem (OCP). We derive bounds on the loss of performance (regret) and on the difference between suboptimal SHMPC and optimal solutions. This analysis provides insights and practical guidelines for the implementation of SHMPC under computational limitations. A numerical example of axisymmetric spacecraft spin stabilization is reported. The suboptimal implementation of SHMPC is shown to be capable of steering the system from an initial state into a known terminal set while satisfying control constraints.



On Constrained Feedback Control of Spacecraft Orbital Transfer Maneuvers

July 2024

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5 Reads

The paper revisits a Lyapunov-based feedback control to implement spacecraft orbital transfer maneuvers. The spacecraft equations of motion in the form of Gauss Variational Equations (GVEs) are used. By shaping the Lyapunov function using barrier functions, we demonstrate that state and control constraints during orbital maneuvers can be enforced. Simulation results from orbital maneuvering scenarios are reported. The synergistic use of the reference governor in conjunction with the barrier functions is proposed to ensure convergence to the target orbit (liveness) while satisfying the imposed constraints.


Fig. 1: Barycentric frame b and Body-fixed frame B in the Sun-Earth-Moon system.
Time Shift Governor for Constrained Control of Spacecraft Orbit and Attitude Relative Motion in Bicircular Restricted Four-Body Problem

July 2024

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66 Reads

This paper considers constrained spacecraft rendezvous and docking (RVD) in the setting of the Bicircular Restricted Four-Body Problem (BCR4BP), while accounting for attitude dynamics. We consider Line of Sight (LoS) cone constraints, thrust limits, thrust direction limits, and approach velocity constraints during RVD missions in a near rectilinear halo orbit (NRHO) in the Sun-Earth-Moon system. To enforce the constraints, the Time Shift Governor (TSG), which uses a time-shifted Chief spacecraft trajectory as a target reference for the Deputy spacecraft, is employed. The time shift is gradually reduced to zero so that the virtual target gradually evolves towards the Chief spacecraft as time goes by, and the RVD mission objective can be achieved. Numerical simulation results are reported to validate the proposed control method.






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Citations (33)


... As a way to improve the computational efficiency of PRG, in our earlier work in [16], we trained a regression neural network (NN) offline to approximate the PRG's input-output map. The trained NN was then used in real-time to compute the reference command as shown in Fig. 1(b). ...

Reference:

A Machine Learning-Based Reference Governor for Nonlinear Systems With Application to Automotive Fuel Cells
Reference Governors Based on Offline Training of Regression Neural Networks
  • Citing Conference Paper
  • October 2023

... The TSG adjusts the time shift along the reference trajectory to satisfy constraints and achieve convergence. The TSG has been previously applied to spacecraft formation control in circular Earth orbits [9], RVD in elliptic Earth orbits [10], and RVD in Halo orbits in the CR3BP setting [11], where the attitude dynamics of the spacecraft were not considered. In this paper, we extend the TSG for halo orbit RVD missions in the BCR4BP setting, incorporating coupled translational and attitude dynamics. ...

Time Shift Governor for Spacecraft Proximity Operation in Elliptic Orbits
  • Citing Conference Paper
  • January 2024

... Optimized thermal management strategies, in particular, have been demonstrated to offer improvement potential, but need to be coupled with a prediction of the battery behavior to be implemented in real-world applications [24]. This could be particularly attractive for commercial use cases, in which the route and driving behavior are usually known in advance [25], although approaches exist that also take route uncertainties into account [26]. While heating may offer benefits regarding charging speeds, high temperatures also pose a risk regarding accelerated aging due to side reactions and safety, which also necessitates an appropriate cooling strategy [27]. ...

Robust Model Predictive Control for Enhanced Fast Charging on Electric Vehicles through Integrated Power and Thermal Management
  • Citing Conference Paper
  • December 2023

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Ashley Wiese

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[...]

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... In the presence of an unknown input gain as considered in this paper, the filter is constructed through a feedback gain matrix K ∈ R m×m and an m × m strictly proper transfer function matrix Ds, which lead, for all ω ∈ Ω, to a strictly proper stable low-pass filter Cs ≜ ωKDsI m ωKDs −1 , with steady-state gain C0 I m . The gain K and the filter Ds will be used in the control law in Eq. (49). See also Remark 10 for more insights. ...

Integrated Adaptive Control and Reference Governors for Constrained Systems With State-Dependent Uncertainties
  • Citing Article
  • January 2023

IEEE Transactions on Automatic Control

... Optimized thermal management strategies, in particular, have been demonstrated to offer improvement potential, but need to be coupled with a prediction of the battery behavior to be implemented in real-world applications [24]. This could be particularly attractive for commercial use cases, in which the route and driving behavior are usually known in advance [25], although approaches exist that also take route uncertainties into account [26]. While heating may offer benefits regarding charging speeds, high temperatures also pose a risk regarding accelerated aging due to side reactions and safety, which also necessitates an appropriate cooling strategy [27]. ...

Electric Vehicle Enhanced Fast Charging Enabled by Battery Thermal Management and Model Predictive Control
  • Citing Article
  • January 2023

IFAC-PapersOnLine

... In the second model, named cognitive hierarchy [22], [23], [25], [26], each agent conjectures that the rest of the agents have a cognitive level that is lower than theirs, but follows a distribution instead of being deterministic. In the third model, a predictor-corrector structure is employed to correct the agents' expectations of other agents' behaviors [27]. The tutorial showcases that bounded rationality models can in fact be effective in realworld settings, such as in autonomous driving. ...

Safe and Human-Like Autonomous Driving: A Predictor–Corrector Potential Game Approach
  • Citing Article
  • January 2023

IEEE Transactions on Control Systems Technology

... The TSG adjusts the time shift along the reference trajectory to satisfy constraints and achieve convergence. The TSG has been previously applied to spacecraft formation control in circular Earth orbits [9], RVD in elliptic Earth orbits [10], and RVD in Halo orbits in the CR3BP setting [11], where the attitude dynamics of the spacecraft were not considered. In this paper, we extend the TSG for halo orbit RVD missions in the BCR4BP setting, incorporating coupled translational and attitude dynamics. ...

Time Shift Governor for Constraint Satisfaction during Low-Thrust Spacecraft Rendezvous in Near Rectilinear Halo Orbits
  • Citing Conference Paper
  • August 2023

... Overall, many studies aim to enhance vehicle energy efficiency through optimized speed and gear usage based on driving conditions [13], [14], [15], [16]. However, most assume straight-road driving and only consider longitudinal dynamics, neglecting the impact of corners on energy consumption. ...

Real-Time Implementation Comparison of Urban Eco-Driving Controls

IEEE Transactions on Control Systems Technology

... But then, the real-time implementation will become more time-consuming due to the solving of an online optimization problem. Furthermore, for controllers with limited hardware power, this difficulty may lead to computational unfeasibility or instability due to the so-called early termination [21], [22] (i.e., the search for the optimal control is interrupted due to the limited execution time). ...

Robust to Early Termination Model Predictive Control
  • Citing Article
  • January 2023

IEEE Transactions on Automatic Control

... Secondly, the uncertainties in long-term forecasting of vehicle speed can degrade the performance. In our previous work [16], we investigated the impact of specific types of uncertainties and proposed a location-dependent constraint adjustment strategy to enhance robustness. However, a major assumption in [16] is that the trip route is predetermined. ...

Robust Thermal Management of Electric Vehicles Using Model Predictive Control With Adaptive Optimization Horizon and Location-Dependent Constraint Handling Strategies
  • Citing Article
  • September 2023

IEEE Transactions on Control Systems Technology