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Abstract In this work, we propose the integration of Koopman operator methodology with Lyapunov‐based model predictive control (LMPC) for stabilization of nonlinear systems. The Koopman operator enables global linear representations of nonlinear dynamical systems. The basic idea is to transform the nonlinear dynamics into a higher dimensional space using a set of observable functions whose evolution is governed by the linear but infinite dimensional Koopman operator. In practice, it is numerically approximated and therefore the tightness of these linear representations cannot be guaranteed which may lead to unstable closed‐loop designs. To address this issue, we integrate the Koopman linear predictors in an LMPC framework which guarantees controller feasibility and closed‐loop stability. Moreover, the proposed design results in a standard convex optimization problem which is computationally attractive compared to a nonconvex problem encountered when the original nonlinear model is used. We illustrate the application of this methodology on a chemical process example.
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Command Governors Based on Bilevel Optimization for Constrained Spacecraft Orbital Transfer
The use of Command governors (CGs) to enforce pointwise-in-time state and control constraints by minimally altering reference commands to closed-loop systems has been proposed for a range of aerospace applications. In this paper, we revisit the design of the CG and describe approaches to its implementation based directly on a bilevel (inner loop + outer loop) optimization problem in the formulation of CG. Such approaches do not require offline construction and storage of constraint admissible sets nor the use of online trajectory prediction, and hence can be beneficial in situations when the reference command is high-dimensional and constraints are nonlinear and change with time or are reconfigured online. In the case of linear systems with linear constraints, or in the case of nonlinear systems with linear constraints for which a quadratic Lyapunov function is available, the inner loop optimization problem is explicitly solvable and the bilevel optimization reduces to a single stage optimization. In other cases, a reformulation of the bilevel optimization problem into a mathematical programming problem with equilibrium constraints (MPEC) can be used to arrive at a single stage optimization problem. By applying the bilevel optimization-based CG to the classical low thrust orbital transfer problem, in which the dynamics are represented by Gauss-Variational Equations (GVEs) and the nominal controller is of Lyapunov type, we demonstrate that constraints, such as on the radius of periapsis to avoid planetary collision, on the osculating orbit eccentricity and on the thrust magnitude can be handled. Furthermore, in this case the parameters of the Lyapunov function can be simultaneously optimized online resulting in faster maneuvers.
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- Award ID(s):
- 1904394
- PAR ID:
- 10525258
- Publisher / Repository:
- American Institute of Aeronautics and Astronautics
- Date Published:
- ISBN:
- 978-1-62410-711-5
- Format(s):
- Medium: X
- Location:
- Orlando, FL
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2024-0097
