Optimizing Shifted Stabilizers with Asymmetric Input Saturation

A stabilizing controller design for linear systems subject to asymmetric actuator saturation is proposed. Stabilization is achieved by focusing on shifted equilibria selected via the solution of an optimization problem ensuring convergence to the origin of the shifted equilibrium. To enable the comp...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2024-08, p.1-16
Main Authors: Braun, P., Giordano, G., Kellett, C. M., Shames, I., Zaccarian, L.
Format: Article
Language:English
Subjects:
Computer Science
Focusing
Iterative methods
Linear systems
Lyapunov methods
Mathematics
Optimization
Optimization and Control
Predictive control
Systems and Control
Vectors
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Summary:A stabilizing controller design for linear systems subject to asymmetric actuator saturation is proposed. Stabilization is achieved by focusing on shifted equilibria selected via the solution of an optimization problem ensuring convergence to the origin of the shifted equilibrium. To enable the computational time required by the optimizer, we impose sampled-data updates of the shifted equilibria and cast our description within a hybrid dynamical systems formulation. Two feedback solutions are given, using exact and inaccurate optimization algorithms, thus establishing interesting trade-offs between continuous-time dynamics and computationally expensive iterative discrete-time parametric optimization schemes. Through numerical examples, estimates of the region of attraction obtained through the method outlined in this paper are compared to other methods in the literature. Additionally, the real-time applicability of the control law is illustrated on numerical examples.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2024.3436728