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ROBUSTNESS and OPTIMIZATION IN ANTI-WINDUP CONTROL
[Thesis]. Manchester, UK: The University of Manchester; 2014.
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Abstract
This thesis is broadly concerned with online-optimizing anti-windup control. These are control structures that implement some online-optimization routines to compensate for the windup effects in constrained control systems. The first part of this thesis examines a general framework for analyzing robust preservation in anti-windup control systems. This framework - the robust Kalman conjecture - is defined for the robust Lur’e problem. This part of the thesis verifies this conjecture for first-order plants perturbed by various norm-bounded unstructured uncertainties. Integral quadratic constraint theory is exploited to classify the appropriate stability multipliers required for verification in these cases. The remaining part of the thesis focusses on accelerated gradient methods. In particular, tight complexity-certificates can be obtained for the Nesterov gradient method, which makes it attractive for implementation of online-optimizing anti-windup control. This part of the thesis presents a proposed algorithm that extends the classical Nesterov gradient method by using available secant information. Numerical results demonstrating the efficiency of the proposed algorithm are analysed with the aid of performance profiles. As the objective function becomes more ill-conditioned, the proposed algorithm becomes significantly more efficient than the classical Nesterov gradient method. The improved performance bodes well for online-optimization anti-windup control since ill-conditioning is common place in constrained control systems. In addition, this thesis explores another subcategory of accelerated gradient methods known as Barzilai-Borwein gradient methods. Here, two algorithms that modify the Barzilai-Borwein gradient method are proposed. Global convergence of the proposed algorithms for all convex functions is established by using discrete Lyapunov theorems.
Keyword(s)
Fast Gradient Methods, Nonmonotonic Lyapunov Functions; First Order Methods, Nesterov Gradient Method; Gradient Methods, Barzilai-Borwein Gradient Method; Robust Kalman Conjecture, Integral Quadratic Constraints; Robust Preservation in Anti-windup Control, Kalman Conjecture; Unconstrained Optimization, Quasi-Newton Method
Bibliographic metadata
- Robust Kalman Conjecture, Integral Quadratic Constraints
- First Order Methods, Nesterov Gradient Method
- Gradient Methods, Barzilai-Borwein Gradient Method
- Unconstrained Optimization, Quasi-Newton Method
- Robust Preservation in Anti-windup Control, Kalman Conjecture
- Fast Gradient Methods, Nonmonotonic Lyapunov Functions