This paper focuses on the robustness analysis of discrete‐time, linear time‐varying (LTV) systems subject to various uncertainties, such as static and dynamic, time‐invariant and time‐varying, linear perturbations, and unknown initial conditions. The proposed approach is based on integral quadratic constraint theory and allows for a potentially more accurate characterization of the set in which the initial state resides by imposing separate constraints on the initial values of the state variables as opposed to simply requiring the initial state to lie in some ellipsoid. The adopted problem formulation facilitates the analysis of uncertain LTV systems subject to disturbance inputs that are bounded pointwise in time, and the developed results enable determining useful pointwise bounds on the performance outputs given such inputs. The main analysis result is given for eventually periodic nominal systems, which include linear time‐invariant, finite horizon, and periodic systems as special cases. The analysis conditions are expressed as linear matrix inequalities. Two additional results stemming from the main analysis theorem are provided that can be used to determine overapproximated ellipsoidal reachable sets. Finally, the utility of the proposed approach is demonstrated in an illustrative example.
This article presents a dissipativity approach for robustness analysis using the framework of integral quadratic constraints (IQCs). The derived results apply for linear time‐varying nominal systems with uncertain initial conditions. IQC multipliers are used to describe the sets of allowable uncertainty operators, and signal IQC multipliers are used to describe the sets of allowable disturbance signals. The novel concepts of dichotomic nodes and their corresponding factorizations are introduced, which allow for the aforementioned multipliers to be general time‐varying operators. The results are illustrated via the robustness analysis of a flight controller for an unmanned aircraft system tasked to perform a Split‐S maneuver.
more » « less- Award ID(s):
- 1650465
- NSF-PAR ID:
- 10454314
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal of Robust and Nonlinear Control
- Volume:
- 31
- Issue:
- 3
- ISSN:
- 1049-8923
- Page Range / eLocation ID:
- p. 733-758
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such inputoutput analysis is the use of Integral Quadratic Constraints (IQCs), which considers the interconnection of a nominal linear system with an unmodelled nonlinear or uncertain subsystem with known input-output properties. Although these methods are widely used for Ordinary Differential Equations (ODEs), there have been fewer attempts to extend IQCs to infinitedimensional systems. In this paper, we present an IQC-based framework for Partial Differential Equations (PDEs) and Delay Differential Equations (DDEs). First, we introduce infinitedimensional signal spaces, operators, and feedback interconnections. Next, in the main result, we propose a formulation of hard IQC-based input-output stability conditions, allowing for infinite-dimensional multipliers. We then show how to test hard IQC conditions with infinite-dimensional multipliers on a nominal linear PDE or DDE system via the Partial Integral Equation (PIE) state-space representation using a sufficient version of the Kalman-Yakubovich-Popov lemma (KYP). The results are then illustrated using four example problems with uncertainty and nonlinearity.more » « less
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This paper addresses the problem of hybrid control for a class of switched uncertain systems. The switched system under consideration is subject to structured uncertain dynamics in a linear fractional transformation (LFT) form and time-varying input delays. A novel hybrid controller is proposed, which consists of three major components: the integral quadratic constraint (IQC) dynamics, the continuous dynamics, and the jump dynamics. The IQC dynamics are developed by leveraging methodologies from robust control theory and are utilised to address the effects of time-varying input delays. The continuous dynamics are structured by feeding back not only measurement outputs but also some system's internal signals. The jump dynamics enforce a jump (update/reset) at every switching time instant for the states of both IQC dynamics and continuous dynamics. Based on this, robust stability of the overall hybrid closed-loop system is established under the average dwell time framework with multiple Lyapunov functions. Moreover, the associated control synthesis conditions are fully characterised as linear matrix inequalities, which can be solved efficiently. An application example on regulation of a nonlinear switched electronic circuit system has been used to demonstrate effectiveness and usefulness of the proposed approach.more » « less
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