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In this paper, we address the leaderless consensus control problem for a class of linear multi-agent systems (MASs) subject to nonlinear time-varying input delays and unknown external disturbances. The MAS is considered to be non-introspective, meaning that each individual agent is not able to measure the absolute plant state/output of its own but can sense relative information from its neighbours. A novel dynamic relative output-feedback (DROF) controller structure is proposed by leveraging the integral quadratic constraints (IQCs) from robust control theory. This new DROF controller is compelling in the sense that it utilises not only the relative plant outputs, but also the relative controller states and relative IQC-induced dynamics states for distributed feedback control. Based on this, the associated consensus control synthesis conditions that guarantee optimal H ∞ disturbance attenuation performance in the presence of time-varying input delays are derived and formulated as linear matrix inequalities (LMIs), which can be solved efficiently via convex optimisation. Effectiveness of the proposed theoretical results is demonstrated through simulation studies. [ABSTRACT FROM AUTHOR]

We consider the problem of analysing and designing gradient-based discrete-time optimisation algorithms for a class of unconstrained optimisation problems having strongly convex objective functions with Lipschitz continuous gradient. By formulating the problem as a robustness analysis problem and making use of a suitable adaptation of the theory of integral quadratic constraints, we establish a framework that allows to analyse convergence rates and robustness properties of existing algorithms and enables the design of novel robust optimisation algorithms with prespecified guarantees capable of exploiting additional structure in the objective function. [ABSTRACT FROM AUTHOR]

Principal component active control is of great interest in recent times because of its extensive use in vibration and noise reduction applications. Existing analyses for such control systems mainly focus on simplified representations of the closed-loop system to obtain robust stability conditions, but they exclude key practical considerations, such as open-loop dynamics, periodic time-varying effects generated by the transformations between the time-domain harmonic signals and the estimation of their Fourier coefficients, multirate issues caused by the plant and the controller operating at different sampling rates, modeling errors, and particular ways of scaling the control actions. The contribution of this work is to include all the afore-mentioned effects to provide more accurate robustness conditions, which complement existing controller tuning procedures. The robustness analysis is conducted by first exploiting the time-lifting method to reformulate the linear-periodic-time-variant part of the discrete-time system into an equivalent linear-time-invariant representation. Then using the theoretical tool of integral quadratic constraints, standard forms of plant uncertainty and scaling of the control actions are incorporated. A vibration control example based on the Airbus EC-145 helicopter main rotor with On-Blade actuators is included to demonstrate the benefits of the contributions. The proposed design results are benchmarked against the mixed-sensitivity H∞ method, highlighting strengths, and weaknesses by each approach for this particular application. [ABSTRACT FROM AUTHOR]

This paper improves and implements a framework based on robustness analysis to aid in the certification of unmanned aircraft system (UAS) flight controllers. The approach first models the UAS using a linear fractional transformation on uncertainties and then conducts robustness analysis on the uncertain system via integral quadratic constraint (IQC) theory. By expressing the set of desired UAS flight paths with an uncertainty, the framework considers the analysis of the uncertain UAS flying about any level path whose radius of curvature is bounded. The approach is capable of analyzing trajectory-tracking and path-following controllers, and an accurate expression of UAS path-following dynamics in the presence of nonzero wind is derived. To demonstrate the versatility of this technique, we use IQC analysis to tune trajectory-tracking and path-following controllers that are designed via $\mathcal {H}_{2}$ or $\mathcal {H}_\infty $ synthesis methods. IQC analysis is also used to tune path-following PID controllers. By employing a nondeterministic simulation environment and conducting numerous flight tests, we see that the uncertain UAS framework reliably predicts loss of control, compares the robustness of different controllers, and provides tuned controllers that are sufficiently robust. Finally, this work demonstrates that signal IQCs have an important role in obtaining IQC analysis results that are less conservative and more consistent with observations from flight test data. [ABSTRACT FROM AUTHOR]

In the residual generator design problem, a method to ensure the residual’s fault sensitivity is to minimize the difference between the fault-to-residual response and a reference model. However, an inappropriate reference model with unattainable ratios between sensitivities from multiple faults can have a detrimental impact on disturbance decoupling performance. This impact is reduced in the proposed design method for uncertain linear parameter-varying systems by optimizing these sensitivity ratios. The synthesis method involves solving an induced- $\mathcal {L}_{2}$ robust estimator synthesis problem, in which parameter uncertainty is handled via integral quadratic constraints. Optimization of the sensitivity ratios is integrated into the ensuing a semidefinite program. The resulting residual generator synthesis method achieves perfect decoupling when this is possible, and more generally improves performance compared with when arbitrary references are used, without the precomputation of an attainable reference as seen in other approaches. The effectiveness of this method is demonstrated in a vehicle lateral dynamics application and validated using experimental data. [ABSTRACT FROM AUTHOR]

Two approaches to tackle the nonlinear robust stability problem of an aerospace system are compared. The first employs a combination of the describing function method and $\mu $ analysis, while the second makes use of integral quadratic constraints (IQCs). The model analyzed consists of an open-loop wing’s airfoil subject to freeplay and linear time-invariant parametric uncertainties. The key steps entailed by the application of the two methodologies and their main features are critically discussed. Emphasis is put on the available insight on the nonlinear postcritical behavior known as limit cycle oscillation. It is proposed a strategy to apply IQCs, typically used to find absolute stability certificates, in this scenario, based on a restricted sector bound condition for the nonlinearity. Another contribution of this paper is to understand how the conservatism usually associated with the IQCs multipliers selection can be overcome by using information coming from the first approach. Nonlinear time-domain simulations showcase the prowess of these approaches in estimating qualitative trends and quantitative response’s features. [ABSTRACT FROM AUTHOR]

A robust analysis framework for mathematical validation of flight control systems is presented. The framework is specifically developed for the complete uncertainty characterization, quantification, and analysis of small fixed-wing unmanned aircraft systems (UAS). The analytical approach presented within is based on integral quadratic constraint (IQC) analysis and uses linear fractional transformations on uncertainties to represent system models. While IQC analysis has a sound theoretical foundation, there remains a lack of literature on applying IQCs to complex engineering systems and evaluating their effectiveness with physical data. One difficulty lies in appropriately characterizing and quantifying the uncertainties such that the resulting uncertain model is representative of the physical system while forming a computationally tractable problem that is not overly conservative. This paper addresses these challenges by applying IQC analysis tools to analyze the robustness of a UAS flight control system. Uncertainties are characterized and quantified based on mathematical models and flight test data obtained in-house for a small commercial off-the-shelf platform with a custom autopilot. Furthermore, an established gradient-based minimization routine is implemented with IQC analysis to demonstrate how IQC analysis can guide the control design process. This approach also reveals the controlled system’s sensitivities to uncertainties, thereby assisting the designer in determining how much uncertainty allowance ought to exist in certain aspects of the UAS. Finally, these methods are tested in physical flight to showcase the effectiveness of IQC analysis and assess the conservativeness of the approach. The proposed framework is also transferable to other fixed-wing UAS platforms, effectively taking IQC analysis beyond academic examples to practical application in UAS system design, control design, and airworthiness certification. [ABSTRACT FROM AUTHOR]

Input delay is an important type of actuator nonlinearity in control systems. In this paper, we will address the output-feedback control synthesis problem for linear systems with time-varying input delay under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear output-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. By using quadratic Lyapunov functions incorporated with dynamic IQC multipliers, the resulting dynamic output-feedback delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. Moreover, the corresponding result on memoryless control is also derived for the case when the plant input-delay information is not available for feedback control. An application to network systems has been used to illustrate the effectiveness and usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the \mathcal L2 -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired \mathcal L2 -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies. [ABSTRACT FROM PUBLISHER]

SUMMARY Analogously to the existing μ-synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time-varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector-bounded and slope restricted nonlinearities or time-varying parametric uncertainties and uncertain time-varying time-delays, both with bounds on the rate-of-variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve-fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Synchrotrons are used to generate light for academic and industry research by accelerating electrons travelling in a circular path to relativistic speeds. In order to achieve optimum performance, electron beam stability is a crucial parameter for synchrotrons. This paper describes the design of a beam stabilisation controller, using Internal Model Control. Basis functions are used to identify the controllable components of the system and it is demonstrated how by selecting dynamics for each spatial mode, enhanced performance is achieved. The robust stability of the controller in the presence of spatial uncertainties is developed within an Integral Quadratic Constraint framework using two methods of spatial decomposition: Singular Value decomposition and Fourier decomposition. The controller has been implemented at Diamond Light Source, the UK׳s national synchrotron science facility. Results from the controller implementation are presented and it is demonstrated how the controller design and robust stability analysis are used to tradeoff performance and robustness. [Copyright &y& Elsevier]

A robust stability test for a class of constrained cross-directional controllers is found. Under special circumstances, the stability test is executed on a mode-by-mode basis and greatly simplified to a frequency-domain criterion. The test is also exploited to develop tuning algorithms. The control system involves a quadratic program embedded within an internal model control antiwindup structure and achieves optimal steady-state performance when the plant is known. Both the nonlinearity in the controller and the plant uncertainty satisfy certain integral quadratic inequalities. This allows us to obtain conditions for robust stability that can be expressed as linear matrix inequalities via the Kalman–Yakubovich–Popov lemma. [ABSTRACT FROM AUTHOR]

The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQC5 on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning. [ABSTRACT FROM AUTHOR]

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal gradient method and its variants, thereby generalizing gradient descent to a nonsmooth setup. In this paper, we view proximal algorithms as dynamical systems and leverage techniques from control theory to study their global properties. In particular, for problems with strongly convex objective functions, we utilize the theory of integral quadratic constraints to prove the global exponential stability of the equilibrium points of the differential equations that govern the evolution of proximal gradient and Douglas–Rachford splitting flows. In our analysis, we use the fact that these algorithms can be interpreted as variable-metric gradient methods on the suitable envelopes and exploit structural properties of the nonlinear terms that arise from the gradient of the smooth part of the objective function and the proximal operator associated with the nonsmooth regularizer. We also demonstrate that these envelopes can be obtained from the augmented Lagrangian associated with the original nonsmooth problem and establish conditions for global exponential convergence even in the absence of strong convexity. [ABSTRACT FROM AUTHOR]