| 1. |
- Helmersson, Anders, 1957-
(author)
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µ Synthesis and LFT Gain Scheduling with Real Uncertainties
- 1998
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In: International Journal of Robust and Nonlinear Control. - 1049-8923 .- 1099-1239. ; 8:7, s. 631-642
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Journal article (peer-reviewed)abstract
- This paper presents a solution to synthesis of gain scheduling controllers based on μ-analysis and linear fractional transformations (LFTs). The system is assumed to have parameter dependencies described by LFTs. The goal of the controller is, with real-time knowledge of the parameters, to provide disturbance and error attenuation. The paper treats both complex and real parametric dependencies. © 1998 John Wiley & Sons, Ltd.
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| 2. |
- Adib Yaghmaie, Farnaz, et al.
(author)
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Differential graphical games for H-infinity control of linear heterogeneous multiagent systems
- 2019
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In: International Journal of Robust and Nonlinear Control. - : WILEY. - 1049-8923 .- 1099-1239. ; 29:10, s. 2995-3013
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Journal article (peer-reviewed)abstract
- Differential graphical games have been introduced in the literature to solve state synchronization problem for linear homogeneous agents. When the agents are heterogeneous, the previous notion of graphical games cannot be used anymore and a new definition is required. In this paper, we define a novel concept of differential graphical games for linear heterogeneous agents subject to external unmodeled disturbances, which contain the previously introduced graphical game for homogeneous agents as a special case. Using our new formulation, we can solve both the output regulation and H-infinity output regulation problems. Our graphical game framework yields coupled Hamilton-Jacobi-Bellman equations, which are, in general, impossible to solve analytically. Therefore, we propose a new actor-critic algorithm to solve these coupled equations numerically in real time. Moreover, we find an explicit upper bound for the overall L2-gain of the output synchronization error with respect to disturbance. We demonstrate our developments by a simulation example.
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| 3. |
- Aguilar, Luis T., et al.
(author)
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Generating oscillations in inertia wheel pendulum via two-relay controller
- 2012
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In: International Journal of Robust and Nonlinear Control. - Malden : Wiley-Blackwell. - 1049-8923 .- 1099-1239. ; 22:3, s. 318-330
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Journal article (peer-reviewed)abstract
- The problem of generating oscillations of the inertia wheel pendulum is considered. We combine exact feedback linearization with two-relay controller, tuned using frequency-domain tools, such as computing the locus of a perturbed relay system. Explicit expressions for the parameters of the controller in terms of the desired frequency and amplitude are derived. Sufficient conditions for orbital asymptotic stability of the closed-loop system are obtained with the help of the Poincare map. Performance is validated via experiments. The approach can be easily applied for a minimum phase system, provided the behavior of the states of the zero dynamics is of no concern. Copyright (C) 2011 John Wiley & Sons, Ltd.
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| 4. |
- Alisic, Rijad, et al.
(author)
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Change time estimation uncertainty in nonlinear dynamical systems with applications to COVID-19
- 2022
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239.
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Journal article (peer-reviewed)abstract
- The impact that each individual non-pharmaceutical intervention (NPI) had on the spread rate of COVID-19 is difficult to estimate, since several NPIs were implemented in rapid succession in most countries. In this article, we analyze the detectability of sudden changes in a parameter of nonlinear dynamical systems, which could be used to represent NPIs or mutations of the virus, in the presence of measurement noise. Specifically, by taking an agnostic approach, we provide necessary conditions for when the best possible unbiased estimator is able to isolate the effect of a sudden change in a model parameter, by using the Hammersley–Chapman–Robbins (HCR) lower bound. Several simplifications to the calculation of the HCR lower bound are given, which depend on the amplitude of the sudden change and the dynamics of the system. We further define the concept of the most informative sample based on the largest (Formula presented.) distance between two output trajectories, which is a good indicator of when the HCR lower bound converges. These results are thereafter used to analyze the susceptible-infected-removed model. For instance, we show that performing analysis using the number of recovered/deceased, as opposed to the cumulative number of infected, may be an inferior signal to use since sudden changes are fundamentally more difficult to estimate and seem to require more samples. Finally, these results are verified by simulations and applied to real data from the spread of COVID-19 in France.
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| 5. |
- Amrr, Syed, et al.
(author)
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Event-driven fault-tolerant attitude control of spacecraft with finite-time disturbance observer under input saturation
- 2023
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In: International Journal of Robust and Nonlinear Control. - : WILEY. - 1049-8923 .- 1099-1239. ; 33:5, s. 3227-3246
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Journal article (peer-reviewed)abstract
- This paper investigates the attitude stabilization problem for a bandwidth-constrained spacecraft subjected to model uncertainty, external disturbances, actuator faults, and saturated input. The proposed attitude controller is developed by combining the disturbance observer with an event-trigger technique to provide disturbance attenuation meanwhile respecting the constraint on the wireless control network. The proposed disturbance observer estimates the lumped disturbance within a finite time, and its output is then fed to the composite control law. The presented control scheme relaxes the use of a priori upper bound knowledge of disturbance and resolves the unwinding problem in the quaternion-based attitude representation. The closed-loop stability analysis under the proposed algorithm shows the uniformly ultimately bounded convergence of state trajectories. Moreover, the designed event trigger approach avoids the Zeno behavior. The numerical simulation with comparative analysis illustrates the efficacy of the proposed controller in terms of convergence time, steady-state bound, rate of control update, and energy consumption.
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| 6. |
- Andersson, Viktor, 1995, et al.
(author)
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Controlled Descent Training
- 2024
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In: International Journal of Robust and Nonlinear Control. - 1099-1239 .- 1049-8923.
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Journal article (peer-reviewed)abstract
- In this work, a novel and model-based artificial neural network (ANN) training method is developed supported by optimal control theory. The method augments training labels in order to robustly guarantee training loss convergence and improve training convergence rate. Dynamic label augmentation is proposed within the framework of gradient descent training where the convergence of training loss is controlled. First, we capture the training behavior with the help of empirical Neural Tangent Kernels (NTK) and borrow tools from systems and control theory to analyze both the local and global training dynamics (e.g. stability, reachability). Second, we propose to dynamically alter the gradient descent training mechanism via fictitious labels as control inputs and an optimal state feedback policy. In this way, we enforce locally H2 optimal and convergent training behavior. The novel algorithm, Controlled Descent Training (CDT), guarantees local convergence. CDT unleashes new potentials in the analysis, interpretation, and design of ANN architectures. The applicability of the method is demonstrated on standard regression and classification problems.
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| 7. |
- Bemporad, Alberto, et al.
(author)
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Hybrid model predictive control based on wireless sensor feedback : An experimental study
- 2010
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 20:2, s. 209-225
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Journal article (peer-reviewed)abstract
- Design and experimental validation of model predictive control (MPC) of a hybrid dynamical laboratory process with wireless sensors is presented. The laboratory process consists of four infrared lamps, controlled in pairs by two on/off switches, and of a transport belt, where moving parts equipped with wireless sensors are heated by the lamps. The process, which is motivated by heating processes in the plastic and printing industry, presents interesting hybrid dynamics. By approximating the stationary heat spatial distribution as a piecewise affine function of the position along the belt, the resulting plant model is a hybrid dynamical system. The control architecture is based on the reference governor approach: the process is actuated by a local controller, while a hybrid MPC algorithm running on a remote base station sends optimal belt velocity setpoints and lamp on/off commands over a wireless link, exploiting the sensor information received through the wireless network. A discrete-time hybrid model of the process is used for the hybrid MPC algorithm and for the state estimator. The physical modelling of the process and the hybrid MPC algorithm are presented in detail, together with the hardware and software architectures. The experimental results show that the presented theoretical framework is well suited for control of the new laboratory process, and that the process can be used as a prototype system for evaluating hybrid and networked control strategies.
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| 8. |
- Boyd, Stephen, et al.
(author)
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MIMO PID Tuning via Iterated LMI Restriction
- 2015
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1099-1239 .- 1049-8923. ; 26:8, s. 1718-1731
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Journal article (peer-reviewed)abstract
- We formulate multi-input multi-output (MIMO) proportional-integral-derivative (PID) controller design as an optimization problem that involves nonconvex quadratic matrix inequalities. We propose a simple method that replaces the nonconvex matrix inequalities with a linear matrix inequality (LMI) restriction, and iterates to convergence. This method can be interpreted as a matrix extension of the convex-concave procedure, or as a particular majorization-minimization (MM) method. Convergence to a local minimum can be guaranteed. While we do not know that the resulting controller is globally optimal, the method works well in practice, and provides a simple automated method for tuning MIMO PID controllers. The method is readily extended in many ways, for example to the design of more complex, structured controllers.
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| 9. |
- Briat, Corentin
(author)
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Robust stability and stabilization of uncertain linear positive systems via integral linear constraints : L-1-gain and L-infinity-gain characterization
- 2013
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 23:17, s. 1932-1954
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Journal article (peer-reviewed)abstract
- Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L-1-gain and L-gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration.
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| 10. |
- Byrnes, Christopher I., et al.
(author)
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Interior point solutions of variational problems and global inverse function theorems
- 2007
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In: International Journal of Robust and Nonlinear Control. - : Wiley. - 1049-8923 .- 1099-1239. ; 17:5-6, s. 463-481
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Journal article (peer-reviewed)abstract
- Variational problems and the solvability of certain nonlinear equations have a long and rich history beginning with calculus and extending through the calculus of variations. In this paper, we are interested in 'well-connected' pairs of such problems which are not necessarily related by critical point considerations. We also study constrained problems of the kind which arise in mathematical programming. We are also interested in interior minimizing points for the variational problem and in the well-posedness (in the sense of Hadamard) of solvability of the related systems of equations. We first prove a general result which implies the existence of interior points and which also leads to the development of certain generalization of the Hadamard-type global inverse function theorem, along the theme that uniqueness quite often implies existence. This result is illustrated by proving the non-existence of shock waves for certain initial data for the vector Burgers' equation. The global inverse function theorem is also illustrated by a derivation of the existence of positive definite solutions of matrix Riccati equations without first analysing the nonlinear matrix Riccati differential equation. The main results on the existence of solutions to geometrically constrained well-connected pairs are then presented and illustrated by a geometric analysis of the existence of interior points for linear programming problems.
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