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linear-matrix-inequality
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Hybrid Control of an Unmanned Helicopter System Maneuver
, M.Sc. Thesis Sharif University of Technology ; Salarieh, Hassan (Supervisor)
Abstract
As a subset of hybrid systems, piecewise affine (PWA) systems are capable of approximating the behavior of a wide range of nonlinear systems. Considering the preliminaries regarding these systems and the vast literature gathered around them, the main contributions of the current study are presented in two separate sections. In the first section a class of uncertain piecewise affine systems subject to additive noise are studied. The problem of minimizing the bound on the variance of the steady response of these systems, by means of a piecewise affine observer-controller, is formulated as an optimization problem subject to a number of constraints in the form of matrix inequalities. Then the...
Computational Load Reduction in Model Predictive Control of Multi-Input Nonlinear Systems
, Ph.D. Dissertation Sharif University of Technology ; Haeri, Mohammad (Supervisor)
Abstract
In this thesis, computational load reduction in linear matrix inequality based model predictive control for nonlinear multi-input systems is studied. The main idea is decomposing the system into several smaller interacting subsystems and computing each control input separately. The main challenge is how to consider the effects of interactions among subsystems in the control design. Three approaches are investigated in this thesis. In the first approach, a static approximation of the effects of other subsystems is augmented in the local model of each subsystem, to improve the closed loop performance than fully decentralized methods. In the second approach, considering the mutual interactions...
Non-fragile Static Output Feedback Control with Sparse Gain Matrix
, M.Sc. Thesis Sharif University of Technology ; Tavazoei, Mohammad Saleh (Supervisor) ; Nobakhti, Amin (Supervisor)
Abstract
One of the issues in the design and synthesis of the state or output feedback controller is the issue of fragility as the existence of disturbance in the coefficients of the designed controller causes instability in the controlled closed-loop system or leads to deterioration of its performance. The need to consider this point results in some novel approaches for designing the non-fragile controllers. Accordingly, defining criteria for measuring fragility is crucial.As well, due to the considered practical problems in the implementation of ordinary designed robust and optimal controllers, non-reachability of all the states of dynamical systems, and the boundedness for the quantity of the...
Stochastic piecewise affine control with application to pitch control of helicopter
, Article Nonlinear Analysis: Hybrid Systems ; Vol. 15 , 2015 , pp. 86-97 ; ISSN: 1751570X ; Salarieh, H ; Alasty, A ; Meghdari, A ; Sharif University of Technology
Abstract
In this paper, at first the stability condition which gives an upper stochastic bound for a class of Stochastic Hybrid Systems (SHS) with deterministic jumps is derived. Here, additive noise signals are considered that do not vanish at equilibrium points. The presented theorem gives an upper bound for the second stochastic moment or variance of the system trajectories. Then, the linear case of SHS is investigated to show the application of the theorem. For the linear case of such stochastic hybrid systems, the stability criterion is obtained in terms of Linear Matrix Inequality (LMI) and an upper bound on state covariance is obtained for them. Then utilizing the stability theorem, an output...
On the stability issues for fuzzy large-scale systems
, Article Fuzzy Sets and Systems ; Volume 174, Issue 1 , July , 2011 , Pages 31-49 ; 01650114 (ISSN) ; Sadati, N ; Zarif, M. H ; Sharif University of Technology
2011
Abstract
The main objective of this paper is to investigate the stability and stabilization problem of fuzzy large-scale systems in which the system is composed of a number of Takagi-Sugeno fuzzy subsystems with interconnection. Instead of fuzzy parallel distributed compensation (PDC) design, nonlinear state feedback controllers are used in stabilization of the overall large-scale system. Based on Lyapunov stability theory, linear matrix inequalities (LMIs) conditions are derived for asymptotic and exponential stability. Two numerical examples are given to confirm the analytical results and illustrate the effectiveness of the proposed strategy
Direct synthesis of fixed-order h∞ controllers
, Article IEEE Transactions on Automatic Control ; Volume 60, Issue 10 , July , 2015 , Pages 2704-2709 ; 00189286 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
This technical note considers the fixed-order H∞ output feedback control design problem for linear time invariant (LTI)systems. The objective is to design a fixed-order controller with guaranteed stability and closed-loop H∞ performance. This problem is NP-hard due to the non-convex rank constraint which appears in the formulation. We propose an algorithm for non-iterative direct synthesis (NODS) of reduced order robust controllers. NODS entails initial computation of two positive-definite matrices via full-order convex LMI conditions. These are then utilized by appropriate eigenvalue decomposition to directly obtain a suboptimal convex formulation for the fixed-order controller
Stochastic piecewise affine control with application to pitch control of helicopter
, Article Nonlinear Analysis: Hybrid Systems ; Volume 15 , February , 2015 , Pages 86-97 ; 1751570X (ISSN) ; Salarieh, H ; Alasty, A ; Meghdari, A ; Sharif University of Technology
Elsevier Ltd
2015
Abstract
In this paper, at first the stability condition which gives an upper stochastic bound for a class of Stochastic Hybrid Systems (SHS) with deterministic jumps is derived. Here, additive noise signals are considered that do not vanish at equilibrium points. The presented theorem gives an upper bound for the second stochastic moment or variance of the system trajectories. Then, the linear case of SHS is investigated to show the application of the theorem. For the linear case of such stochastic hybrid systems, the stability criterion is obtained in terms of Linear Matrix Inequality (LMI) and an upper bound on state covariance is obtained for them. Then utilizing the stability theorem, an output...
LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties
, Article Transactions of the Institute of Measurement and Control ; Volume 37, Issue 10 , 2015 , Pages 1207-1216 ; 01423312 (ISSN) ; Abooee, A ; Haeri, M ; Sharif University of Technology
SAGE Publications Ltd
2015
Abstract
In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order α is a known constant belonging to 0 < α < 1. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and...
Integrated guidance and control of elastic flight vehicle based on robust MPC
, Article International Journal of Robust and Nonlinear Control ; Volume 25, Issue 15 , 2015 , Pages 2608-2630 ; 10498923 (ISSN) ; Nikravesh, S. K. Y ; Haeri, M ; Sharif University of Technology
John Wiley and Sons Ltd
2015
Abstract
Integrated guidance and control of an elastic flight vehicle based on constrained robust model predictive control is proposed. The design is based on a partial state feedback control law that minimizes a cost function within the framework of linear matrix inequalities. It is shown that the solution of the defined optimization problem stabilizes the nonlinear plant. Nonlinear kinematics and dynamics are taken into account, and internal stability of the closed-loop nonlinear system is guaranteed. The performance and effectiveness of the proposed integrated guidance and control against non-maneuvering and weaving targets are evaluated using computer simulations
Robust controllability assessment via semi-definite programming
, Article Systems and Control Letters ; Volume 98 , 2016 , Pages 1-7 ; 01676911 (ISSN) ; Nobakhti, A ; Sharif University of Technology
Elsevier B.V
2016
Abstract
This paper presents a new framework for systematic assessment of the controllability of uncertain linear time-invariant (LTI) systems. The objective is to evaluate controllability of an uncertain system with norm-bounded perturbation over the entire uncertain region. The method is based on a singular-value minimization problem, over the entire complex plane. To solve the problem, first, a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane, and to verify the controllability of directed and undirected networks in a single step. Secondly, the results are utilized to formulate the problem as two Lyapunov-based linear matrix inequalities...
Hybrid control of the dc-dc SRC operating below resonance
, Article IET Power Electronics ; Volume 10, Issue 1 , 2017 , Pages 1-9 ; 17554535 (ISSN) ; Tahami, F ; Molla Ahmadian, H ; Sharif University of Technology
Institution of Engineering and Technology
2017
Abstract
Control and stabilisation of the resonant converters are essential problems in power electronics. The conventional model of the dc-dc series resonant converter (SRC) is derived using the sinusoidal approximation and generalised averaging followed by linearisation about an operating point. This model involves considerable approximation and is not applicable for large variation of load and supply voltage. The authors have already proposed a direct piece-wise affine (DPWA) modelling and control approach for the SRC that operates above resonant frequency. However, the DPWA technique is not applicable to an SRC that operates below resonance because of the presence of harmonics. In this study, a...
Modeling and solving a sustainable closed loop supply chain problem with pricing decisions and discounts on returned products
, Article Journal of Cleaner Production ; Volume 207 , 2019 , Pages 163-181 ; 09596526 (ISSN) ; Haghighi, F ; Akhavan Niaki, S. T ; Sharif University of Technology
Elsevier Ltd
2019
Abstract
Increasing rates of environmental and social concerns involved in various communities have recently attracted researchers’ attention to consider them in proper designs of sustainable supply chains (SSCs). In this paper, the planning problem of a multi-period multi-echelon sustainable closed loop supply chain (SCLSC) is investigated. A comprehensive model that seriously takes into account the social and environmental aspects of the supply chain (SC) decisions and measures their social and environmental effects using the GRI (Global Reporting Initiative) guideline indicators is proposed. The proposed planning model includes tactical decisions comprising the price of the product and logistic...
Voltage regulation of DC-DC series resonant converter operating in discontinuous conduction mode: The hybrid control approach
, Article International Journal of Engineering, Transactions B: Applications ; Volume 32, Issue 11 , 2019 , Pages 1610-1619 ; 1728144X (ISSN) ; Tahami, F ; Sharif University of Technology
Materials and Energy Research Center
2019
Abstract
Dynamic modeling and control of DC-DC series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely continuous dynamics based on the sinusoidal approximation and averaging. However, an SRC may be purposely designed to operate in DCM so the sinusoidal approximation is no longer acceptable. Therefore, it is essential to analyze the stability using a more sophisticated model. This paper presents a novel...
Voltage regulation of DC-DC series resonant converter operating in discontinuous conduction mode: the hybrid control approach
, Article International Journal of Engineering, Transactions B: Applications ; Volume 32, Issue 11 , 2019 , Pages 1610-1619 ; 1728144X (ISSN) ; Tahami, F ; Sharif University of Technology
Materials and Energy Research Center
2019
Abstract
Dynamic modeling and control of DC-DC series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely continuous dynamics based on the sinusoidal approximation and averaging. However, an SRC may be purposely designed to operate in DCM so the sinusoidal approximation is no longer acceptable. Therefore, it is essential to analyze the stability using a more sophisticated model. This paper presents a novel...
LMI-based cooperative distributed model predictive control for Lipschitz nonlinear systems
, Article Optimal Control Applications and Methods ; Volume 41, Issue 2 , 2020 , Pages 487-498 ; Haeri, M ; Sharif University of Technology
John Wiley and Sons Ltd
2020
Abstract
In this paper, a distributed model predictive control is proposed to control Lipschitz nonlinear systems. The cooperative distributed scheme is considered where a global infinite horizon objective function is optimized for each subsystem, exploiting the state and input information of other subsystems. Thus, each control law is obtained separately as a state feedback of all system's states by solving a set of linear matrix inequalities. Due to convexity of the design, convergence properties at each iteration are established. Additionally, the proposed algorithm is modified to optimize only one control input at a time, which leads to a further reduction in the computation load. Finally, two...
Global stabilization of uncertain lotka-volterra systems via positive nonlinear state feedback
, Article IEEE Transactions on Automatic Control ; Volume 65, Issue 12 , 2020 , Pages 5450-5455 ; Tavazoei, M. S ; Yazdanpanah, M. J ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020
Abstract
This article deals with stabilization of Lotka-Volterra (LV) systems in the presence of interval uncertainty and a physical limitation on the control input, which restricts this input to be strictly positive. Considering the positiveness property of LV systems, a quasi-monomial structure for the state feedback based control input is proposed. Considering this structure, stability of the closed-loop system with no uncertainty is analyzed. This analysis leads to an algebraic inequality, whose satisfaction guarantees stability of the closed-loop system. To extend this result to uncertain LV systems with interval parameter uncertainty, a new approach, by which stability of the positive...
Eigenvectors of deformed Wigner random matrices
, Article IEEE Transactions on Information Theory ; 18 November , 2020 ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020
Abstract
We investigate eigenvectors of rank-one deformations of random matrices B = A + θuu* in which A ∈ RN×N is a Wigner real symmetric random matrix, θ ∈ R+, and u is uniformly distributed on the unit sphere. It is well known that for θ > 1 the eigenvector associated with the largest eigenvalue of B closely estimates u asymptotically, while for θ < 1 the eigenvectors of B are uninformative about u. We examine O(1/N) correlation of eigenvectors with u before phase transition and show that eigenvectors with larger eigenvalue exhibit stronger alignment with deforming vector through an explicit inverse law 1/θ*-x with θ* := θ + 1/θ. This distribution function will be shown to be the ordinary...
Robust H∞ control design for PFC rectifiers
, Article 7th International Conference on Power Electronics and Drive Systems, PEDS 2007, Bangkok, 27 November 2007 through 30 November 2007 ; 2007 , Pages 948-952 ; 1424406455 (ISBN); 9781424406456 (ISBN) ; Molla Ahmadian, H ; Moallem, A ; Sharif University of Technology
2007
Abstract
Power factor correction (PFC) converter circuits are non-linear system due to the contribution of their multiplier. This non-linearity reflects the difficulty of analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. Our goal is to design a controller that achieves some performance specifications despite these uncertainties in modeling. This paper addresses a robust H∞ control problem for switched circuits with parameter uncertainties. The necessary and sufficient conditions for existence of strong robust H∞ dynamic compensators and static output feedback controllers are...
Model-free LQR design by Q-function learning
, Article Automatica ; Volume 137 , 2022 ; 00051098 (ISSN) ; Babazadeh, M ; Sharif University of Technology
Elsevier Ltd
2022
Abstract
Reinforcement learning methods such as Q-learning have shown promising results in the model-free design of linear quadratic regulator (LQR) controllers for linear time-invariant (LTI) systems. However, challenges such as sample-efficiency, sensitivity to hyper-parameters, and compatibility with classical control paradigms limit the integration of such algorithms in critical control applications. This paper aims to take some steps towards bridging the well-known classical control requirements and learning algorithms by using optimization frameworks and properties of conic constraints. Accordingly, a new off-policy model-free approach is proposed for learning the Q-function and designing the...