Sharif Digital Repository

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... 

In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure... 

In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure... 

Industrial processes are inherently nonlinear with input, state, and output constraints. A proper control system should handle these challenging control problems over a large operating region. The robust model predictive controller (RMPC) could be an linear matrix inequality (LMI)-based method that estimates stability region of the closed-loop system as an ellipsoid. This presentation, however, restricts confident application of the controller on systems with large operating regions. In this paper, a dual-mode control strategy is employed to enlarge the stability region in first place and then, trajectory reversing method (TRM) is employed to approximate the stability region more accurately.... 

In this study, an auxiliary damping controller based on a robust controller considering the active and reactive power control loops for a doubly-fed induction generator for wind farms is proposed. The presented controller is able to improve the inter-area oscillation damping. In addition, the proposed controller applies only one accessible local signal as the input; however, it can improve the inter-area oscillation damping and, consequently the system stability for the various working conditions and uncertainties. The oscillatory modes of the system are appointed using the linear analysis. Then, the controller’s parameters are determined using the robust control approaches (H∞/ H2) with the... 

This paper introduces a new methodology for the design of fixed-order multi-objective output feedback controllers. The problem comprises a set of linear matrix inequalities and an additional rank constraint. The primary idea is to classify convex subsets of the set of rank constrained matrices in such formulations, based on which two noniterative and relatively fast methods are developed. The proposed methods require solving a convex optimization problem at each step and can be applied with any weighted summation of design objectives such as (Formula presented.) performance, (Formula presented.) performance, passivity, and regional pole assignment. Several benchmark systems with performance... 

This paper considers the problem of high-performance global stabilization of an integrator chain via a bounded control at the presence of input disturbance. While nested saturated feedback (NSF) is known as the most inspiring existing solution in the literature, we shall highlight the inherent shortcomings of this approach which cause a poor performance in terms of convergence rate. Then, a novel dual-mode control scheme combining an improved NSF law with a linear matrix inequality (LMI)-based model predictive controller (MPC) is developed to overcome the weaknesses of pure NSF. By offline calculations, a set of nested robust invariant attraction regions and their attributed feedback gains... 

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... 

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... 

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... 

This paper presents a new framework for the optimal placement of actuators in uncertain dynamic networks. The objective is to select a subset of nodes from a set of potential actuator placements, such that the controllability of the network with norm-bounded perturbation is preserved over the entire uncertain region. Evaluation of robust controllability is known to be computationally intractable. The recent results of Babazadeh and Nobakhti (2016) are utilized to establish equivalent conditions for robust controllability of uncertain networks. It is shown that for a large class of dynamic systems, including undirected networks, the exact distance to uncontrollability is evaluated by solving... 

This paper deals with the stabilization of the feasible equilibrium point of a special class of nonlinear quadratic systems known as Lotka-Volterra (LV) systems, in the presence of interval uncertainty via a fixed linear state feedback (FLSF). It is well known that for a linear time-invariant system with interval uncertainty, stability at the vertices of a polytope implies stability in the interior of the whole polytope. It has been shown that this idea can be extended to examine the stability of LV systems in the presence of interval uncertainty, recently. In fact, it has been proved that in spite of nonlinear nature of the system, stability at a special vertex guarantees stability at all... 

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... 

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... 

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... 

In this paper, a decentralized model predictive control approach is proposed for discrete linear systems with a high number of inputs and states. The system is decomposed into several interacting subsystems. The interaction among subsystems is modeled as external disturbances. Then, using the concept of robust positively invariant ellipsoids, a robust model predictive control law is obtained for each subsystem solving several linear matrix inequalities. Maintaining the recursive feasibility while considering the attenuation of mutual coupling at each time step and the stability of the overall system are investigated. Moreover, an illustrative simulation example is provided to demonstrate the... 

This paper presents a novel fault-tolerant control strategy to compensate the time-varying loss of actuators’ effectiveness. It considers intermediate situations where the fault is not determined precisely (unlike active approaches) but overall estimations about its rate and final value are available through the previous experiences and/or experiments. Based on the estimations, two upper and lower time-varying bounds on the actuators’ effectiveness are established to be exploited in the procedure of controller design. In a special case, where these bounds are constant, the method will be reduced to the conventional passive approach. Also, actuator saturation and the effects of (Formula... 

The aim of this study is to reduce the computational load in model predictive control of multi-input nonlinear systems. First, the nonlinear system which has a high number of states and inputs is decomposed into several subsystems by solving a linear integer programming problem offline. Then, the model of each subsystem is revised by considering the effect of coupling and interactions of other subsystems. Next, the robust model predictive technique based on linear matrix inequalities is employed to compute control signal for each subsystem. An industrial chemical reaction example is used to illustrate the effectiveness of the proposed method. © 2017 IEEE  

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... 

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...