Sharif Digital Repository

This brief presents a systematic approach for the design of sparse dynamic output feedback control structures. A supplementary complexity cost function term is used to promote sparsity in the structure while optimizing an H2 performance cost simultaneously. Optimization problems in which a combinatorial sparsity measure is combined with a nonlinear performance cost function are NP-hard. NP-hard problems do not have tractable solutions, requiring either a numerical solution or a relaxation into a solvable form. Relaxations will introduce conservatism, but at the same time retain stability and performance guarantees. In this brief, a new relaxation methodology is proposed, which allows the... 

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... 

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 optimal trade-off between control structures and achievable closed-loop performance is addressed. Incorporation of sparsity promoting regularization terms to the primary objective function is a well-suited approach in feature selection and compressed sensing. By the evolving role of distributed and large-scale applications, modern optimal control problems have been equipped with regularization tools as well. However, the system dynamics and convex/nonconvex constraints in optimal control framework limits the effectiveness and applicability of regularization, enforce iterative or non-convex heuristics, and pose extensive exploration. In fact, available regularized feedback... 

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 vulnerability of large-dimensional dynamic networks to false data injections is analysed. The malicious data can manipulate input injection at the control nodes and affect the outputs of the network. The objective is to analyse and quantify the potential vulnerability of the dynamics by such adversarial inputs when the opponents try to avoid being detected as much as possible. A joint set of most effective actuation nodes and most vulnerable target nodes are introduced with minimal detectability by the monitoring system. Detection of this joint set of actuation-target nodes is carried out by introducing a Gramian-based measure and reformulating the vulnerability problem as... 

In this study, an inventory system consisting of a single product, one supplier, and multiple identical retailers is considered. Each retailer replenishes inventory from the supplier according to the well known (R,Q) policy. Transit times are constant and retailers face independent Poisson demand. The supplier utilizing the retailers' information in decision making for replenishment policy with a given order size starts with m initial batches (of size Q) and places an order in a batch of size Q to an outside source when a new order is placed. In this inventory system, excess demand is backordered, delayed orders are satisfied on a first-come first-serve basis, and no partial shipment is... 

In this paper, a continuous review inventory system is considered in which an order in a batch of size Q is placed immediately after the inventory position reaches R. Transportation time is constant and demands are assumed to be generated by a stationary Poisson process with one unit demand at a time. Demands not covered immediately from the inventory are backordered. In a recent paper, the exact evaluation of batch-ordering policies for two-level inventory systems was derived. This evaluation is based on a recursive procedure for determining the exact policy costs in case of one-for-one replenishment policies. In this paper, we show how this result can be applied to find the optimal... 

This paper presents a robust control scheme for an islanded microgrid in the presence of structured uncertainties. The microgrid consists of parallel connection of two Distributed Generation (DG) units and a passive load. The DG units are connected to the passive load by using the power electronics converters. The microgrid model is structurally uncertain due to the large perturbations in the load parameters. To deal with the uncertainties, a Linear Fractional Representation (LFR) of the parametrically uncertain system is obtained. To achieve robust performance, the μ-synthesis approach is applied to the derived LFR model to design a μ controller. The resultant controller is structurally... 

This paper presents a new robust control strategy for an islanded microgrid in the presence of load unmodeled dynamics. The microgrid consists of parallel connection of several electronically interfaced distributed generation units and a local load. The load is parametrically uncertain and topologically unknown and, thus, is the source of unmodeled dynamics. The objective is to design a robust controller to regulate the load voltage in the presence of unmodeled dynamics. To achieve the objective, the problem is first characterized by a two-degree-of-freedom (2DOF) feedback-feedforward controller. The 2DOF control design problem is then transformed to a nonconvex optimization problem.... 

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... 

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  

This paper presents a new robust control strategy for islanded operation of a microgrid consisting of several distributed generation (DG) units with arbitrary topology. Each DG unit is connected to its local load through a voltage-source converter, a series RL filter and a step-up transformer. The multi-DG microgrid with arbitrary connectivity graph is modeled as a linear time-invariant system subject to a parametric, norm-bounded uncertain block. By utilizing the developed model for multi-DG microgrids, a systematic approach for the design of structured dynamic output feedback control is proposed. A convex optimization problem is developed which yields a low-order dynamic controller of... 

A globally convergent algorithm for synthesis of sparse optimal state feedback (SOSF) control of linear time-invariant (LTI) systems is proposed. This problem is known to be NP-hard due to its combinatorial nature. A structured H2 norm controller design problem is intrinsically non-convex, even if a fixed structure is known in advance. The proposed algorithm minimizes the H2 norm performance index, simultaneously regularizes the sparsity of the control structure using the norm. It guarantees that the solution converges to a stationary point of the original problem. The algorithm is implemented using Linear Matrix Inequalities (LMIs) which are efficient, reliable and extendable to other... 

This paper presents a new robust control strategy for islanded operation of a microgrid consisting of several distributed generation (DG) units with arbitrary topology. Each DG unit is connected to its local load through a voltage-source converter (VSC), a series RL filter and a step-up transformer. The multi-DG microgrid with arbitrary connectivity graph is modeled as a linear time-invariant (LTI) system subject to a parametric, norm-bounded uncertain block. By utilizing the developed model for multi-DG microgrids, a systematic approach for the design of structured dynamic output feedback control is proposed. A convex optimization problem is developed which yields a low-order dynamic... 

Optimal control frameworks are very important in optimization of multiple-arm robotic systems, although complexity, non-linearity and having large scales usually cause some computational problems in the capacity and time needed. In this paper, coordination of multiple-arm robotic systems in order to carry a rigid object is considered and the state space equations for the overall system are developed. Coordination of the robot arms is done through minimizing a related cost function based on the gradient method. This method is simple and easy to be used  

In this article, optimal control of bilinear positive systems with uncertain evolutionary dynamics is studied. The first objective is to determine optimal control signals such that the effect of the disturbance signals on the outputs of the nominal dynamics is minimized in terms of the H2 norm performance index. Properties of the positive systems, Metzler matrices, and the exploitable structure of the problem are utilized to show that the underlying problem is representable as a standard convex optimization problem. Next, the optimal strategy is examined in the presence of polytopic uncertainties. In this case, the optimization problem is a semi-infinite min-max problem. It is shown that...