Sharif Digital Repository

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... 

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... 

The averaged switch modeling approach is a powerful method for representing the behavior of a wide variety of converters through equivalent circuits. The model is not linear and it is common to perform a small signal linearization about an operating point and design a linear controller. Models obtained with such method involve considerable approximation and produce results that are limited for high performance controller designs. In this paper a piecewise affine approximation technique is introduced for modeling PWM converters. This model is much more precise in predicting the dynamic response of averaged nonlinear model comparing the linear model. This paper also presents a piecewise linear... 

Recently, moment dual approach of sums of squares relaxations developed for polynomial optimization problems was successfully extended to optimization problems with polynomial matrix inequality constraints. In this paper, we first derive an efficient polynomial formulization for matrix rank minimization problem which does not add any slack variable or additional equality or inequality constraint. Using the aforementioned theory, then we propose a hierarchy of convex LMI relaxations to provide a sequence of increasingly tight lower bounds on the global minimum rank of an arbitrary matrix under linear and polynomial matrix inequality constraints. Surprisingly enough, these lower bounds are... 

An application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system is presented. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H∞controller subject to the H∞-norm of a frequency-weighted error between the approximated controller and the high-order H∞ controller is minimized. However, because solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with a nuclear-norm that can be reduced to a semidefinite program so that it can be solved efficiently. Application to the active... 

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... 

We present an application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H ∞ controller subject to the H∞ norm of a frequency-weighted error between the approximated controller and high-order H∞ controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a semidefinite program, so that it can be solved efficiently. Application to the active... 

This paper considers the problem of stabilizing a class of linear time-invariant large-scale systems composed of a number of subsystems using several local dynamic output feedback controllers. For this problem, a sufficient condition on each closed-loop individual subsystem is derived under which the decentralized controller composed of the local controllers designed for individual subsystems, achieves stability for the overall system. This condition is used to convert the decentralized stabilization problem to a set of the H∞ disturbance rejection subproblems  

This paper considers the problem of stabilizing a class of linear time-invariant large-scale systems composed of a number of subsystems using several local dynamic output feedback controllers. For this problem, a sufficient condition on each closed-loop individual subsystem is derived under which the decentralized controller composed of the local controllers designed for individual subsystems, achieves stability for the overall system. This condition is used to convert the decentralized stabilization problem to a set of the H∞ disturbance rejection subproblems  

This paper develops a stability and performance preserving controller order reduction method for linear time-invariant continuous-time single-input, single-output systems. In this method, the error between the complementary sensitivity functions of the nominal closed-loop system and closed-loop system using the reduced-order controller is converted to a frequency-weighted error between the Youla parameters of the full-order and reduced-order controllers and then the H∞norm of this error, subject to a set of linear matrix inequality constraints, is minimized. The main ideas of order reduction and stability preservation are contained in the constraints of the optimization problem. However,... 

H∞ controller order reduction with stability and performance preservation pose unique challenges to designers. In the paper, an approach for controller order reduction based on minimization of the rank of a matrix variable, subject to linear matrix inequality constraints, is presented. In this approach, the rank of a residue matrix of a high-order controller subject to the error between the loop gain of the closed-loop nominal system and the loop gain of the closed-loop system with the reduced order controller is minimized. However, since solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with the nuclear-norm that can be reduced to a... 

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...