Eduardo N. Gonçalves

New Approach to Robust

This note presents a new approach to robust D-stability analysis of linear time-invariant systems with polytope-bounded uncertainty. The proposed approach combines sufficient conditions for robust D-stability in terms of feasibility problems with linear matrix inequalities (LMI) constraints and a new polytope partition technique. If the initial polytope does not attain the robust D- stability sufficient condition, the polytope is successively subdivided until all subpolytopes attain the sufficient condition, in the case of robustly D-stable uncertain system, or it is found a subpolytope vertex that does not attain the regional pole-placement constraints, in the case of an uncertain system that is not robustly D-stable. It is presented a new general format polytope partition technique that allows the implementation of the proposed approach. The efficiency of the proposed approach is verified by means of illustrative examples and three different LMI-based analysis formulations

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In this paper, a new robust stability analysis approach is developed for uncertain discrete-time linear time-invariant systems with polytopic or affine parameter-dependent uncertainty models. The proposed approach is based on a combination of a branch-and-bound like strategy with linear matrix inequality (LMI) based analysis formulations. Two sufficient conditions are considered, one for the robust stability of the uncertain system and other one for the contrary situation. If both sufficient conditions fail to characterize the polytope, then it is iteratively subdivided into subpolytopes until some one proves to be unstable or all ones are verified to be robustly stable. The polytope subdivision is implemented by means of a specially developed simplex subdivision algorithm. Exhaustive numerical tests prove the efficiency of the proposed approach when compared with the most recent LMI-based formulations.

-Stability Analysis of Linear Time-Invariant Systems With Polytope-Bounded Uncertainty

This article presents a simple efficient algorithm for the subdivision of a <i>d</i>-dimensional simplex in <i>k</i>^<i>d</i> simplices, where <i>k</i> is any positive integer number. The algorithm is an extension of Freudenthals subdivision method. The proposed algorithm deals with the more general case of <i>k</i>^<i>d</i> subdivision, and is considerably simpler than the <i>RedRefinementND</i> algorithm for implementation of Freudenthals strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.

New strategy for robust stability analysis of discrete-time uncertain systems

This article presents a new approach for or robust model reduction for uncertain systems based on an optimisation algorithm applied directly in the space of reduced-order model parameters. The proposed approach can be applied to both polytopic or affine parameter-dependent models as well as for continuous or discrete-time systems.The developed procedure is capable of computing both fixed reduced-order model as well as uncertain reduced-order model keeping the original uncertainty structure. The resulting reduced-order model is guaranteed to be robust stable.

Algorithm 860: SimpleS—an extension of Freudenthal's simplex subdivision

This article presents a new strategy to design robust model matching dynamic output-feedback controllers that guarantee tracking response specifications, disturbance rejection and noise attenuation. The proposed synthesis methodology, based on a multi-objective optimisation problem, can be applied to uncertain continuous or discrete-time linear time-invariant systems with polytopic uncertainty, leading to both full-order and reduced-order robust-performance dynamic controllers. The objective functions represent the ℋ∞-norm of the difference between the closed-loop transfer function matrix, from the reference signals and the plant outputs and the reference model matrix, the ℋ∞-norm of the closed-loop transfer function matrix from the disturbances and the plant outputs and the ℋ2-norm of the closed-loop transfer function matrix from the measurement noises and the control inputs. An integral control action is also introduced in order to achieve zero steady-state error. In the case of MIMO systems, the proposed strategy can be applied to decouple the closed-loop control system choosing an appropriated reference model matrix. Two examples are presented to illustrate both SISO and MIMO systems control synthesis.

Robust model reduction of uncertain systems maintaining uncertainty structure

International Standards ANSI C84.1-2006 and IEEE std 1250-1995 specify the range of supply voltage to electronics equipment from 0.9 to 1.05 per-unit (pu) of nominal voltage. From this information, it is possible to feed electronics equipment with a voltage level below of nominal voltage without failures. The Conservation Voltage Reduction (CVR) is a technique that aims to achieve the reduction of power consumption by reducing the level of supply voltage, giving at the customer location a lowest possible level of voltage compatible with both nominal values of equipment and the levels stipulated by the regulatory agency. It is essential obtaining a good model that describes the behavior of the loads connected to grid to evaluate the effectiveness of the CVR application. This paper presents an evaluation of three static load model techniques, being two ZIP load models and an exponential model. The model parameters were estimated for samples obtained from measurements performed on residential/commercial loads, through the variation of supply voltage within the operational acceptable range. The data collection was performed at three different periods of times to mitigate the grids influence on the results. The load models are obtained through an optimization algorithm based on the collected data. The ellipsoidal optimization algorithm was applied to estimate the parameters of each model, searching for the best feasible solution. Some papers in the literature exhibit mathematical solutions for load models without physical meaning. Unlike that, this algorithm is not limited only to find a mathematical solution but also a physical one.

Robust ℋ2/ℋ∞/reference model dynamic output-feedback control synthesis

This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞guaranteed cost of time-delay continuous-time linear time-invariant systems subjected to polytopic uncertainties. The proposed analysis approach is based on a branch-and-bound algorithm that incorporates a recent LMI-based analysis formulation and a new polytope partition strategy. In the branch-and-bound algorithm, the upper bound function is defined as the worst case guaranteed H∞disturbance attention level computed for the subpolytopes achieved with successive partitions of the polytope which describes the uncertainty domain. The lower bound function is defined as the worst case H∞norm computed in the polytope and subpolytope vertices. The difference between the upper and lower bound functions converges to zero as the initial polytope is split into smaller subpolytopes resulting in the H∞guaranteed cost for the whole initial polytope with the required accuracy. It is also presented an algorithm to implement a d−dimensional simplex subdivision technique to be used in the branch-and-bound algorithm.

Comparison between static models of commercial/residential loads and their effects on Conservation Voltage Reduction

This paper presents a computational tool intended to calculate and minimize the electric fields at ground level of high surge impedance loading transmission lines (TLs). This type of TL achieves higher power transmission rates utilizing optimized configuration for the phase conductors. This method is advantageous over other actions taken by the utility company, such as increasing the maximum operation temperature of the line, increasing the size of the conductors, or the utilization of multiple conductors per phase. In this paper, an enhanced deep-cut ellipsoidal method is applied to find a new optimized configuration for the phase conductors. The new proposed configuration results in reduced profiles of electric fields. Two different TLs are analyzed and optimized.

H &#8734; Guaranteed Cost Computation for Uncertain Time-Delay Systems

This work presents a mono-objective optimization for a Yagi-Uda antenna applying the ellipsoid algorithm. For problems which the objective function is not known, like function that represents the Yagi-Uda antenna behavior, the ellipsoid algorithm has some features that make it more interesting compared to other optimization methods. To obtain antenna electromagnetic characteristics it is used the electric field integral equation (Pocklington integral equation) numerically evaluated by the Method of Moments (MoM). The ellipsoid optimization leads to antenna geometry with superior directivity than those presented in the available literature.

An Adaptive Deep-Cut Ellipsoidal Algorithm Applied to the Optimization of Transmission Lines

Abstract This paper deals with the output tracking control problem for nonlinear networked control systems (NCSs) described by Takagi-Sugeno (T-S) fuzzy models. Due to the existence of inherent constraints in NCS as communication time-delays and limitation of data transmission capacity, a recent event-triggered scheme proposed in the literature is implemented to reduce the bandwidth utilization. On the other hand, the communication time-delay imposes an asynchronously operation between the proposed T-S fuzzy controller and the T-S fuzzy system handled via new LMI based conditions. Furthermore, a synchronous model operation is also proposed in this paper which allows to design a linear controller which is much simpler to implement. The main results are derived following the selection of an appropriate fuzzy Lyapunov Krasovskii Functional (LKF) together with alternative integral inequalities which lead to less conservative conditions when compared to recent results in the literature. An example illustrates the effectiveness of the proposed output tracking control for NCSs fuzzy models.