Aleksandar I. Zecevic

Control of Large-Scale Systems: Beyond Decentralized Feedback

In this paper, we present an array of new results that are aimed at broadening the scope of control design under information structure constraints. Both structural and algebraic enhancements of decentralized feedback will be considered, with convex optimization as a common mathematical framework. This approach leads to computationally efficient design strategies that are well suited for large-scale applications. In all cases, the obtained feedback laws guarantee robustness with respect to a wide range of nonlinear uncertainties, both within the subsystems and in the interconnections.

Design of robust static output feedback for large-scale systems

The design of static output feedback is of fundamental importance in control theory. In this note, we propose a new approach to this problem, based on linear matrix inequalities. A distinguishing feature of the method is its ability to handle large-scale problems with additive nonlinearities. The resulting control is robust with respect to uncertainties, and can incorporate several types of information structure constraints. The effectiveness of the proposed strategy is demonstrated by application to a practical large-scale system.

Robust decentralized exciter control with linear feedback

A new strategy is developed for the design of robust decentralized exciter control in power systems. The method is computationally attractive and the resulting feedback is linear, which allows for easy implementation. Experiments on the IEEE 39 bus system demonstrate that such a control is robust with respect to the fault location and to variations in the system operating point.

A new approach to control design with overlapping information structure constraints

In this paper, a new strategy is proposed for decentralized state feedback design with overlapping information structure constraints. The method combines linear matrix inequalities and the inclusion principle in a way that eliminates controllability problems that are inherent to standard decentralized control design in the expanded space. This approach can be extended to include an important class of uncertain nonlinearities, and its validity is demonstrated through applications to strings of moving vehicles.

Brief paper: Control design with arbitrary information structure constraints

In this paper, a new method is proposed for designing robust control laws that are subject to arbitrary information structure constraints. The computation of the gain matrix is formulated in terms of a static output feedback problem, which can be efficiently solved using linear matrix inequalities. The resulting control laws ensure stability with respect to a broad class of additive nonlinear uncertainties in the system.

Balanced decompositions of sparse systems for multilevel parallel processing

The objective of this paper is to present a recursive algorithm for permuting sparse matrices into the bordered block diagonal form. An outstanding feature of this algorithm is the resulting balance between the border size and the size of the diagonal blocks, which gives rise to an efficient multilevel scheme for parallel matrix factorization. This scheme is characterized by good load balancing and low interprocessor communications. In addition, it is specifically designed to minimize fill in within the factored matrix in order to preserve the original sparsity. Applications to power transmission systems are presented, together with a discussion of relevant parallelization and sparsity issues. >

Stabilization of nonlinear systems with moving equilibria

This note provides a new method for the stabilization of nonlinear systems with parametric uncertainty. Unlike traditional techniques, our approach does not assume that the equilibrium remains fixed for all parameter values. The proposed method combines different optimization techniques to produce a robust control that accounts for uncertain parametric variations, and the corresponding equilibrium shifts. Comparisons with analytical gain scheduling are provided.

Global low-rank enhancement of decentralized control for large-scale systems

This note proposes a new control strategy which is computationally attractive for systems of large dimensions. The main idea is to supplement decentralized feedback with a global additive term, which is computed as a product of two low-rank matrices. This feature is of critical importance for systems that cannot be adequately stabilized using standard decentralized control. The low-rank matrices can be efficiently obtained using linear matrix inequalities, and the resulting control is suitable for implementation in a multiprocessor environment. Simulations on a platoon of vehicles demonstrate that such a control can significantly improve the robustness of the closed-loop system with respect to uncertain nonlinearities.

Coherency recognition using epsilon decomposition

This paper proposes a new algorithm for the identification of coherent generators, which is based on epsilon decompositions of the Jacobian. By using the Jacobian, the algorithm overcomes some major drawbacks of other methods for coherency recognition; in addition, it can be directly integrated into programs for transient stability analysis. Test results on a 48 machine system are presented to evaluate the method.

An improved block-parallel Newton method via epsilon decompositions for load-flow calculations

The objective of this paper is to present a new method for parallel load-flow calculations based on an effective decomposition of the network. In the solution process, the authors utilize the block-parallel Newton method which involves only diagonal blocks of the Jacobian. The underlying structure is obtained by applying the epsilon decomposition algorithm which eliminates weak coupling elements from the matrix. They demonstrate that the iterative process can be significantly accelerated by making certain modifications in mismatch evaluation for buses connecting different blocks. Experiments on the hypercube confirm that the proposed method is indeed effective, particularly for problems where a good initial approximation is available (such as outage assessment).