Large-scale Linear Control Systems Research Articles

BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems

This paper studies the interconnected stability and cooperative control of large-scale linear systems. Using the technique of the bilinear matrix inequality (BMI), the necessary and sufficient conditions are given for interconnected stability and cooperative stabilization of two subsystems. It is shown that the systems can be cooperatively stabilized even if the subsystems are not stable. It is not necessary for us to presume the stability of the subsystems. Furthermore, the problems of designing interconnected and cooperative controllers are converted into the optimization problems using BMI constraints. To solve these problems, certain optimal alternate algorithms are proposed, and the proof for the convergence of the algorithms is presented. Finally, several examples are given to illustrate the optimization results.

Numerical Solution for Large-Scale Systems with General Multiple Linear-Quadratic Structure

A class of large-scale linear control systems, where the overall objective function is a nonlinear function of multiple quadratic performance indices, is investigated in this paper. Chebyshev spectral approximation technique is used for state and control variables. Numerical example has been given at the end of this paper.

Hierarchical control for large-scale systems with general multiple linear-quadratic structure

A class of large-scale linear control systems, where the overall objective function is a nonlinear function of multiple quadratic performance indices, is investigated in this paper. This type of large-scale control problem with a general multiple linear-quadratic structure is nonseparable in the sense of conventional hierarchical control. Hierarchical control is extended in this paper to large-scale nonseparable control problems, where multiobjective optimization is used as a separation strategy. The large-scale general multiple linear-quadratic control problem is embedded, under certain conditions, into a family of the weighted Lagrangian formulation. The weighted Lagrangian formulation is separable with respect to subsystems and can be effectively solved using the interaction prediction approach at the two lower levels in the proposed three-level solution structure. At the third level, the weighting vector for the weighted Lagrangian formulation is adjusted iteratively to search the optimal weighting vector with which the optimal control of the original large-scale nonseparable control problem is attained. One feature of this hierarchical control scheme is a derived analytical solution for the large-scale general multiple linear-quadratic control.

Singular Perturbation Method for a Sub-Optimal Control of Large-Scale Linear Systems

Singular Perturbation Method for a Sub-Optimal Control of Large-Scale Linear Systems