# Suboptimal Control of Large-Scale Dynamic Systems

TL;DR: A method is proposed to determine a suboptimal control law using more than one reduced order aggregated models and a mathematical programming technique that ensures stability, gives better performance and is computationally attractive for large-scale systems.

Abstract: A method is proposed to determine a suboptimal control law using more than one reduced order aggregated models and a mathematical programming technique. The proposed control law ensures stability, gives better performance and is computationally attractive for large-scale systems.

##### References

More filters

•

01 Jun 1984

TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.

Abstract: Volume 2: XI. Complex symmetric, skew-symmetric, and orthogonal matrices: 1. Some formulas for complex orthogonal and unitary matrices 2. Polar decomposition of a complex matrix 3. The normal form of a complex symmetric matrix 4. The normal form of a complex skew-symmetric matrix 5. The normal form of a complex orthogonal matrix XII. Singular pencils of matrices: 1. Introduction 2. Regular pencils of matrices 3. Singular pencils. The reduction theorem 4. The canonical form of a singular pencil of matrices 5. The minimal indices of a pencil. Criterion for strong equivalence of pencils 6. Singular pencils of quadratic forms 7. Application to differential equations XIII. Matrices with non-negative elements: 1. General properties 2. Spectral properties of irreducible non-negative matrices 3. Reducible matrices 4. The normal form of a reducible matrix 5. Primitive and imprimitive matrices 6. Stochastic matrices 7. Limiting probabilities for a homogeneous Markov chain with a finite number of states 8. Totally non-negative matrices 9. Oscillatory matrices XIV. Applications of the theory of matrices to the investigation of systems of linear differential equations: 1. Systems of linear differential equations with variable coefficients. General concepts 2. Lyapunov transformations 3. Reducible systems 4. The canonical form of a reducible system. Erugin's theorem 5. The matricant 6. The multiplicative integral. The infinitesimal calculus of Volterra 7. Differential systems in a complex domain. General properties 8. The multiplicative integral in a complex domain 9. Isolated singular points 10. Regular singularities 11. Reducible analytic systems 12. Analytic functions of several matrices and their application to the investigation of differential systems. The papers of Lappo-Danilevskii XV. The problem of Routh-Hurwitz and related questions: 1. Introduction 2. Cauchy indices 3. Routh's algorithm 4. The singular case. Examples 5. Lyapunov's theorem 6. The theorem of Routh-Hurwitz 7. Orlando's formula 8. Singular cases in the Routh-Hurwitz theorem 9. The method of quadratic forms. Determination of the number of distinct real roots of a polynomial 10. Infinite Hankel matrices of finite rank 11. Determination of the index of an arbitrary rational fraction by the coefficients of numerator and denominator 12. Another proof of the Routh-Hurwitz theorem 13. Some supplements to the Routh-Hurwitz theorem. Stability criterion of Lienard and Chipart 14. Some properties of Hurwitz polynomials. Stieltjes' theorem. Representation of Hurwitz polynomials by continued fractions 15. Domain of stability. Markov parameters 16. Connection with the problem of moments 17. Theorems of Markov and Chebyshev 18. The generalized Routh-Hurwitz problem Bibliography Index.

9,334 citations

••

TL;DR: Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.

Abstract: A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by "aggregating" the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.

505 citations

••

TL;DR: In this paper, a brief review of the F-test and Akaike-based methods for model structure testing is presented, and it is shown that they are asymptotically equivalent.

Abstract: In system identification it is assumed in many cases that the order of the system is known. Thus it is important to perform tests for determining the correct model order. For a single-input, single-output system the order is the only structural parameter, but for multivariable systems there are several structural parameters. It is in such cases not enough to test only for the order but to investigate if a model structure is appropriate or not. The paper contains a brief review of some methods for model structure testing. Two methods proposed by Akaike and the F-test are compared and it is shown that they are asymptotically equivalent. The methods are analysed theoretically through analytical calculations. The results are also illustrated with simulations.

171 citations

••

TL;DR: Several methods for approximate estimation and control of large scale systems, mostly based on the notions of aggregation and disaggregation are presented.

Abstract: The paper presents several methods for approximate estimation and control of large scale systems, mostly based on the notions of aggregation and disaggregation. After introducing the notions for static systems in Section II, aggregation and disaggregation in dynamic systems are discussed in Section III. The condition for perfect aggregation is relaxed in two ways. One is to restrict the class of dynamic systems and the other is to restrict the state space. These two approaches are shown to provide useful approximation to the more restrictive notions of perfect aggregation and disaggregation. Section IV is devoted to improving performance measures for large scale systems.

63 citations