Nagini Devarakonda

Sign-Stability Concept of Ecology for Control Design with Aerospace Applications

The main aim of this research is to understand the underlying features of natural systems like Eco/Bio systems, which tend to be highly robust under perturbations, and then apply these principles to build a robust engineering system. Toward this direction, some fundamental qualitative features of ecological sign stability are reviewed and transformed into a set of mathematical results in matrix theory with quantitative information, which is usually encountered in engineering sciences. In particular, the effect of the signs of elements of a matrix on the matrix properties such as eigenvalues and condition number is shown. Similarly, it is also shown that under some assumptions on the magnitudes of the elements, predator-prey phenomena render some special properties like normality to matrices. These properties in turn are shown to impart superior robustness bounds for a class of sign-stable matrices. Then the issue of controller design is addressed, and efforts are made to identify target closed-loop systems that incorporate the desirable features of ecological systems. For a closed-loop system satisfying these properties, an algorithm for the design of controller is given. This control design procedure is illustrated with the help of two applications in the Aerospace field: satellite attitude control and aircraft lateral dynamics control. The results presented in this paper can assist in the use of ecological system principles to build highly robust engineering systems.

Ecological Sign Stability and its use in robust control design for aerospace applications

Recently, the idea of using ecological sign stability approach for designing robust controllers for engineering systems has attracted attention with promising results. In this paper, continued research on this topic is presented. It is well known that, in the field of control systems, key to a good controller design is the choice of the appropriate nominal system. Since it is assumed that the perturbations are about this nominal, the extent of allowed perturbation to maintain the stability and/or performance very much depends on this dasianominalpsila system. In this paper, we propose that the stability robustness measures for parameter perturbation are considerably improved if the dasianominalpsila system is taken (or driven) to be a dasiasign stablepsila system. Motivated by this observation, a new method for designing a robust controller for linear uncertain time invariant state space systems using ecological sign stability approach is presented along with conditions under which such a controller exists. The resulting controller design method is illustrated with examples in the flight control area including aircraft lateral flight dynamics control and satellite formation flying control.

Qualitative Principles of Ecology and Their Implications in Quantitative Engineering Systems

In this paper, we briefly review some fundamental qualitative features of ecological sign stability and transform these principles of ecology to a set of mathematical results in matrix theory with quantitative information, which is usually encountered in engineering sciences. This type of cross fertilization of ideas of life sciences and engineering sciences is deemed to be highly beneficial to both fields. In particular, we show in this paper what effect the signs of elements of a matrix have on the matrix properties such as eigenvalues and condition number. Similarly, it is also shown that under some assumptions on the magnitudes of the elements, predator-prey phenomenon in ecology renders some special properties like ‘normality’ to matrices. It is also shown that these predator-prey models have better robustness properties when compared to other matrices. The results presented in this paper can assist in the use of ecological system principles to build highly robust engineering systems.Copyright

Qualitative Robustness and Its Role in the Robust Control of Uncertain Engineering Systems

This paper addresses the issue of robustness of linear uncertain systems. In addition to the conventional notion of robustness based on quantitative information, in this paper, a new and novel perspective of qualitative robustness is introduced. The qualitative robustness measure is inspired by ecological principles and is based on the nature of interactions and interconnections of the system. Thus, using the proposed framework, the robustness of engineering systems can be assessed both from quantitative as well as qualitative information. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts it is shown that a specific quantitative set of matrices labeled ‘Target Sign Stable Matrices’ are the best nominal matrices. These concepts are then extended to closed loop control systems and problem of control design and for ease in design a new set of matrices ‘Target Pseudosymmetric Matrices’ are introduced which enhance the class of desirable closed loop system matrices. Examples are included to illustrate these concepts.Copyright

A New Robust Control Design for Linear Systems With Norm Bounded Time Varying Real Parameter Uncertainty

In this paper, a new methodology for robust control design of linear systems with time varying real parameter uncertainty is presented. The distinctive feature of this method is that it specifically offers robustness guarantees to real parameter uncertainty thereby providing a much needed alternative design method compared to existing design methods such as H∞ and μ-synthesis methods which tend to be conservative when specialized to real parameter uncertainty. The proposed robust control design method is inspired by sign (qualitative) stability idea from ecology, leading to a specific structure in the desired closed loop system matrix involving pseudosymmetry. The design procedure is simple and straightforward without requiring intensive computation. The proposed design algorithm is illustrated with aerospace applications. This algorithm is quite promising with considerable scope for extensions and improvements, finally adding to the bank of available control design methods for linear state space systems.Copyright

Eco-Inspired Robust Control Design Algorithms For Linear Systems with Real Parameter Uncertainty

This paper addresses the issue of robust control design of linear dynamical systems with real parameter uncertainty. It is well known that existing robust control design methodologies such as H-infinity and μ synthesis become very conservative when dealing with real parameter uncertainty. In robust control design methods that currently exist in the literature, which use Lyapunov and Riccati based methods, the control gains are functions of the perturbation data. The proposed robust control design algorithms in this paper differ from these in the sense that they focus on the control design to achieve a specific structure of the closed loop system matrix that guarantees as high stability robustness index as possible without the need for any information on the perturbation data. The proposed robust control design in which the structure of closed loop system matrix plays a central role, is inspired by the principles of ecology, wherein the desired closed loop matrix consists of self regulated species with predator-pray interactions among these species. A set of matrices labelled ‘Target Pseudo symmetric Matrices’ are used as the class of desirable closed loop system matrices. Based on these matrices, which capture the maximum achievable robustness index, robust control design is carried out such that the eventual closed loop system possesses a stability robustness index as close to the maximum achievable index as possible. Two separate robust control design algorithms are presented, which are relatively simple to implement. The algorithms are illustrated with several examples. It is hoped that the proposed robust control design algorithms aid in the revival of the field of robust control with new insights provided by ecological principles.

Robust Stability and Control of Linear Interval Parameter Systems Using Quantitative (State Space) and Qualitative (Ecological) Perspectives

The problem of maintaining the stability of a nominally stable linear time invariant system subject to linear perturbation has been an active topic of research for quite some time. The recent published literature on this `robust stability’ problem can be viewed mainly from two perspectives, namely i) transfer function (input/output) viewpoint and ii) state space viewpoint. In the transfer function approach, the analysis and synthesis is essentially carried out in frequency domain, whereas in the state space approach it is basically carried out in time domain. Another perspective that is especially germane to this viewpoint is that the frequency domain treatment involves the extensive use of `polynomial’ theory while that of time domain involves the use of ‘matrix’ theory. Recent advances in this field are surveyed in [1]-[2]. Even though in typical control problems, these two theories are intimately related and qualitatively similar, it is also important to keep in mind that there are noteworthy differences between these two approaches (‘polynomial’ vs ‘matrix’) and this chapter (both in parts I and II) highlights the use of the direct matrix approach in the solution to the robust stability and control design problems.

A new and simple robust control design for linear systems with structured time varying real parameter uncertainty

In this paper, a new methodology for robust control design of linear systems with structured real parameter uncertainty is presented. The distinctive feature of this method is that it explicitly offers robustness guarantees for real parameter uncertainty. This provides a much needed alternative design method compared to existing robust control design methods such as H∞ and μ -synthesis which tend to be conservative when specialized to real parameter uncertainty. The proposed robust control design method is inspired by the concept of sign (qualitative) stability in ecology, leading to a specific structure of the desired closed loop system matrix involving pseudosymmetry. Thus, this design method focuses on achieving a specific closed loop system structure that promises the desired robustness measure as opposed to building a controller as a function of the uncertainty. This design procedure is simple and straightforward without requiring intensive computation. The proposed algorithm is promising with considerable scope for extensions and improvements adding to the bank of available control design methods for linear state space systems.

Determination of Most Desirable Nominal Closed-Loop State Space System Via Qualitative Ecological Principles

This paper addresses the issue of determining the most desirable “nominal closed-loop matrix” structure in linear state space systems, from stability robustness point of view, by combining the concepts of “quantitative robustness” and “qualitative robustness.” The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts, it is shown that three classes of quantitative matrices labeled “target sign stable (TSS) matrices,” “target pseudosymmetric (TPS) matrices,” and finally “quantitative ecological stable (QES) matrices” have features which qualify them as the most desirable nominal closed-loop system matrices. In this paper, we elaborate on the special features of these sets of matrices and justify why these classes of matrices are well suited to be the most desirable nominal closed-loop matrices in the linear state space framework. Establishment of this most desirable nominal closed-loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.

Determination of Most Desirable Nominal Closed Loop State Space System via Qualitative Ecological Principles

This paper addresses the issue of determining the most desirable ‘Nominal Closed Loop Matrix’ structure in linear state space systems, by combining the concepts of ‘Quantitative Robustness’ and ‘Qualitative Robustness’. The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts it is shown that a specific quantitative set of matrices labeled ‘Quantitative Ecological Stable (QES) Matrices’ have features which qualify them as the most desirable nominal closed loop system matrices. Thus in this paper, we expand on the special features of the determinant of a matrix in terms of self-regulation, interactions and interconnections and specialize these features to the class of ‘Quantitative Ecological Stable (QES)’ matrices and show that for checking its Hurwitz stability, it is sufficient to check the positivity of only the constant coefficient of the characteristic polynomial of a matrix in a higher dimensional ‘Kronecker’ space. In addition, it is shown that these matrices possess the most attractive property among any matrix class, namely that their Determinants possess convexity property. Establishment of this optimal nominal closed loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.Copyright