SDRE Control Stability Criteria and Convergence Issues: Where Are We Today Addressing Practitioners' Concerns?

This paper has three purposes: 1) to provide a survey on the State-Dependent Riccati Equation (SDRE) stability analysis methodologies developed to date; these stability analysis techniques produce either a guarantee or a high degree of confidence that the closed-loop system is asymptotically stable over a domain of interest, 2) to present an argument that practical rules of thumb can be just as important as theoretical stability proofs with regard to real world implementation, and 3) to justify support of the above argument using some forms of actual implementation. The paper neither favors any particular stability analysis technique nor introduces a new stability analysis framework. Rather it presents a view of stability reasoned judgment and practical justification for actual implementation. The reasoned judgment and justification are mainly based on the space access vehicle control and the satellite attitude control examples whose performance becomes unstable in the presence of high gain magnitude conditions. The fundamental argument of this new view (i.e., reasoned judgment and justification) is that for even linear and static gain controllers such as the Linear Quadratic Regulator (LQR), stability of the system depends on the operational domain under practical implementation with nonlinear limiters in the loop. Therefore, for a variable gain or nonlinear controller like the SDRE method, the task of determining a region of stability either practically or theoretically is much more difficult as compared to a linear LQRbased approach. The SDRE designs of a space access vehicle control, a helicopter flight control, and a satellite attitude control are presented with a set of practical rules defined and applied to it as a practical design benchmark problem on how to pass the SDRE stability concern gate. The paper concludes with the recommendation of some practical design rules of thumb for practitioners

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