Streamlining the state-dependent Riccati Equation controller algorithm

  • Authors:

  • Sergey Katsev;Juan C. Cockburn

  • Affiliations:

  • Rochester Institute of Technology, Rochester, NY;Rochester Institute of Technology, Rochester, NY

  • Venue:
  • CA '07 Proceedings of the Ninth IASTED International Conference on Control and Applications
  • Year:
  • 2007

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Abstract

The State Dependent Riccati Equation (SDRE) controller design is a relatively new practical approach for nonlinear control problems that is closely related to the classical linear quadratic regulator. The SDRE control algorithm relies on the solution of a continuous-time Riccati equation at each time update. This approach has been recently applied to control experimental autonomous air vehicles with relative success. To make the SDRE approach practical in applications where the computational resources are limited and the dynamic models are complex, it is necessary to streamline this control algorithm and its implementation. This paper takes a first step towards this goal by studying the behavior of several iterative algorithms to solve continuous-time Riccati equations. It is shown that Kleinman's algorithms is superior to other iterative algorithms. Furthermore, it is demonstrated that the maximum number of iterations, before the algorithms stops, should be considered a design parameter. This design parameters can be used to trade-off stability and performance. If chosen properly, it is possible to reduce the time complexity of the algorithm without significantly degrading the performance of the closed loop system.