Streamlining the State-Dependent Riccati Equation Controller Algorithm

S. Katsev and J.C. Cockburn (USA)


Riccati Equations, Kleinman iterations, Real-time systems, SDRE control


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 lin ear quadratic regulator. The SDRE control algorithm re lies on the solution of a continuous-time Riccati equation at each time update. This approach has been recently ap plied 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 study ing the behavior of several iterative algorithms to solve continuous-time Riccati equations. It is shown that Klein man’s algorithms is superior to other iterative algorithms. Furthermore, it is demonstrated that the maximum number of iterations, before the algorithms stops, should be con sidered 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.

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