Streamlining the state-dependent Riccati Equation controller algorithm

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.

[1]  Harvey Thomas Banks,et al.  Feedback Control Methodologies for Nonlinear Systems , 2000 .

[2]  John Hunt,et al.  State-Dependent Riccati Equation Control of a Small Unmanned Helicopter , 2003 .

[3]  Tung-Sang Ng,et al.  A fast Newton/Smith algorithm for solving algebraic Riccati equations and its application in model order reduction , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  J. Cloutier.  State-dependent Riccati equation techniques: an overview , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Evrin Bilge Erdem.  Analysis and Real-Time Implementation of State -Dependent Riccati Equation Controlled Systems , 2001 .

[6]  D. Kleinman.  Stabilizing a discrete, constant, linear system with application to iterative methods for solving the Riccati equation , 1974 .

[7]  J. R. Cloutier,et al.  The state-dependent nonlinear regulator with state constraints , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[8]  P. K. Menon,et al.  Real-time computational methods for SDRE nonlinear control of missiles , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[9]  Jr. N. Sandell.  On Newton's method for Riccati equation solution , 1974 .

[10]  D. Kleinman,et al.  An easy way to stabilize a linear constant system , 1970 .

[11]  D. Kleinman.  On an iterative technique for Riccati equation computations , 1968 .

[12]  Alan J. Laub,et al.  A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case , 1998 .

[13]  Peter Benner,et al.  An exact line search method for solving generalized continuous-time algebraic Riccati equations , 1998, IEEE Trans. Autom. Control..

[14]  A. Laub.  A schur method for solving algebraic Riccati equations , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[15]  Mario Sznaier,et al.  On the recoverability of nonlinear state feedback laws by extended linearization control techniques , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[16]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..