Some Properties of Algorithmic Control for Real-time Optimization

Some convergence properties of the real-time calculation method for nonlinear optimal control problems are proved. We adopt the so-called 'algorithmic control' as one of the real-time optimization methods, which is based on the iterative algorithms for obtaining the numerical solutions. In this paper, we prove that either the necessary condition of optimality is satisfied or the value of the performance index is improved through the design process

[1]  J. Imae,et al.  A Riccati-equation-based algorithm for nonlinear optimal control problems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[2]  Guisheng Zhai,et al.  Real-time optimization for nonlinear systems using algorithmic control , 2005 .

[3]  M. Ciletti,et al.  The computation and theory of optimal control , 1972 .

[4]  David Q. Mayne,et al.  Differential dynamic programming , 1972, The Mathematical Gazette.

[5]  G. Franklin,et al.  A second-order feedback method for optimal control computations , 1967, IEEE Transactions on Automatic Control.

[6]  Toshiyuki Ohtsuka,et al.  A continuation/GMRES method for fast computation of nonlinear receding horizon control , 2004, Autom..

[7]  C. W. Merriam,et al.  A Computational Method for Feedback Control Optimization , 1965, Inf. Control..

[8]  Daniel Matthys Murray,et al.  DIFFERENTIAL DYNAMIC PROGRAMMING FOR THE EFFICIENT SOLUTION OF OPTIMAL CONTROL PROBLEMS , 1978 .

[9]  John B. Moore,et al.  Enhancing optimal controllers via techniques from robust and adaptive control , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  J. Imae,et al.  A unified approach to computational methods of nonlinear optimal control problems with possible jumps in states , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[11]  J. R. Cloutier,et al.  Nonlinear regulation and nonlinear H{sub {infinity}} control via the state-dependent Riccati equation technique: Part 3, examples , 1994 .

[12]  John B. Moore,et al.  Enhancing optimal controllers via techniques from robust and adaptive control , 1992 .

[13]  G. Zhai,et al.  Algorithmic control for real-time optimization of constrained nonlinear systems: swing-up problems of inverted pendulums , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[14]  G. Zhai,et al.  Algorithmic control for real-time optimization of nonlinear systems: Simulations and experiments , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[15]  N. Nedeljkovic.  New algorithms for unconstrained nonlinear optimal control problems , 1981 .