A new non-iterative solution for a class of difference Riccati equations

Recently, two non-iterative solutions for difference Riccati equations (DREs) have been developed employing max-plus primal and dual space fundamental solution semigroups. These solutions provide explicit formulas that allow the non-iterative computation of the DRE solution corresponding to any initial condition in a specific well-defined set. In this paper, a third non-iterative solution to a class of difference Riccati equation is developed. It is shown that this new non-iterative solution avoids some specific drawbacks observed in the two existing max-plus based non-iterative solutions at the expense of a semigroup property.

[1]  William M. McEneaney,et al.  A max-plus method for optimal control of a diffusion equation , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[2]  Huan Zhang,et al.  A max-plus method for the approximate solution of discrete time linear regulator problems with non-quadratic terminal payoff , 2013, SIAM Conf. on Control and its Applications.

[3]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[4]  Peter M. Dower,et al.  A max-plus based fundamental solution for a class of discrete time linear regulator problems ☆ , 2013, 1306.5060.

[5]  Lorenzo Ntogramatzidis,et al.  On the solution of the Riccati differential equation arising from the LQ optimal control problem , 2010, Syst. Control. Lett..

[6]  William M. McEneaney,et al.  A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations , 2014, SIAM J. Control. Optim..

[7]  Zheng Qu,et al.  Contraction of Riccati flows applied to the convergence analysis of the max-plus curse of dimensionality free method , 2013, 2013 European Control Conference (ECC).

[8]  M. Ran.  Linear quadratic problems with indefinite cost for discrete time systems , 2010 .

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[10]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[11]  Huan Zhang,et al.  Max-plus fundamental solution semigroups for a class of difference Riccati equations , 2014, Autom..

[12]  G. Bilardi,et al.  The role of terminal cost/reward in finite-horizon discrete-time LQ optimal control , 2007 .

[13]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[14]  Ian R. Petersen,et al.  Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples☆ , 1985 .

[15]  William M. McEneaney,et al.  A max-plus based fundamental solution for a class of infinite dimensional Riccati equations , 2011, IEEE Conference on Decision and Control and European Control Conference.

[16]  Edward J. Davison,et al.  The numerical solution of the matrix Riccati differential equation , 1973 .

[17]  Kiyotsugu Takaba,et al.  A characterization of solutions of the discrete-time algebraic Riccati equation based on quadratic difference forms , 2006 .

[18]  D. Mayne,et al.  On the discrete time matrix Riccati equation of optimal control , 1970 .

[19]  William M. McEneaney,et al.  A new fundamental solution for differential Riccati equations arising in control , 2008, Autom..

[20]  Huan Zhang,et al.  A max-plus based fundamental solution to a class of linear regulator problems with non-quadratic terminal payoff , 2013, 2013 European Control Conference (ECC).