A new algorithm for a class of deterministic drift counteraction optimal control problems

A new algorithm is presented to solve a class of deterministic drift counteraction optimal control (DCOC) problems for nonlinear discrete-time systems. The objective is to find a control policy that maximizes the time until the system violates prescribed constraints for the first time. We analyze convergence of the algorithm and show that it is more accurate compared to the conventional value iteration algorithm from dynamic programming. Two numerical DCOC examples of a forced van der Pol oscillator and of north-south station keeping of a geostationary satellite are reported.

[1]  Ilya Kolmanovsky,et al.  An Integrated Software Environment For Powertrain Feasibility Assessment Using Optimization And Optimal Control , 2006 .

[2]  Bong Wie,et al.  Space Vehicle Dynamics and Control , 1998 .

[3]  J. J. Pocha.  An Introduction to Mission Design for Geostationary Satellites , 1987 .

[4]  Ali Heydari,et al.  Revisiting Approximate Dynamic Programming and its Convergence , 2014, IEEE Transactions on Cybernetics.

[5]  Derong Liu,et al.  Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems , 2016, IEEE Transactions on Cybernetics.

[6]  Bong Wie,et al.  Space Vehicle Dynamics and Control, Second Edition , 2008 .

[7]  John N. Tsitsiklis,et al.  Neuro-dynamic programming: an overview , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[9]  Derong Liu,et al.  Neural-Network-Based Optimal Control for a Class of Unknown Discrete-Time Nonlinear Systems Using Globalized Dual Heuristic Programming , 2012, IEEE Transactions on Automation Science and Engineering.

[10]  Michael Malisoff.  Viscosity Solutions of the Bellman Equation for Exit Time Optimal Control Problems with Vanishing Lagrangians , 2002, SIAM J. Control. Optim..

[11]  G. Barles,et al.  Exit Time Problems in Optimal Control and Vanishing Viscosity Method , 1988 .

[12]  R Bellman,et al.  On the Theory of Dynamic Programming. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[13]  On asymptotic exit-time control problems lacking coercivity , 2014 .

[14]  Ilya V. Kolmanovsky,et al.  Deterministic drift counteraction optimal control and its application to satellite life extension , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[15]  Ilya Kolmanovsky,et al.  Geostationary satellite station keeping using Drift Counteraction Optimal Control , 2016 .

[16]  Piermarco Cannarsa,et al.  Semiconcavity for optimal control problems with exit time , 2000 .

[17]  Jean-Jacques E. Slotine,et al.  Neural Network Control of Unknown Nonlinear Systems , 1989, 1989 American Control Conference.

[18]  Alain-Philippe Blanc.  Deterministic Exit Time Control Problems With Discontinuous Exit costs , 1997 .

[19]  Ilya Kolmanovsky,et al.  Deterministic Drift Counteraction Optimal Control for Attitude Control of Spacecraft with Time-Varying Mass , 2016 .

[20]  Ilya V. Kolmanovsky,et al.  Discrete-time drift counteraction stochastic optimal control: Theory and application-motivated examples , 2008, Autom..