Constrained Control Design for Linear Systems with Geometric Adversary Constraints

Inspired by some practical applications concerning collision avoidance topics, this paper focuses on the optimal control of linear dynamical systems in the presence of a set of adversary constraints. In our opinion, one of the novelties is the type of constraints introduced in the receding horizon optimization problem. These constraints can be considered as "adversary" by their non convex characteristics which make the convergence of the systems' dynamics towards the "natural" equilibrium position an impossible task. The present paper proposes a dual-mode control strategy which builds on an optimization based controller and a fixed constrained control law whenever the adversary constraints are activated. In order to illustrate the benefits of the proposed method, typical applications involving the control of Multi-Agent Systems are considered.

[1]  Manfred Morari,et al.  Robust obstacle avoidance for constrained linear discrete time systems: A set-theoretic approach , 2007, 2007 46th IEEE Conference on Decision and Control.

[2]  Alexandre Trofino,et al.  Sufficient LMI conditions for output feedback control problems , 1999, IEEE Trans. Autom. Control..

[3]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[4]  Stephen J. Wright,et al.  Existence and computation of infinite horizon model predictive control with active steady-state input constraints , 2003, IEEE Trans. Autom. Control..

[5]  Ionela Prodan,et al.  Predictive control for tight group formation of Multi-Agent Systems , 2011 .

[6]  Jonathan P. How,et al.  Model predictive control of vehicle maneuvers with guaranteed completion time and robust feasibility , 2003, Proceedings of the 2003 American Control Conference, 2003..

[7]  M. Jünger,et al.  50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art , 2010 .

[8]  Z. Rekasius,et al.  On an inverse problem in optimal control , 1964 .

[9]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[10]  Ionela Prodan,et al.  Enhancements on the hyperplane arrangements in mixed integer techniques , 2011, IEEE Conference on Decision and Control and European Control Conference.

[11]  J. Borges de Sousa,et al.  Coordinated control of agent formations in uncertain, dynamic environments , 2001, 2001 European Control Conference (ECC).

[12]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

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

[14]  G. Lafferriere,et al.  Graph theoretic methods in the stability of vehicle formations , 2004, Proceedings of the 2004 American Control Conference.

[15]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[16]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[17]  D. Chmielewski,et al.  On constrained infinite-time linear quadratic optimal control , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[18]  George Bitsoris,et al.  Positive invariance, monotonicity and comparison of nonlinear systems , 2011, Syst. Control. Lett..

[19]  David Q. Mayne,et al.  Robust Model Predictive Control for Obstacle Avoidance: Discrete Time Case , 2007 .

[20]  Ionela Prodan,et al.  Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques , 2012, J. Optim. Theory Appl..

[21]  Ionela Prodan,et al.  On the hyperplanes arrangements in mixed-integer techniques , 2011, Proceedings of the 2011 American Control Conference.

[22]  Jean-Pierre Aubin,et al.  Viability Theory: New Directions , 2011 .

[23]  Yasushi Hada,et al.  Constrained Model Predictive Control , 2006 .

[24]  G. Goodwin,et al.  Global analytical model predictive control with input constraints , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).