Distributed receding horizon control of spatially invariant systems

We present a rigorous framework for the study of distributed spatially invariant systems with input and state constraints. The proposed approach is based on blending tools from operator theory and Fourier analysis of spatially invariant systems with receding horizon control and multi parametric quadratic programming (MPQP). Our contributions are twofold: on one hand, we extend the recent results of Bamieh et al. on infinite-horizon optimal control of spatially invariant systems to finite receding horizon control with input and state constraints. On the other hand, our results can be interpreted as an extension of the finite dimensional MPQP-based analysis of receding horizon control to distributed, spatially invariant systems. It is assumed that the dynamics of each subsystem is uncoupled to the others, but the coupling appears through the finite horizon cost function. Specifically, we prove that for spatially invariant systems with constraints, optimal receding horizon controllers are piecewise affine (represented as a convolution sum plus an offset). Moreover, the kernel of each convolution sum decays exponentially in the spatial domain mirroring the unconstrained infinite-horizon case. Simulation results are provided for a simple example with 5 identical systems coupled in a loop

[1]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[2]  S. Melzer,et al.  Optimal regulation of systems described by a countably infinite number of objects , 1971 .

[3]  A. Jadbabaie,et al.  Receding Horizon Control of Spatially Distributed Systems over Arbitrary Graphs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[4]  William B. Dunbar,et al.  Distributed Receding Horizon Control With Application to Multi-Vehicle Formation Stabilization , 2004 .

[5]  Eric Feron,et al.  Optimal distributed actuator control grouping schemes , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[6]  S. Engell,et al.  Decentralized vs. model predictive control of an industrial glass tube manufacturing process , 1998, Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104).

[7]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[8]  Yi Guo,et al.  Nonlinear decentralized control of large-scale power systems , 2000, Autom..

[9]  Raffaello D'Andrea,et al.  Distributed Control of Spatially Reversible Interconnected Systems with Boundary Conditions , 2005, SIAM J. Control. Optim..

[10]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

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

[12]  Eduardo Camponogara,et al.  Distributed model predictive control , 2002 .

[13]  James B. Rawlings,et al.  Constrained linear quadratic regulation , 1998, IEEE Trans. Autom. Control..

[14]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[15]  Fernando Paganini,et al.  Distributed control of spatially invariant systems , 2002, IEEE Trans. Autom. Control..

[16]  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).

[17]  P. S. Krishnaprasad,et al.  Equilibria and steering laws for planar formations , 2004, Syst. Control. Lett..

[18]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[19]  Geir E. Dullerud,et al.  Distributed control of heterogeneous systems , 2004, IEEE Transactions on Automatic Control.

[20]  Mihailo R. Jovanovic,et al.  On the ill-posedness of certain vehicular platoon control problems , 2005, IEEE Transactions on Automatic Control.

[21]  Cédric Langbort,et al.  Distributed control design for systems interconnected over an arbitrary graph , 2004, IEEE Transactions on Automatic Control.

[22]  Sarosh N. Talukdar,et al.  Distributed Model Predictive Control for Electric Grids , 2004 .

[23]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[24]  R. A. Silverman,et al.  Introductory Real Analysis , 1972 .

[25]  Gregory Hagen,et al.  Distributed control design for parabolic evolution equations: application to compressor stall control , 2004, IEEE Transactions on Automatic Control.

[26]  L. Acar,et al.  Some examples for the decentralized receding horizon control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[27]  Eduardo Camponogara,et al.  Distributed Model Predictive Control: Synchronous and Asynchronous Computation , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[28]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[29]  M. Athans,et al.  On the optimal error regulation of a string of moving vehicles , 1966 .

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

[31]  P. Krishnaprasad,et al.  Homogeneous interconnected systems: An example , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

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

[33]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[34]  Geir E. Dullerud,et al.  Distributed control design for spatially interconnected systems , 2003, IEEE Trans. Autom. Control..

[35]  N. Motee,et al.  Optimal partitioning in distributed model predictive control , 2003, Proceedings of the 2003 American Control Conference, 2003..

[36]  J. A. Fax,et al.  Graph Laplacians and Stabilization of Vehicle Formations , 2002 .