A hierarchical MPC scheme for interconnected systems

This paper describes a hierarchical control scheme for interconnected systems. The higher layer of the control structure is designed with robust Model Predictive Control (MPC) based on a reduced order dynamic model of the overall system and is aimed at optimizing long-term performance, while at the lower layer local regulators acting at a higher frequency are designed for the full order models of the subsystems to refine the control action. A simulation experiment concerning the control of the temperature inside a building is reported to witness the potentialities of the proposed approach

A novel distributed algorithm for estimation and control of large-scale systems

In this paper we propose a novel algorithm based on linear matrix inequalities for the design of distributed controllers and state estimators for large-scale systems inspired by linear quadratic regulators and Kalman filters, respectively. With respect to similar state-of-the art methods, the scheme proposed here allows to reduce the conservativeness due to the approximations used for the covariance distributed iterative computation. The theoretical properties of the proposed scheme are thoroughly investigated. The controllers and observers obtained using the proposed approach are applied to a simulated dynamical system and their performances are thoroughly compared to those obtained with state-of-the-art schemes, showing the potentialities of the scheme

Block-wise discretization accounting for structural constraints

This paper presents an approximate discretization method, named Mixed Euler-ZOH (mE-ZOH), which can be applied to any continuous-time linear system. This method has been explicitly developed to preserve the system sparsity, a property that is particularly important when dealing with the analysis and design of distributed controllers for large-scale systems. In terms of stability preservation as a function of the sampling interval, we show that mE-ZOH outperforms the classical forward Euler (fE) approach, which is the only known discretization method guaranteeing the preservation of sparsity for all possible sampling times. It is then shown that this new discretization method is capable of preserving stability for all sampling times for a wide classes of dynamical systems, including the important class of positive systems. Besides stability, also positivity of the resulting discrete-time system is preserved, contrarily to what happens for the fE approach. A couple of examples are reported to illustrate the main theoretical results of the paper

On The Discretisation Of Sparse Linear Systems

This paper addresses the discretisation problem for sparse linear systems. Classical discretisation methods usually destroy sparsity patterns of continuous-time systems, since they do not consider structural constraints. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem adequately, tools from convex optimisation can be then applied. Error bounds for the approximation are provided for special classes of matrices that arise in practical applications. Numerical examples are included.3742Alsace Region,et al.,Groupement de Recherche - Modeling, Analysis and Control of Dynamical Systems (GdR MACS),MathWorks,Siemens,Strasbourg.euFranklin, G.F., Powell, J.D., Workman, M.L., (1997) Digital Control of Dynamic Systems, , 3rd ed. Englewood Cliffs, NJ: Prentice HallChen, T., Francis, B.A., (1995) Optimal Sampled-Data Control Systems, , London, UK: Springer-VerlagSouza, M., Deaecto, G.S., Geromel, J.C., Daafouz, J., Selftriggered linear quadratic networked control (2013) Optim. Control Appl. Meth.Hespanha, J.P., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proc. of the IEEE - Special Issue on Technology of Networked Control Systems, 95 (1), pp. 138-162Schlote, A., Häusler, F., Hecker, T., Bergmann, A., Crisostomi, E., Radusch, I., Shorten, R., Cooperative regulation and trading of emissions using plug-in hybrid vehicles IEEE Trans. Intell. Transport. Syst.Lunze, J., (1992) Feedback Control of Large Scale Systems, , ser. Systems and Control Engineering. Upper Saddle River, NJ: Prentice HallSiljac, D.D., (1991) Decentralized Control of Complex Systems, , New York, NY: Academic PressWang, F.-Y., Liu, D., (2008) Networked Control Systems: Theory and Applications, , London, UK: Springer-VerlagSeiler, P., Sengupta, R., Analysis of communication losses in vehicle control problems (2001) Proc. of the Americal Control Conference, , Arlington, VA, JuneWen, J.T., Arcak, M., A unifying passivity framework for network flow control (2004) IEEE Trans. on Automat. Contr., 49 (2), pp. 162-174. , FebruaryFarina, M., Colaneri, P., Scattolini, R., Block-wise discretization accounting for structural constraints (2013) Automatica, 49 (11), pp. 3411-3417. , NovemberColaneri, P., Farina, M., Kirkland, S., Scattolini, R., Shorten, R., (2013) Hybrid Systems and Constraints, pp. 1-20. , ISTE-Wiley, ch. Positive linear systems: discretization with positivity and structural constraintsAnderson, B.D.O., Moore, J.B., (2007) Optimal Control: Linear Quadratic Methods, , Mineola, NY: Dover PublicationsChen, C.-T., (1999) Linear System Theory and Design, , 3rd ed. New York, NY: Oxford University PressGolub, G.H., Van Loan, C.F., (1996) Matrix Computations, , 3rd ed. Baltimore, MD: Johns Hopkins University PressMoler, C., Van Loan, C., Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later (2003) SIAM Review, 45 (1), pp. 3-49Baker, G.A., Jr., Graves-Morris, P., (1996) Pade Approximants, , 2nd ed. Cambridge, UK: Cambridge University PressRossi, F., Colaneri, P., Shorten, R.N., Pade discretization for linear systems with polyhedral lyapunov functions (2011) IEEE Trans. on Automat. Contr., 56 (11), pp. 2717-2722. , NovemberShorten, R.N., Corless, M., Sajja, S., Solmaz, S., On pade approximations, quadratic stability and discretization of switched linear systems (2011) Systems & Control Letters, 60 (9), pp. 683-689. , SemptemberKaplan, W., (2002) Advanced Calculus, , 5th ed. Boston, MA: PearsonFiedler, B., Gedeon, T., A lyapunov function for tridiagonal competitive-cooperative systems (1999) SIAM J. Math. Anal., 30 (3), pp. 469-478. , MarchGyllenberg, M., Wang, Y., Periodic tridiagonal systems modeling competitive-cooperative ecological interactions (2005) Discrete and Continuous Dynamical Systems - Series B, 5 (2), pp. 289-298. , MayLévine, J., Rouchon, P., Quality control of binary distillation columns via nonlinear aggregate models (1991) Automatica, 27 (3), pp. 463-480. , MayFarina, L., Rinaldi, S., (2000) Positive Linear Systems: Theory and Applications, , New York, NY: John Wiley & SonsMeyer, C.D., (2000) Matrix Analysis and Applied Linear Algebra, , Philadelphia, PA: SIAMLuenberger, D.G., (1979) Introduction to Dynamic Systems: Theory, Models and Applications, , New York, NY: John Wiley & Son