電氣工程及其自動(dòng)化專業(yè)畢設(shè)外文翻譯--采樣數(shù)據(jù)模型預(yù)測(cè)控制（英文）

1、Sampled-Data Model Predictive Control for Nonlinear Time-Varying Systems: Stability and Robustness?Fernando A.C.C. Fontes1, Lalo Magni2, and ´ Eva Gyurkovics31 Officina Mathematica, Departamento de Matem´ atica

2、 para a Ci? encia e Tecnologia, Universidade do Minho, 4800-058 Guimar? aes, Portugal ffontes@mct.uminho.pt 2 Dipartimento di Informatica e Sistimistica, Universit` a degli Studi di Pavia, via Ferrata 1, 27100 Pavia, Ita

3、ly lalo.magni@unipv.it 3 Budapest University of Technology and Economics, Institute of Mathematics, Budapest H-1521, Hungary gye@math.bme.huSummary. We describe here a sampled-data Model Predictive Control framework that

4、 uses continuous-time models but the sampling of the actual state of the plant as well as the computation of the control laws, are carried out at discrete instants of time. This framework can address a very large class o

5、f systems, nonlinear, time-varying, and nonholonomic. As in many others sampled-data Model Predictive Control schemes, Barbalat’s lemma has an important role in the proof of nominal stability results. It is argued that t

6、he generalization of Barbalat’s lemma, described here, can have also a similar role in the proof of robust stability results, allowing also to address a very general class of nonlinear, time-varying, nonholonomic systems

7、, subject to disturbances. The possibility of the framework to accommodate discontinuous feedbacks is essential to achieve both nominal stability and robust stability for such general classes of systems.1 IntroductionMan

8、y Model Predictive Control (MPC) schemes described in the literature use continuous-time models and sample the state of the plant at discrete instants of time. See e.g. [3, 7, 9, 13] and also [6]. There are many advantag

9、es in considering a continuous-time model for the plant. Nevertheless, any implementable MPC scheme can only measure the state and solve an optimization problem at discrete instants of time. In all the references cited a

10、bove, Barbalat’s lemma, or a modification of it, is used as an important step to prove stability of the MPC schemes. (Barbalat’s? The financial support from MURST Project “New techniques for the iden- tification and adap

11、tive control of industrial systems”, from FCT Project POCTI/MAT/61842/2004, and from the Hungarian National Science Foundation for Scientific Research grant no. T037491 is gratefully acknowledged.R. Findeisen et al. (Eds

12、.): Assessment and Future Directions, LNCIS 358, pp. 115–129, 2007. springerlink.com c ? Springer-Verlag Berlin Heidelberg 2007Sampled-Data MPC for Nonlinear Time-Varying Systems 117at time t0, a given function f : I R &

13、#215; I Rn × I Rm → I Rn, and a set U ? I Rm of possible control values. We assume this system to be asymptotically controllable on X0 and that for all t ≥ 0 f(t, 0, 0) = 0. We further assume that the function f is

14、continuous and locally Lipschitz with respect to the second argument. The construction of the feedback law is accomplished by using a sampled- data MPC strategy. Consider a sequence of sampling instants π := {ti}i≥0 with

15、 a constant inter-sampling time δ > 0 such that ti+1 = ti+δ for all i ≥ 0. Consider also the control horizon and predictive horizon, Tc and Tp, with Tp ≥ Tc > δ, and an auxiliary control law kaux : I R×I Rn →

16、I Rm. The feedback control is obtained by repeatedly solving online open-loop optimal control problems P(ti, xti, Tc, Tp) at each sampling instant ti ∈ π, every time using the current measure of the state of the plant xt

17、i.P(t, xt, Tc, Tp): Minimizet+Tp ?tL(s, x(s), u(s))ds + W(t + Tp, x(t + Tp)), (2)subject to:˙ x(s) = f(s, x(s), u(s)) a.e. s ∈ [t, t + Tp], (3)x(t) = xt,x(s) ∈ X for all s ∈ [t, t + Tp],u(s) ∈ U a.e. s ∈ [t, t + Tc],u(s)

18、 = kaux(s, x(s)) a.e. s ∈ [t + Tc, t + Tp],x(t + Tp) ∈ S. (4)Note that in the interval [t + Tc, t + Tp] the control value is selected from a sin- gleton and therefore the optimization decisions are all carried out in the

19、 interval [t, t + Tc] with the expected benefits in the computational time. The notation adopted here is as follows. The variable t represents real time while we reserve s to denote the time variable used in the predicti

20、on model. The vector xt denotes the actual state of the plant measured at time t. The process (x, u) is a pair trajectory/control obtained from the model of the system. The trajectory is sometimes denoted as s ?→ x(s; t,

21、 xt, u) when we want to make explicit the dependence on the initial time, initial state, and control function. The pair (¯ x, ¯ u) denotes our optimal solution to an open-loop optimal control problem. The proce

22、ss (x?, u?) is the closed-loop trajectory and control resulting from the MPC strategy. We call design parameters the variables present in the open-loop optimal control problem that are not from the system model (i.e. var

23、iables we are able to choose); these comprise the control horizon Tc, the prediction horizon Tp, the running cost and terminal costs functions L and W, the auxiliary control law kaux, and the terminal constraint set S ?