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)測控制-電氣類-展示頁
2025-05-26 20:21本頁面
【正文】 → 0 as t → ∞ ). This stability property can be deduced for a very general class of nonlinear systems: including timevarying systems, nonholonomic systems, systems allowing discontinuous feedbacks, etc. If, in addition, the value functionpossesses some continuity properties, then Lyapunov stability (. the trajectory stays arbitrarily close to the origin provided it starts close enough to the origin) can also be guaranteed (see . [11]). However, this last property might not be possible to achieve for certain classes of systems, for example a carlike vehicle (see [8] for a discussion of this problem and this example). A similar approach can be used to deduce robust stability of MPC for systems allowing uncertainty. After establishing monotone decrease of the value function, we would want to guarantee that the state trajectory asymptotically approaches some set containing the origin. But, a difficulty encountered is thatthe predicted trajectory only coincides with the resulting trajectory at specificsampling instants. The robust stability properties can be obtained, as we show,using a generalized version of Barbalat’s lemma. These robust stability resultsare also valid for a very general class of nonlinear timevarying systems allowing discontinuous feedbacks. The optimal control problems to be solved within the MPC strategy are here formulated with very general admissible sets of controls (say, measurable control functions) making it easier to guarantee, in theoretical terms, the existence of solution. However, some form of finite parameterization of the control functionsis required/desirable to solve online the optimization problems. It can be shown that the stability or robustness results here described remain valid when the optimization is carried out over a finite parameterization of the controls, such as piecewise constant controls (as in [13]) or as bangbang discontinuous feedbacks (as in [9]). 2 A SampledData MPC Framework We shall consider a nonlinear plant with input and state constraints, where the evolution of the state after time t0 is predicted by the following model. The data of this model prise a set containing all possible initial states at the initial time t0, a vector xt0 that is the state of the plant measured at time t0, a given function 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 continuous and locally Lipschitz with respect to the second argument. The construction of the feedback law is acplished by using a sampleddata MPC strategy. Consider a sequence of sampling instants π := {ti}i≥0 with a constant intersampling 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 : IRIRn → IRm. The feedback control is obtained by repeatedly solving online openloop 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 xti . Note that in the interval [t + Tc, t + Tp] the control value is selected from a singleton and therefore the optimization decisions are all carried out in the interval [t, t + Tc] with the expected benefits in the putational 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 prediction 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。 fontes 和 magni [ 9 ]描述的應(yīng)用，這參數(shù) 是 一個(gè) unicycle 移動(dòng)機(jī)器人須有界擾動(dòng)。在邦邦反饋策略， 管制的價(jià)值觀的策略是只允許在其中一個(gè)極端它的范圍。因此，只要設(shè)定可接受的控制值 U 的常數(shù)所有的時(shí)間，輕而易舉的事，但無論如何，重要的是，必然前穩(wěn)定結(jié)果如下 如果我們考慮到一套接納控制功能（包括輔警控制法）是一個(gè)有限 parameterizable設(shè)置這樣的一套受理的控制值是不斷為所有的時(shí)間，那么雙方的名義穩(wěn)定性和魯棒穩(wěn)定的結(jié)果，這里所描述的仍然有效。問題的離散逼近，詳細(xì)討論了如在 [ 16 ]及 [ 12 ] ?？刂瓶蓞?shù)為分段常數(shù)控制（如 [ 13 ] ） ，多項(xiàng)式或樣條所描述的一個(gè)有限的數(shù)目 coeficients ，砰 砰管制（例如， [ 9 ， 10 ] ）
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