非线性系统多模型迭代学习控制

83 浏览量更新于2024-09-01 收藏 557KB PDF 举报

"本文探讨了基于迭代学习控制（Iterative Learning Controller, ILC）的多模型方法，重点关注在非线性系统中的应用。ILC利用系统模型在每次迭代中优化输入，以达到良好的稳态性能。尽管ILC的模型不必完全精确，但更准确的模型可以减少迭代次数。研究中涉及的非线性系统可由时间不变模型和时间变模型共同描述。已知的时间不变模型常用于建立ILC，而未知的时间变模型则被视为误差模型。为了近似可能的变化行为，文章采用了多个模糊神经网络（Fuzzy Neural Network, FNN）模型进行建模。" 正文：迭代学习控制器（ILC）是一种基于系统模型的控制策略，其核心思想是通过在每个试验周期中不断更新输入来逐步提高系统的性能，特别是在稳态条件下表现优异。ILC的设计并不严格要求精确的系统模型，但一个更精确的模型有助于更快地收敛，减少所需的迭代次数。本研究关注的是非线性系统的ILC问题，该系统可由两部分模型描述：一部分是时间不变模型，另一部分是时间变模型。时间不变模型是已知的，并且通常用于构建ILC算法。然而，对于时间变模型，由于其不确定性，通常视为误差模型，难以精确预测。这种模型的处理是ILC在非线性系统中的一大挑战。为了解决这个问题，文章提出了使用多个模糊神经网络模型（FNN）来近似可能的时间变行为。模糊神经网络结合了模糊逻辑的灵活性和神经网络的学习能力，能够有效地处理不确定性和非线性特性。通过多个FNN模型，系统可以更好地适应环境变化和不确定性，从而改进ILC的性能。每个FNN模型都可以看作是对系统在不同条件或状态下的局部描述，这些模型的组合可以提供更全面、更动态的系统行为理解。通过训练和调整这些FNN模型，ILC算法能够逐渐学习和补偿时间变模型带来的误差，进而实现更优的控制效果。这篇论文揭示了如何利用多模型和模糊神经网络技术来改善非线性系统的迭代学习控制。这种方法不仅可以应对模型不确定性，还有助于提高系统性能，减少迭代次数，是ILC领域的一个重要进展。通过这种创新方法，未来的研究可以进一步探索如何在更复杂的非线性系统和动态环境中应用ILC，以达到更高的控制精度和鲁棒性。

of time invariant part,a model set of the nonlinear system can

be given.Multiple model iterative learning controller will be ob-

tained based on this model set.An index function with the form

of integral of output error between diﬀerent models and the ac-

tual system will be given for the decision of the best model.The

ILC based on this best model will improve the transient re-

sponse of ILC system greatly.

In the ﬁrst part of this paper, the ILC of nonlinear system and

its stability analysis will be given.In the second part,the struc-

ture and the training procedure of fuzzy neural network will be

proposed.Then the ILC based on multiple models can be ob-

tained in the third part. Finally, simulation cases will be given

to show the eﬀectiveness of the proposed method.

2. System description and ILC

Consider a class of discrete-time nonlinear dynamic systems

described by the following equations:

x(t + 1) = f(x(t), t) + B(x(t), t)u(t) (1)

where 0 ≤ t ≤ T − 1, x(t) ∈ R

and u(t) ∈ R

(t ∈ 0, 1, · · · , T)

denotes the state and control vector of the system respectively.

Suppose that the system is all-state output,and also we know

that the estimated model of {f, B} is {

B}.The desired trajectory

is given as x

(t)(0 ≤ t ≤ T),when B is column full rank ,the

desired control u

(t) can be obtained by Eqn.(2)

(t) = B

(t), t)[x

(t + 1) − f(x

(t), t)] (2)

where B

(t), t) = [B

(t), t)B(x

(t), t)]

−1

(t), t).By

imposing an arbitrarily selected continuous control u

(t)(0 ≤

t ≤ T) onto system (1),the error between the output trajectory

(t) and the desired trajectory x

(t) will be decided by the error

of the control sequences below:

∆u

(t) =u

(t) − u

(t)

(t), t)[x

(t + 1) − f(x

(t), t)]

− B

(t), t)[x

(t + 1) − f(x

(t), t)]

(3)

The approximation of the control error ∆u

(t) can be obtained

at several levels by using the model {

∆u

(t) ≈

(t), t)[x

(t + 1) −

f(x

(t), t)]

−

(t), t)[x

(t + 1) −

f(x

(t), t)] (4)

∆u

(t) ≈

(t), t)[x

(t + 1) − x

(t + 1)−

f(x

(t), t) +

f(x

(t), t)] (5)

∆u

(t) ≈

(t), t)[e

(t + 1) −

f(e

(t), t)] (6)

where e

(t) = x

(t)−x

(t).Apparently ,the input can be adjusted

by the approximation of control error.Here Eqn.(5) is used :

k+1

(t) = u

(t)+

(t), t)[e

(t+1)−

f(x

(t), t)+

f(x

(t), t)] (7)

where k indicates the iterative times.

Suppose that f,

f,B are globally uniformly Lipschitz in the

sense of

kf(x

, k) − f(x

, k)k ≤ c

− x

f(x

(k)) −

f(x

(k))k ≤ c

− x

and

kB(x

, k) − B(x

, k)k ≤ c

− x

for positive constants c

and c

.Simultaneously B,

B are

bounded.

For system (1),when control strategy (7) is applied,the fol-

lowing theorem can guarantee the eventual convergence.[5]

Theorem 1. For accessible desired trajectory x

(t)(0 ≤ t ≤

T),if system(1) satisﬁes the following conditions

1. kI −

(e(t), t)B(x(t), t)k < 1 (0 ≤ t ≤ T)

2. x

(0) = x

(0)

Then by the eﬀect of learning algorithm(7),ke

(t)k → 0(k →

∞)(0 ≤ t ≤ T).

P. From Eqn.(7)

k+1

(t) = u

(t) +

(t), t)[e

(t + 1) −

f(x

(t), t) +

f(x

(t), t)]

for

(t + 1) =B(x

(t), t)∆u

(t) + f(x

(t), t) − f(x

(t), t)+

[B(x

(t), t) − B(x

(t), t)]u

(t) (8)

∆u

k+1

(t) =∆u

(t) −

(t), t)B(x

(t), t)∆u

(t)−

(t), t)[B(x

(t), t) − B(x

(t), t)]u

(t)−

(t), t)[f(x

(t), t) − f(x

(t), t) −

f(x

(t), t)+

f(x

(t), t)]

(9)

Taking norms of both sides of Eqn.(8) gives

(t + 1)k ≤kB(x

(t), t)kk∆u

(t)k + c

(t) − x

(t)k

+ k

(t) − x

(t)kku

(t)k

= k

1,t

k∆u

(t)k + k

2,t

(t)k (10)

where k

1,t

= kB(x

(t), t)k,k

2,t

= c

+ k

(t)k,and k

2,t

is irrele-

vant with k.

Taking norms of both sides of Eqn.(9) gives

k∆u

k+1

(t)k ≤kρ

(t)kk∆u

(t)k + k

(t), t)k(k

(t)kku

(t)k

+ c

(t)k + c

(t)k)

=kρ

(t)kk∆u

(t)k + k

(

t)k (11)

where ρ

(t) = I −

(t), t)B(x

(t), t), k

(t), t)k(k

(t)k + c

+ c

).They are both relevant

with k.

Using Eqn.(10) and Eqn.(11),we obtain

k∆u

k+1

(t)k ≤kρ

(t)kk∆u

(t)k + k

1,t−1

k∆u

(t − 1)k

+ k

2,t−1

(t − 1)k)

≤kρ

(t)kk∆u

(t)k + K

t−1

k∆u

(t − 1)k

+ · · · + K

k∆u

(0)k (12)

剩余11页未读，继续阅读

weixin_38650951

粉丝: 5
资源: 927

非线性系统多模型迭代学习控制

Real-time Iterative Learning Control

实现迭代学习控制.zip_iterative learning_跟踪 控制_轨迹跟踪_轨迹跟踪控制

迭代学习控制matlab

iterative model

an iterative solver was used for this model. however, a direct solver may en

迭代学习控制算法ilc

迭代学习控制和PI控制器结合

MATLAB迭代学习控制

ilc simulink

迭代学习控制simulnik

最新资源

实现迭代学习控制.zip_iterative learning_跟踪控制_轨迹跟踪_轨迹跟踪控制