Asymptotic tracking and dynamic regulation of SISO non‐linear system based on discrete multi‐dimensional Taylor network

Intl J Robust & Nonlinear

2019

Self Cite

Summary In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.

Section: Multidimensional Taylor Networkmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

Zhang

Intl J Robust & Nonlinear

2019

Self Cite

“…The multidimensional Taylor network (MTN, whose idea was proposed by Hong-Sen Yan in 2010 and realization was completed by Bo Zhou who is Yan's Ph.D. student) is commonly applied to the analysis of time series prediction [21][22][23][24][25][26][27][28]. MTN, a simple function of the state and input, is good at analyzing and solving the problems in point due to its polynomials.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Multidimensional Taylor Network Optimal Control of MIMO Nonlinear Systems without Models for Tracking by Output Feedback

Sun

Mathematical Problems in Engineering

2017

The actual controlled objects are generally multi-input and multioutput (MIMO) nonlinear systems with imprecise models or even without models, so it is one of the hot topics in the control theory. Due to the complex internal structure, the general control methods without models tend to be based on neural networks. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural network control unable to meet the real-time requirements. The newly developed multidimensional Taylor network (MTN) requires only addition and multiplication, so it is easy to realize real-time control. In the present study, the MTN approach is extended to MIMO nonlinear systems without models to realize adaptive output feedback control. The MTN controller is proposed to guarantee the stability of the closed-loop system. Our experimental results show that the output signals of the system are bounded and the tracking error goes nearly to zero. The MTN optimal controller is proven to promise far better real-time dynamic performance and robustness than the BP neural network self-adaption reconstitution controller.

“…For this problem, the idea of multidimensional Taylor network (MTN) optimal control was proposed by Hong‐Sen Yan in 2010. Besides, the control theory is further improved . In addition, the optimal adjustment controller based on the multidimensional network (MTN) was proposed in the work of Sun and Yan .…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Taylor network optimal control of SISO nonlinear systems for tracking by output feedback

Optim Control Appl Methods

Sun

Zhou

2017

Summary It is difficult or even impossible for the existing nonlinear system control methods to realize the real‐time tracking control of nonlinear systems in the presence of modeling errors by output feedback. For that sake, multidimensional Taylor network (MTN) optimal control method is proposed for the real‐time optimal tracking control of the SISO nonlinear constant system with modeling errors as such. On the basis of the original MTN, the control input item is added to the nonlinear dynamic model, which is then termed as the MTN optimal controller (MTNOC). Its initial parameters are trained by the conjugate gradient method and the minimum principle, according to the calculated optimal input and output of the controlled object in open‐loop status. The propagation learning algorithm is adopted to improve the MTN product term weights and eliminate the modeling errors during the real system adjustment process. Simulation results show that the MTNOC promises a high response rate. Despite the errors in the modeling process, MTNOC manages to stabilize the system for tracking the desired output. The experiment of overlaying an additional signal on the input signal proves MTNOC to be of excellent tracking characteristics, capable of inhibiting the disturbance signal to some extent. In short, by realizing the optimal closed‐loop tracking control of the SISO nonlinear constant system by output feedback, MTNOC guarantees its real‐time control accuracy, dynamic performance, robustness, and anti‐disturbance capability.