Near-Optimal Control Without Solving HJB Equations and Its Applications

Zhang, Yinyan; Li, Shuai; Jiang, Xiangyuan

doi:10.1109/tie.2018.2793233

Cited by 24 publications

(11 citation statements)

References 35 publications

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“…All trajectories of system ( 16) are uniformly ultimately bounded using the control law (53) with adaptation laws (44). Proof: Outside the boundary layer for 𝜖 ≤ |S i |, the control law is the same as (34). Using the same analysis written in Section 3 results in V < −S T AS or V < 0.…”

Section: A New Taylor-based Boundary Layer Asmc Schemementioning

confidence: 99%

“…Taylor expansion has found various applications in control methods such as model predictive control [33], near-optimal control [34,35], model-based proportional integral derivative control [36], and Taylor-based adaptive control [30,31,37]. It is pointed out that the Taylor expansion can only be applied for a differentiable function around a given point.…”

Section: Introductionmentioning

confidence: 99%

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Taylor‐based adaptive sliding mode control method for robot manipulators

Fateh

Momeni

Masouleh

2023

IET Control Theory & Appl

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This paper develops a novel Taylor‐based adaptive sliding mode control method (ASMC) for robot manipulators. In the first new scheme, sliding mode control (SMC) is effectively enhanced using the Taylor expansion for achieving a less conservative sign‐function gain that enables chattering attenuation. After that, a new Taylor‐based adaptive SMC scheme is proposed without prior knowledge of the upper bound of uncertainty and the Taylor expansion coefficients. Then, a new Taylor‐based boundary layer ASMC scheme is proposed for chattering attenuation. As a fact, no chattering is expected to be observed as long as the sliding surface remains an invariant set. However, the sliding surface will not be an invariant set unless the sign‐function is precisely determined on the sliding surface. It is verified that the sign‐function cannot be precisely determined on the sliding surface due to the presence of uncertainty, hence, the chattering phenomenon. In the new Taylor‐based boundary layer ASMC scheme, the conventional ASMC is modified by removing the sign‐function in the vicinity of the sliding surface and using the Taylor expansion to estimate and compensate for the uncertainty. Compared to a time‐delay ASMC applied to a robot manipulator, the Taylor‐based ASMC scheme exhibits a less conservative sign‐function gain resulting in chattering attenuation.

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Section: A New Taylor-based Boundary Layer Asmc Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Taylor‐based adaptive sliding mode control method for robot manipulators

Fateh

Momeni

Masouleh

2023

IET Control Theory & Appl

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“…In our previous work, Taylor expansion was introduced to facilitate the controller design for the near-optimal control of affine nonlinear systems without input delay [21]- [23]. Different from [21]- [23], in this paper, Taylor expansion is used to facilitate the input delay estimation. Since the accuracy of the expansion depends on the residual term, an additional constraint on the second-order derivative of the input is introduced.…”

Section: Introductionmentioning

confidence: 99%

Input Delay Estimation for Input-Affine Dynamical Systems Based on Taylor Expansion

Zhang

Liao

2021

IEEE Trans. Circuits Syst. II

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Time delay is an important factor that degrades the performance of control systems in practice. While there are many existing results addressing the control problem of dynamical systems with known input delay or unknown delay but with conservative conclusions, how to effectively estimate unknown input delay is still a challenging problem. In this paper, we propose a novel method based on the Taylor expansion for the estimation of general input delay for a class of affine dynamical systems. Under mild conditions, the proposed method guarantees the asymptotic convergence of the estimation error to zero. Illustrative simulation examples are given to validate the theoretical result and the performance of the proposed method. In addition, an application to the input delay estimation of a continuous stirred tank reactor system is also presented to further show the effectiveness of the proposed method and its potential in practical systems.

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“…Therefore, optimal control has become one of the main topics of modern control theory [2]. Unlike the optimal control problem of linear systems, the optimal control problems of nonlinear systems usually require solving nonlinear Hamilton-Jacobi-Bellman (HJB) equations [3]. However, it is very difficult to solve nonlinear partial differential equations, even though some equations cannot be solved under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Nonlinear Near-Optimal Regulation Based on Multi-Dimensional Taylor Network Dynamic Programming

et al. 2020

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Using the data-driven control formulation, an iterative dynamic programming approach which is based on a multi-dimensional Taylor network is established to design the near optimal regulation of discrete-time nonlinear systems. For discrete-time general nonlinear systems, the iterative adaptive dynamic programming algorithm is developed and proved to guarantee the property of convergence and optimality. Three networks are constructed, namely, the identification network, critic network and action network. Moreover, a globalized dual heuristic programming technique with detailed implementation is developed. The cost function and its derivative can be approximated by this novel architecture. Besides, without the consideration of the system dynamics, this technique can learn the near-optimal control law simultaneously and adaptively. In addition, this technique greatly improves the existing results of the iterative adaptive dynamic programming algorithm in terms of reducing the requirement of the control matrix. Furthermore, because of the approach that is based on the multi-dimensional Taylor network, the amount of calculation needed is also greatly reduced. The simulation experiment is described to illustrate the effectiveness of the data-driven optimal regulation method proposed in this paper. INDEX TERMS Adaptive dynamic programming, data-driven control, multi-dimensional Taylor network, nonlinear control.

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Near-Optimal Control Without Solving HJB Equations and Its Applications

Cited by 24 publications

References 35 publications

Taylor‐based adaptive sliding mode control method for robot manipulators

Taylor‐based adaptive sliding mode control method for robot manipulators

Input Delay Estimation for Input-Affine Dynamical Systems Based on Taylor Expansion

Data-Driven Nonlinear Near-Optimal Regulation Based on Multi-Dimensional Taylor Network Dynamic Programming

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