H<sub>∞</sub> Tracking Control of Discrete-Time System With Delays via Data-Based Adaptive Dynamic Programming

Liu, Yang; Zhang, Huaguang; Yu, Rui; Xing, Zuoxia

doi:10.1109/tsmc.2019.2946397

Cited by 49 publications

(26 citation statements)

References 53 publications

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“…Suppose that the transition rates are completely known. Suppose that the sliding function is given in (14) where K i and P i satisfy (45). For given positive scalar ν if the control law is designed as…”

Section: Corollarymentioning

confidence: 99%

“…The transition rate matrix is given as Then, the sliding surface can be computed by (14). Let the adjustable parameter ν = 0.2, then the SMC law can be obtained by (46).…”

Section: Remarkmentioning

confidence: 99%

“…We assume that the system is affected by uncertain parameters and external disturbances. Thus, the other parameters for the four modes are given as follows: Then, the sliding surface can be computed by (14). Let the adjustable parameter ν = 0.01, then the SMC law can be obtained by (45).…”

Section: Remarkmentioning

confidence: 99%

“…However, there are still several interesting and relevant problems to be addressed. On the other hand, robust control theory and methods have been the focus of the control community in recent decades [14]- [17]. Sliding mode control technology is one of the powerful means of robust controller design.…”

Section: Introductionmentioning

confidence: 99%

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Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Sun

Ren

et al. 2020

IEEE Access

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This paper investigates the problem of sliding mode control (SMC) for one-sided Lipschitz (OSL) nonlinear Markovian jump systems with partially unknown transition rates. Unmatched normbounded uncertainties of state matrices and output matrices are considered. First, a suitable integral-type sliding surface is proposed and a sufficient condition is given such that the sliding mode dynamics is stochastically stable with an H ∞ performance level γ. Next, a SMC law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, two simulation examples are provided to prove the effectiveness of the proposed approach. INDEX TERMS Markovian jump systems, partially unknown transition rates, sliding mode control, onesided Lipschitz.

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Section: Corollarymentioning

confidence: 99%

“…The transition rate matrix is given as Then, the sliding surface can be computed by (14). Let the adjustable parameter ν = 0.2, then the SMC law can be obtained by (46).…”

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Sun

Ren

et al. 2020

IEEE Access

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“…Data-driven research utilizes real-life data measured by sensory sources to achieve the intrinsic information of systems [30] and can solve the problems of switched systems with unknown subsystems, such as the data-driven framework for discovering cyber-physical systems directly from the data [31]. Thereinto, data-driven ADP approaches provide possible solutions for optimal control problems of switched systems [32][33][34] and based on that, the following approach is designed to adapt to the complexity of switched systems which is brought by switching. Then in this paper, the data-driven optimal scheduling approach is investigated for continuous-time switched systems with unknown subsystems.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Suboptimal Scheduling of Switched Systems

Zhang

Gan

Zhao

et al. 2020

Sensors

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In this paper, a data-driven optimal scheduling approach is investigated for continuous-time switched systems with unknown subsystems and infinite-horizon cost functions. Firstly, a policy iteration (PI) based algorithm is proposed to approximate the optimal switching policy online quickly for known switched systems. Secondly, a data-driven PI-based algorithm is proposed online solely from the system state data for switched systems with unknown subsystems. Approximation functions are brought in and their weight vectors can be achieved step by step through different data in the algorithm. Then the weight vectors are employed to approximate the switching policy and the cost function. The convergence and the performance are analyzed. Finally, the simulation results of two examples validate the effectiveness of the proposed approaches.

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Data‐based robust optimal control of discrete‐time systems with uncertainties via adaptive dynamic programming

Liu

Xing

Chen

et al. 2021

Optim Control Appl Methods

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In this article, a new data-based adaptive dynamic programming algorithm is proposed to solve the optimal control policy for discrete-time systems with uncertainties. Firstly, for uncertain systems, the corresponding Hamiltonian function is designed, and then the robust adaptive dynamic programming algorithm is obtained. Next, by using the input and output data of the system, the data-based Bellman equation is constructed, and the data-based robust adaptive dynamic programming algorithm is derived, which does not require the accurate model of the system. Finally, a simulation example shows the effectiveness of the proposed algorithm.

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H_∞ Tracking Control of Discrete-Time System With Delays via Data-Based Adaptive Dynamic Programming

Cited by 49 publications

References 53 publications

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Data-Driven Suboptimal Scheduling of Switched Systems

Data‐based robust optimal control of discrete‐time systems with uncertainties via adaptive dynamic programming

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H∞ Tracking Control of Discrete-Time System With Delays via Data-Based Adaptive Dynamic Programming

Cited by 49 publications

References 53 publications

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Data-Driven Suboptimal Scheduling of Switched Systems

Data‐based robust optimal control of discrete‐time systems with uncertainties via adaptive dynamic programming

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H_∞ Tracking Control of Discrete-Time System With Delays via Data-Based Adaptive Dynamic Programming