Finite-Time Stabilization of Stochastic High-Order Nonlinear Systems With FT-SISS Inverse Dynamics

Jiang, Mengmeng; Xie, Xue‐Jun; Zhang, Kemei

doi:10.1109/tac.2018.2827993

Cited by 115 publications

(61 citation statements)

References 27 publications

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“…Convergence analysis By Lemma , the following inequality holds:

\begin{matrix} alignleft \\ align-1 \sum_{l = 2}^{n} Ψ_{l} & align-2 = \sum_{l = 2}^{n} \int_{ξ_{l}}^{x_{l}} {⌈{⌈ r ⌉}^{\frac{θ}{v_{l}}} - {⌈ ξ_{l} ⌉}^{\frac{θ}{v_{l}}}⌉}^{\frac{4 θ - σ - v_{l}}{θ}} d r \\ align-1 & align-2 \geq \sum_{l = 2}^{n} 2^{\frac{v_{l}}{θ} - 1} \int_{ξ_{l}}^{x_{l}} {(r - ξ_{l})}^{\frac{4 θ - σ - v_{l}}{v_{l}}} d r \\ align-1 & align-2 = \sum_{l = 2}^{n} a_{l} | x_{l} - ξ_{l} |^{\frac{4 θ - σ}{v_{l}}}, \end{matrix}

for positive constants a l ( l =2,…, n ). Discussed as in the work of Jiang et al, we know that

\sum_{l = 2}^{n} {normalΨ}_{l}

is radially unbounded. Since

V_{n} = V_{1} + \sum_{l = 2}^{n} {normalΨ}_{l}

, the radial unboundednes...…”

Section: Resultsmentioning

confidence: 99%

“…It can be found that the stabilization problem for such a kind of nonlinear stochastic system faces many difficulties. Fortunately, the state‐feedback stabilization problem of high‐order stochastic nonlinear systems may be solved by the adding a power integrator method and the Lyapunov‐based recursive design technique . However, it should be noted that the fractional powers of the high‐order systems considered in the existing literature are all required to be not less than one.…”

Section: Introductionmentioning

confidence: 99%

“…Fortunately, the state-feedback stabilization problem of high-order stochastic nonlinear systems may be solved by the adding a power integrator method and the Lyapunov-based recursive design technique. [23][24][25][26] However, it should be noted that the fractional powers of the high-order systems considered in the existing literature are all required to be not less than one. There are few results on finite-time stabilization of high-order stochastic nonlinear systems where the fractional powers are allowed to be any positive odd rational numbers.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Fang

Ding

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, the robust stabilization problem is addressed for a class of high‐order stochastic nonlinear systems with output constraints and disturbances by using finite‐time control technique. One of the features of the considered stochastic systems is that the fractional powers are allowed to be any positive odd rational numbers, rather than grater than or equal to one. By constructing a novel tan‐type barrier Lyapunov function and using the adding a power integrator technique, the explicit steps on how to construct a backstepping‐like finite‐time controller have been developed to handle the robust stabilization and output constraint. Rigorous mathematical proof shows that the system states will finite‐time converge to a small region of the origin and the output constraint can be kept. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

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“…Convergence analysis By Lemma , the following inequality holds:

\begin{matrix} alignleft \\ align-1 \sum_{l = 2}^{n} Ψ_{l} & align-2 = \sum_{l = 2}^{n} \int_{ξ_{l}}^{x_{l}} {⌈{⌈ r ⌉}^{\frac{θ}{v_{l}}} - {⌈ ξ_{l} ⌉}^{\frac{θ}{v_{l}}}⌉}^{\frac{4 θ - σ - v_{l}}{θ}} d r \\ align-1 & align-2 \geq \sum_{l = 2}^{n} 2^{\frac{v_{l}}{θ} - 1} \int_{ξ_{l}}^{x_{l}} {(r - ξ_{l})}^{\frac{4 θ - σ - v_{l}}{v_{l}}} d r \\ align-1 & align-2 = \sum_{l = 2}^{n} a_{l} | x_{l} - ξ_{l} |^{\frac{4 θ - σ}{v_{l}}}, \end{matrix}

for positive constants a l ( l =2,…, n ). Discussed as in the work of Jiang et al, we know that

\sum_{l = 2}^{n} {normalΨ}_{l}

is radially unbounded. Since

V_{n} = V_{1} + \sum_{l = 2}^{n} {normalΨ}_{l}

, the radial unboundednes...…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Fang

Ding

et al. 2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Extensions of this framework for exploring connections between optimal finite‐time stabilization and finite‐time stabilization for stochastic dynamical systems are currently under development. The proposed framework can also allow us to further explore connections with stochastic inverse optimal control, stochastic dissipativity, and stability margins for finite‐time stabilizing regulators that minimize a derived cost functional involving subquadratic terms.…”

Section: Resultsmentioning

confidence: 99%

“…These results provide a generalization of the deterministic meaningful inverse optimal nonlinear regulator stability margins and the classical linear-quadratic optimal regulator gain and phase margins to stochastic nonlinear feedback regulators. Extensions of this framework for exploring connections between optimal finite-time stabilization 27,28 and finite-time stabilization 29 for stochastic dynamical systems are currently under development. The proposed framework can also allow us to further explore connections with stochastic inverse optimal control, stochastic dissipativity, and stability margins for finite-time stabilizing regulators that minimize a derived cost functional involving subquadratic terms.…”

Section: Resultsmentioning

confidence: 99%

Implications of dissipativity, inverse optimal control, and stability margins for nonlinear stochastic feedback regulators

Haddad

Jin

2019

Intl J Robust & Nonlinear

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Summary In this paper, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton‐Jacobi‐Bellman controllers that minimize a nonlinear‐nonquadratic performance criterion with cross‐weighting terms. Furthermore, using the newly developed notion of stochastic dissipativity, we derive a return difference inequality to provide connections between stochastic dissipativity and optimality of nonlinear controllers for stochastic dynamical systems. In particular, using extended Kalman‐Yakubovich‐Popov conditions characterizing stochastic dissipativity, we show that our optimal feedback control law satisfies a return difference inequality predicated on the infinitesimal generator of a controlled Markov diffusion process if and only if the controller is stochastically dissipative with respect to a specific quadratic supply rate.

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Enhanced adaptive control for a benchmark piezoelectric‐actuated system via fuzzy approximation

Yousef

Hamdy

Saleem

et al. 2019

Adaptive Control & Signal

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This paper investigates the problem of the high precision tracking control of piezoelectric actuators (PEAs) without using the inverse of the uncertain hysteresis. Based on fuzzy system approximator and particle swarm optimization (PSO) algorithm, a proposed enhanced  adaptive controller is developed. The proposed controller provides fast and robust adaptation simultaneously with guaranteed desired transient performance. Moreover, it has a simple form and requires fewer adaptation parameters. The adaptation gain is determined via PSO algorithm. The proposed controller is tested on a lab-scale PEA system.Experimental results with comparative studies with different techniques have been developed. The simulation results reveal that the proposed controller outperforms the other controllers in terms of normalized root-mean-square and maximum tracking errors for different frequencies.

show abstract

Finite-Time Stabilization of Stochastic High-Order Nonlinear Systems With FT-SISS Inverse Dynamics

Cited by 115 publications

References 27 publications

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances

Implications of dissipativity, inverse optimal control, and stability margins for nonlinear stochastic feedback regulators

Enhanced adaptive control for a benchmark piezoelectric‐actuated system via fuzzy approximation

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