Stochastic finite-time partial stability, partial-state stabilization, and finite-time optimal feedback control

Rajpurohit, Tanmay; Haddad, Wassim M.

doi:10.1007/s00498-017-0194-9

Cited by 27 publications

(7 citation statements)

References 30 publications

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“…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%

“…≡ 0 of the closed-loop system (27) is locally asymptotically stable in probability and, for every ∈ (0, 1), there exist = ( ) and (x(·))…”

Section: Theorem 3 (Rajpurohit and Haddad 1 )mentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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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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“…It is easy to verify that graph (D) is an undirected and connected topology. According to Theorem 2, the protocol (34) can solve fixed-time consensus problem of SMASs (3). That is to say, agents states converge to final state y(0) in fixed-time in probability, and associated T (x 0 , w) satisfies the following inequality:…”

Section: Proof Letmentioning

confidence: 99%

“…If Assumptions (i)-(iii) hold, then SMASs (3) with the protocol (2) can achieve fixed-time consensus in probability, and associated settling time T (x, 𝜔) satisfies E (T (x, 𝜔)) ≤ c, where c is a positive constant independent of initial conditions.…”

Section: Theorem 3 Consider Smas (3) Under a Detail-balanced Graph (A)mentioning

confidence: 99%

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

Yan

2020

IET Control Theory & Appl

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The paper devotes to study fixed‐time stability of stochastic nonlinear systems and fixed‐time consensus of stochastic multi‐agent systems (SMASs). Firstly, a new fixed‐time stability theorem is established and a high‐precise estimation of settling time is provided. Secondly, as an application, the fixed‐time consensus problem of SMASs is discussed in virtue of the established theorem. A new class of fixed‐time nonlinear consensus protocols with stochastic perturbation is designed by employing the neighbour's information. Based on graph theory, matrix theory and fixed‐time stability theorem, we prove that fixed‐time consensus of SMASs is achieved under the designed protocol. Moreover, some sufficient conditions are proposed to guarantee fixed‐time consensus of SMAS. It is shown that the settling time is not only independent of the initial conditions, but also it has higher precise. In the end, three numerical examples are provided to illustrate correctness of our theoretical results.

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The Role of Systems Biology, Neuroscience, and Thermodynamics in Network Control and Learning

Haddad

2021

Handbook of Reinforcement Learning and Control

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Stochastic finite-time partial stability, partial-state stabilization, and finite-time optimal feedback control

Cited by 27 publications

References 30 publications

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

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

Fixed‐time stability of stochastic nonlinear systems and its application into stochastic multi‐agent systems

The Role of Systems Biology, Neuroscience, and Thermodynamics in Network Control and Learning

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