An inverse optimal approach to design of feedback control: Exploring analytical solutions for the Hamilton‐Jacobi‐Bellman equation

Komaee, Arash

doi:10.1002/oca.2686

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…where the mathematical notation () + indicates the Moore-Penrose inverse. 41 Remark 5. Theorem 1 meets Lagrange's form of D'Alembert's principle, and it formalizes the minimum constraint force rendering constraints (18) to be satisfied.…”

Section: Assumption 2 the Inertia Matrix H(x(t) 𝛿(T) T) Is Positive D...mentioning

confidence: 99%

“…Theorem Assume the uncertainty set

δ (t)

is known and Assumptions and are always satisfied in the underactuated mechanical system ( ). The control force

Q^{c}

(i.e., constraint force) rendering the nominal system ( ) to satisfy servo constraints ( ) for all

(x, \dot{x}, t) \in R^{n} \times R^{n} \times R

can be represented as :

Q^{c} (x, \dot{x}, t) = {(ℜ (x, t) H^{- 1} (x, t) B)}^{+} [b (x, \dot{x}, t) + ℜ (x, t) H^{- 1} (x, t) (C (x, \dot{x}, t) \dot{x} + T (x, \dot{x}, t))],

where the mathematical notation

{()}^{+}

indicates the Moore–Penrose inverse 41 …”

Section: Underactuated Mechanical Systems With Fuzzy Evidence Number ...mentioning

confidence: 99%

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Nash game‐based adaptive robust control design optimization for the underactuated mechanical system with fuzzy evidence theory

Zheng

Zhao

2021

Optim Control Appl Methods

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This article proposes a novel Nash game‐theoretical optimal adaptive robust control design approach to address the constraint‐following control problem for the uncertain underactuated mechanical systems with fuzzy evidence theory. First, the uncertainty is considered bounded and the bound is unknown but lies in a specified fuzzy evidence number. Second, a deterministic adaptive robust control scheme is proposed based on the servo constraint following control method, which renders the uncertain underactuated mechanical system to follow the specified constraints accurately with deterministic performance (guarantee uniform boundedness and uniform ultimate boundedness). It is shown that the designed self‐adjusting leakage‐type adaptive law can compensate for the uncertainty and avoid overcompensation. Third, based on the performance analysis and the fuzzy evidence description of uncertainty, the Nash game theory is introduced into the multi‐parameter optimization design for the two tunable control gains selected as two players. The cost functions for two players are relevant to the system constraint‐following performance and control cost. Then we can obtain the optimal control gains by seeking the Nash equilibrium which is always proved to exist. Ultimately, the simulation results on the two‐wheeled self‐balancing robot demonstrate the availability of the proposed control scheme and the optimal design approach for the underactuated mechanical systems with uncertainties.

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Section: Assumption 2 the Inertia Matrix H(x(t) 𝛿(T) T) Is Positive D...mentioning

confidence: 99%

“…Theorem Assume the uncertainty set

δ (t)

is known and Assumptions and are always satisfied in the underactuated mechanical system ( ). The control force

Q^{c}

(i.e., constraint force) rendering the nominal system ( ) to satisfy servo constraints ( ) for all

(x, \dot{x}, t) \in R^{n} \times R^{n} \times R

can be represented as :

Q^{c} (x, \dot{x}, t) = {(ℜ (x, t) H^{- 1} (x, t) B)}^{+} [b (x, \dot{x}, t) + ℜ (x, t) H^{- 1} (x, t) (C (x, \dot{x}, t) \dot{x} + T (x, \dot{x}, t))],

where the mathematical notation

{()}^{+}

indicates the Moore–Penrose inverse 41 …”

Section: Underactuated Mechanical Systems With Fuzzy Evidence Number ...mentioning

confidence: 99%

Nash game‐based adaptive robust control design optimization for the underactuated mechanical system with fuzzy evidence theory

Zheng

Zhao

2021

Optim Control Appl Methods

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A Simple Model on Streamflow Management with a Dynamic Risk Measure

Yoshioka

2022

Proceedings of the Seventh International Conference on Mathematics and Computing

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We present an exactly-solvable risk-minimizing stochastic differential game for flood management in rivers. The streamflow dynamics follow stochastic differential equations driven by a Lévy process. An entropic dynamic risk measure is employed to evaluate a flood risk under model uncertainty. The problem is solved via a Hamilton-Jacobi-Bellman-Isaacs equation. We explicitly derive an optimal flood mitigation policy along with its existence criteria and the worst-case probability measure. A backward stochastic differential representation as an alternative formulation is also presented.

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Generalized Pair-Wise Logit Dynamic and Its Connection to a Mean Field Game: Theoretical and Computational Investigations Focusing on Resource Management

Yoshioka,

Tsujimura

2024

Dyn Games Appl

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An inverse optimal approach to design of feedback control: Exploring analytical solutions for the Hamilton‐Jacobi‐Bellman equation

Cited by 5 publications

References 20 publications

Nash game‐based adaptive robust control design optimization for the underactuated mechanical system with fuzzy evidence theory

Nash game‐based adaptive robust control design optimization for the underactuated mechanical system with fuzzy evidence theory

A Simple Model on Streamflow Management with a Dynamic Risk Measure

Generalized Pair-Wise Logit Dynamic and Its Connection to a Mean Field Game: Theoretical and Computational Investigations Focusing on Resource Management

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