The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems

Tuffaha, Amjad

doi:10.1007/s00245-023-09969-1

Cited by 4 publications

(8 citation statements)

References 53 publications

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“…According to optimal control theory [28], the linear quadratic regulator optimization controller in the infinite horizon is closed-loop stable. Then, lim a→∞ x T a|k Px a|k = 0 is established and Equation ( 18) can be expressed as…”

Section: Qih-mpc For Usv Path Followingmentioning

confidence: 99%

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Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following

Li,

Zhou,

Zhang

2024

JMSE

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As a flexible, autonomous and intelligent motion platform, underactuated surface vessels (USVs) are expected to be an ideal means of transport in dangerous and complex marine environments. The success and efficiency of maritime missions performed by USVs depend on their ability to accurately follow paths and remain robust against wind and wave disturbances. To this end, this paper focuses on accurate and robust path following control for USVs under wave disturbances. Model predictive control with a quasi-infinite horizon is proposed which converts the objective function from an infinite horizon to an approximate finite horizon, providing the convergence performance in long prediction horizons and reducing the computation load explicitly. To enhance robustness against disturbances, a fixed-time disturbance observer is applied to estimate the time-varying and bounded disturbances. The estimated value is provided to the controller input to form a robust control framework with disturbance feedforward compensation and predictive control feedback correction, which is substantially different from existing works. The convergence and optimality of the proposed algorithm are presented mathematically. Finally, we demonstrate the advantages of the algorithm in both theory and simulation.

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Section: Qih-mpc For Usv Path Followingmentioning

confidence: 99%

“…x 3 = Ux 2 (28) where d(F wave , M wave ) denotes the aggregate bounded disturbance imposed by the disturbance force and moment. We define the tracking error as…”

Section: Fixed-time Observer (Fto) For Disturbance Estimationmentioning

confidence: 99%

Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following

Li,

Zhou,

Zhang

2024

JMSE

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“…Specifically, optimal feedback controls for LQ problems of SEEs are studied in [10,11,12,13,18,19,21,25]. To our best knowledge, [25] is the only published result for SEEs with control-dependent diffusion terms on the infinite time horizon, in which the author set the control weight operator R equal to the identity operator. It is worth noting that a key feature for LQ problems of SDEs/SEEs is that one does not need to assume that R is positive definite.…”

mentioning

confidence: 99%

“…Since we assume that B ∈ L(U ; H) and D ∈ L(U ; L 2 (V ; H)), the main result of this paper (Theorem 3.3) can only be applied to controlled stochastic partial differential equations with internal distributed controls. It is worth noting that, by borrowing some techniques in [25], the proofs in this paper can also be applied when B is an admissible control operator. Nevertheless, to present the key idea in the simplest way, we do not pursue the full technical generality.…”

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confidence: 99%

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Linear quadratic optimal control problems for stochastic evolution equations in infinite horizon

Lü

2024

MCRF

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We study linear quadratic optimal control problems for stochastic evolution equations in an infinite horizon with constant coefficients. We first give a characterization of the non-emptiness of the admissible control set for all initial states by an operator-valued algebraic Lyapunov equation. Then we demonstrate the equivalence between the existence of an optimal control with suitable a prori bound and the existence of an optimal feedback control. This stands in contrast to the stochastic linear quadratic optimal control problems in a finite time horizon. Finally, we prove that the optimal feedback control can be determined via a generalized operator-valued algebraic Riccati equation. 2020 Mathematics Subject Classification. Primary: 93E20. Key words and phrases. Stochastic linear quadratic optimal control problem, infinite time horizon, operator-valued algebraic Riccati equation.

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Stochastic linear–quadratic control problems with affine constraints

Gou,

Huang,

Long

et al. 2024

Systems & Control Letters

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The Stochastic Linear Quadratic Optimal Control Problem on Hilbert Spaces: The Case of Non-analytic Systems

Cited by 4 publications

References 53 publications

Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following

Quasi-Infinite Horizon Model Predictive Control with Fixed-Time Disturbance Observer for Underactuated Surface Vessel Path Following

Linear quadratic optimal control problems for stochastic evolution equations in infinite horizon

Stochastic linear–quadratic control problems with affine constraints

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