Robust RHC for wheeled vehicles with bounded disturbances

Wang, Peng; Feng, Xinxi; Li, Weihua; Ping, Xubin; Yu, Wei

doi:10.1002/rnc.4478

Cited by 18 publications

(26 citation statements)

References 49 publications

(138 reference statements)

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“…Under tube‐based RHC framework, the initial constraint is usually presented in a general form 28,35

\begin{align} {bold-italicz}_{i} false(t_{k} false) \in {\overset{bold-italicz}{true}}_{i} false(t_{k} false| t_{k} false) \oplus 𝕊_{i}, \end{align}

with

𝕊_{i}

being a designed robust positively invariant (RPI) set so that any

z_{i} (τ)

{\overline{z}}_{i} (τ | t_{k}) \oplus 𝕆_{i}

will be maintained in it by an auxiliary controller

κ_{i} (\cdot, \cdot)

. For the simultaneous tracking and regulation problem of single perturbed wheeled vehicle, we have designed a RPI set and an auxiliary controller in our previous works 32,36 (see the set

𝕊

and controller

κ (\cdot, \cdot)

therein), and adopted them to design a RRHC controller 32,37 . Here we can directly adopt these designs with slight modification to design the initial constraint as

{\overline{z}}_{i} (t_{k} | t_{k}) \in 𝕆_{i}^{I} (z_{i} (t_{k})) ≜ \{|\}

…”

Section: Robust Distributed Rhc Controller Designmentioning

confidence: 99%

“…Following the procedures in Sections 3.1 and 3.2 of our previous work, 32 the actually evolved state

z_{i} (τ) \in ℤ_{i}

can be guaranteed for all

τ \geq t_{k}

by constraining nominal predictive state as

c_{i, l} ({\overline{x}}_{i} (τ | t_{k}), {\overline{y}}_{i} (τ | t_{k}), {\overline{θ}}_{i} (τ | t_{k})) \leq {\overline{c}}_{i, l}^{M} ≜ c_{i, l}^{M} - \max_{μ_{x}, μ_{y}, μ_{θ} \in \{- 1, 1\}} c_{i, l} (μ_{x} η_{i}^{I}, μ_{y} η_{i}^{I}, μ_{θ} α_{i, 4}^{I}), l = 1, 2, \dots, s,

and the actual implemented control input

u_{i} (τ) \in 𝕌_{i}

can be guaranteed for all

τ \geq t_{k}

by constraining nominal predictive control input as …”

Section: Robust Distributed Rhc Controller Designmentioning

confidence: 99%

“…For design simplicity, we firstly transform the nominal tracking error

{\overline{z}}_{i r}

into vehicle‐based coordinate as

{\tilde{\overline{z}}}_{i r} (τ | t_{k}) = [{\tilde{\overline{x}}}_{i r} (τ | t_{k}); {\tilde{\overline{y}}}_{i r} (τ | t_{k}); {\tilde{\overline{θ}}}_{i r} (τ | t_{k})] = Φ ({\overline{θ}}_{i} (τ | t_{k})) {\overline{z}}_{i r} (τ | t_{k}) .

Then following the procedure in Section 3.3 of our previous work, 32 conditions (25a) and (25b) can be easily guaranteed by imposing the following constraints

\begin{align} (||, {\overset{\overset{y}{true}}{true}}_{i r} false(τ false| t_{k} false)) \leq a_{i, 1}^{T} (||, {\overset{\overset{x}{true}}{true}}_{i r} false(τ false| t_{k} false) {\overset{\overset{θ}{true}}{true}}_{i r} false(τ false| t) \end{align}

…”

Section: Robust Distributed Rhc Controller Designmentioning

confidence: 99%

“…In contrast, the tube‐based approach constructs optimal control problem in the nominal form by tightening the constraint to directly handle bounded uncertainties, hence its computational complexity is comparable to that of nominal (conventional) RHC. Due to less complexity of its control optimization problem, the tube‐based RHC framework is preferred for robust case, and a synthesis approach is successfully proposed in our previous work 32 for the STRP of single perturbed wheeled vehicle. In this article, the proposed approach is extended for distributed case to address the simultaneous tracking, regulation and formation problem of multiple perturbed wheeled vehicles with collision avoidance.…”

Section: Introductionmentioning

confidence: 99%

“…By first extending the tube‐based RHC proposed for the STRP of single wheeled vehicle in our previous work, 32 the divergence between actually evolved and nominal predictive state trajectories caused by external disturbances can be successfully handled, which leads to the nominal form of control optimization problem. Then through elaborately designing the collision avoidance and compatibility constraints in this article, the recursive feasibility of optimization problem and safety of vehicles can be efficiently guaranteed, which further contributes to ensure convergence of tracking, regulation and formation.…”

Section: Introductionmentioning

confidence: 99%

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A robust distributed receding horizon control synthesis approach for simultaneous tracking, regulation and formation of multiple perturbed wheeled vehicles with collision avoidance

Wang

Feng

et al. 2021

Intl J Robust & Nonlinear

Self Cite

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This article proposes a robust distributed receding horizon control (RDRHC) synthesis approach for the simultaneous tracking, regulation and formation of multiple perturbed wheeled vehicles with collision avoidance. By successfully extending a tube‐based RHC approach proposed in our previous work and elaborately designing the collision avoidance and compatibility constraints, a nominal control optimization problem is constructed for each vehicle with recursive feasibility guarantee, and the associated RDRHC algorithms with and without on‐line optimization are presented for implementation. By applying the presented algorithms, the multiple perturbed wheeled vehicles can be steered to achieve the desired tracking, regulation and formation objective with satisfying the pre‐specified constraints and avoiding collision. Both theoretical properties and practical effectiveness of the proposed approach are verified through a simulation example.

show abstract

“…Under tube‐based RHC framework, the initial constraint is usually presented in a general form 28,35

\begin{align} {bold-italicz}_{i} false(t_{k} false) \in {\overset{bold-italicz}{true}}_{i} false(t_{k} false| t_{k} false) \oplus 𝕊_{i}, \end{align}

with

𝕊_{i}

being a designed robust positively invariant (RPI) set so that any

z_{i} (τ)

{\overline{z}}_{i} (τ | t_{k}) \oplus 𝕆_{i}

will be maintained in it by an auxiliary controller

κ_{i} (\cdot, \cdot)

. For the simultaneous tracking and regulation problem of single perturbed wheeled vehicle, we have designed a RPI set and an auxiliary controller in our previous works 32,36 (see the set

𝕊

and controller

κ (\cdot, \cdot)

therein), and adopted them to design a RRHC controller 32,37 . Here we can directly adopt these designs with slight modification to design the initial constraint as

{\overline{z}}_{i} (t_{k} | t_{k}) \in 𝕆_{i}^{I} (z_{i} (t_{k})) ≜ \{|\}

…”

Section: Robust Distributed Rhc Controller Designmentioning

confidence: 99%

“…Following the procedures in Sections 3.1 and 3.2 of our previous work, 32 the actually evolved state

z_{i} (τ) \in ℤ_{i}

can be guaranteed for all

τ \geq t_{k}

by constraining nominal predictive state as

c_{i, l} ({\overline{x}}_{i} (τ | t_{k}), {\overline{y}}_{i} (τ | t_{k}), {\overline{θ}}_{i} (τ | t_{k})) \leq {\overline{c}}_{i, l}^{M} ≜ c_{i, l}^{M} - \max_{μ_{x}, μ_{y}, μ_{θ} \in \{- 1, 1\}} c_{i, l} (μ_{x} η_{i}^{I}, μ_{y} η_{i}^{I}, μ_{θ} α_{i, 4}^{I}), l = 1, 2, \dots, s,

and the actual implemented control input

u_{i} (τ) \in 𝕌_{i}

can be guaranteed for all

τ \geq t_{k}

by constraining nominal predictive control input as …”

Section: Robust Distributed Rhc Controller Designmentioning

confidence: 99%

“…For design simplicity, we firstly transform the nominal tracking error

{\overline{z}}_{i r}

into vehicle‐based coordinate as

{\tilde{\overline{z}}}_{i r} (τ | t_{k}) = [{\tilde{\overline{x}}}_{i r} (τ | t_{k}); {\tilde{\overline{y}}}_{i r} (τ | t_{k}); {\tilde{\overline{θ}}}_{i r} (τ | t_{k})] = Φ ({\overline{θ}}_{i} (τ | t_{k})) {\overline{z}}_{i r} (τ | t_{k}) .

Then following the procedure in Section 3.3 of our previous work, 32 conditions (25a) and (25b) can be easily guaranteed by imposing the following constraints

\begin{align} (||, {\overset{\overset{y}{true}}{true}}_{i r} false(τ false| t_{k} false)) \leq a_{i, 1}^{T} (||, {\overset{\overset{x}{true}}{true}}_{i r} false(τ false| t_{k} false) {\overset{\overset{θ}{true}}{true}}_{i r} false(τ false| t) \end{align}

…”

Section: Robust Distributed Rhc Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A robust distributed receding horizon control synthesis approach for simultaneous tracking, regulation and formation of multiple perturbed wheeled vehicles with collision avoidance

Wang

Feng

et al. 2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

Grey‐prediction‐based double model predictive control strategy for the speed and current control of permanent magnet synchronous motor

Pan

Huang

Guan

et al. 2022

Asian Journal of Control

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To solve the problems of slow response speed of the permanent magnet synchronous motor (PMSM) system when the external disturbance occurs and the poor disturbance rejection performance, a double model predictive control (MPC) strategy for PMSM to control speed and current is proposed in this paper. Further, in order to improve the dynamic performance and disturbance rejection performance of PMSM control system, a grey prediction is introduced, and then a grey‐prediction‐based double MPC strategy is proposed. To be specific, firstly, the mathematical model of PMSM is established under the dq coordinate system, and the traditional control strategy (outer speed loop PI controller and inner current loop deadbeat prediction controller) is elaborated. Secondly, we propose the double MPC strategy where MPC controller is used in the outer speed loop and deadbeat prediction controller is used in the inner current loop. Finally, the grey‐prediction‐based double MPC strategy is proposed where MPC is combined with grey prediction to improve the dynamic performance in the inner current loop. By comparing the traditional control strategy with the double MPC and the grey‐prediction‐based double MPC strategy, the simulation results show that the double MPC and the grey‐prediction‐based double MPC system have no overshoot and the grey‐prediction‐based double MPC system has better steady‐state performance, faster dynamic response and stronger disturbance rejection performance, which proves the effectiveness of the proposed strategy.

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Interval state estimation‐based robust model predictive control for linear parameter varying systems

Ping

Yang

Xiao³

et al. 2021

Intl J Robust & Nonlinear

Self Cite

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For linear parameter varying (LPV) systems with unknown system states, this article investigates an interval state estimation-based robust model predictive control algorithm. Two interval state estimation approaches, including interval observer systems and zonotope-based box computations, are considered to estimate the upper and lower bounds of system states. The on-line interval estimation error boxes are contained within the scaled and time-varying ellipsoidal robust positively invariant sets. Then, the centers of the state constraint boxes are steered to a region near the origin. When the interval estimation error boxes and the centers of state constraint boxes simultaneously converge to the neighborhood of the origin, the controlled LPV systems are robust stable. K E Y W O R D Sinterval observer, LPV systems, model predictive control, output feedback, set-membership estimation INTRODUCTIONRobust model predictive control (RMPC) has the abilities to predict system future behaviors based on process models, and incorporate both system uncertainties and physical constraints in receding horizon optimal control problems. [1][2][3][4][5] In some practical processes, full system states or partial system states are often difficult to measure and exogenous disturbances and/or noises exist. In these situations, output feedback RMPC is often more practical for real processes with unknown system states. For the researches on output feedback RMPC approaches, it is often required to design the state observer system to estimate system true states. Nevertheless, to satisfy robust stability and physical constraints, it is important to obtain time-varying estimation error bounds. Linear parameter varying (LPV) systems, whose characteristics are dependent on scheduling parameters and bounded in prespecified convex sets, are applicable for representing system nonlinearity and uncertainty. 6 Output feedback RMPC approaches for LPV systems with bounded disturbances and/or noises have been extensively studied. The output feedback RMPC in works 7-10 consider that ellipsoidal estimation error sets are time-varying ellipsoidal robust positively invariant 7026

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Robust RHC for wheeled vehicles with bounded disturbances

Cited by 18 publications

References 49 publications

A robust distributed receding horizon control synthesis approach for simultaneous tracking, regulation and formation of multiple perturbed wheeled vehicles with collision avoidance

A robust distributed receding horizon control synthesis approach for simultaneous tracking, regulation and formation of multiple perturbed wheeled vehicles with collision avoidance

Grey‐prediction‐based double model predictive control strategy for the speed and current control of permanent magnet synchronous motor

Interval state estimation‐based robust model predictive control for linear parameter varying systems

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