Fast Funnel Computation Using Multivariate Bernstein Polynomial

Seo, Hoseong; Son, Clark Youngdong; Kim, H. Jin

doi:10.1109/lra.2021.3057569

Cited by 8 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and the ellipsoid variable {Q k } N k=0 can be obtained via solving (20) with w trf = 0 while ignoring the funnel feasibility. The second way is more systematical since it exploits the result of the separate synthesis and hence gives a better initial guess compared to the solution computed by the straight-line interpolation in the first way.…”

Section: Algorithm Details and Summarymentioning

confidence: 99%

“…Hence, their method is one shot procedure where the nominal trajectory is computed first, and then the computation of the funnel follows. The similar one shot approaches are conducted in References 20 and 21 For the fast computation of the CIF, the work in Reference 20 formulates an optimization problem for establishing the CIF as a linear program (LP) which is computationally cheaper than SOS programming. This research is extended to consider piecewise polynomial systems in Reference 21 These works, however, do not consider the controller synthesis, and hence focus on obtaining the reachable set (funnel) of the given (polynomial) closed‐loop system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Joint synthesis of trajectory and controlled invariant funnel for discrete‐time systems with locally Lipschitz nonlinearities

Kim,

Elango,

Açıkmeşe

2024

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (CIF) for locally Lipschitz nonlinear systems subject to bounded disturbances. The CIF synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. In contrast to existing CIF synthesis methods that compute the CIF with a predefined nominal trajectory, our work aims to optimize the nominal trajectory and the CIF jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost‐optimal nominal trajectory. The proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. The trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the CIF. Then, the funnel update step computes the funnel around the nominal trajectory so that the CIF guarantees an invariance property. As a result, with the optimized trajectory and CIF, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. We validate the proposed method via two applications from robotics.

show abstract

Section: Algorithm Details and Summarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Joint synthesis of trajectory and controlled invariant funnel for discrete‐time systems with locally Lipschitz nonlinearities

Kim,

Elango,

Açıkmeşe

2024

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…The studies in funnel synthesis can be separated into two categories depending on whether they aim to maximize [3], [4], [5] or minimize the size of the funnel [2], [6], [7]. The funnel computation inherently aims to maximize the size of the funnel to have a larger controlled invariant set in the state space.…”

Section: Introductionmentioning

confidence: 99%

Optimization-based Constrained Funnel Synthesis for Systems with Lipschitz Nonlinearities via Numerical Optimal Control

Kim¹,

Elango²,

Reynolds³

et al. 2023

Preprint

View full text Add to dashboard Cite

This paper presents a funnel synthesis algorithm for computing controlled invariant sets and feedback control gains around a given nominal trajectory for dynamical systems with locally Lipschitz nonlinearities and bounded disturbances. The resulting funnel synthesis problem involves a differential linear matrix inequality (DLMI) whose solution satisfies a Lyapunov condition that implies invariance and attractivity properties. Due to these properties, the proposed method can balance maximization of initial invariant funnel size, i.e., size of the funnel entry, and minimization of the size of the attractive funnel for disturbance attenuation. To solve the resulting funnel synthesis problem with the DLMI as one of the problem constraints, we employ a numerical optimal control approach that uses a multiple shooting method to convert the problem into a finite dimensional semidefinite programming problem. This framework avoids the need for piecewise linear system matrices and funnel parameters, which are typically assumed in recent related work. We illustrate the proposed funnel synthesis method with a numerical example.

show abstract

“…Introducing fast-solving methods for the HJB equation reduces the computational time for TRCC command generation [24,25]. However, the current direct solution approaches for the HJB equation mentioned above remain insufficient to meet the demands of online applications.…”

Section: Introductionmentioning

confidence: 99%

Fast Tube-Based Robust Compensation Control for Fixed-Wing UAVs

Wang

Zheng

Wang³

et al. 2023

Drones

View full text Add to dashboard Cite

When considering the robust control of fixed-wing Unmanned Aerial Vehicles (UAVs), a conflict often arises between addressing nonlinearity and meeting fast-solving requirements. In existing studies, the less nonlinear robust control methods have shown significant improvements that parallel computing and dimensionality reduction techniques in real-time applications. In this paper, a nonlinear fast Tube-based Robust Compensation Control (TRCC) for fixed-wing UAVs is proposed to satisfy robustness and fast-solving requirements. Firstly, a solving method for discrete trajectory tubes was proposed to facilitate fast parallel computation. Subsequently, a TRCC algorithm was developed that minimized the trajectory tube to enhance robustness. Additionally, considering the characteristics of fixed-wing UAVs, dimensionality reduction techniques such as decoupling and stepwise approaches are proposed, and a fast TRCC algorithm that incorporates the control reuse method is presented. Finally, simulations verify that the proposed fast TRCC effectively enhances the robustness of UAVs during tracking tasks while satisfying the requirements for fast solving.

show abstract

Fast Funnel Computation Using Multivariate Bernstein Polynomial

Cited by 8 publications

References 15 publications

Joint synthesis of trajectory and controlled invariant funnel for discrete‐time systems with locally Lipschitz nonlinearities

Joint synthesis of trajectory and controlled invariant funnel for discrete‐time systems with locally Lipschitz nonlinearities

Optimization-based Constrained Funnel Synthesis for Systems with Lipschitz Nonlinearities via Numerical Optimal Control

Fast Tube-Based Robust Compensation Control for Fixed-Wing UAVs

Contact Info

Product

Resources

About