Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems

IEEE Trans. Syst. Man Cybern, Syst.

Brown

McIsaac

2021

Self Cite

Two novel nonlinear pose (i.e, attitude and position) filters developed directly on the Special Euclidean Group SE (3) able to guarantee prescribed characteristics of transient and steady-state performance are proposed. The position error and normalized Euclidean distance of attitude error are trapped to arbitrarily start within a given large set and converge systematically and asymptotically to the origin from almost any initial condition. The transient error is guaranteed not to exceed a prescribed value while the steady-state error is bounded by a predefined small value. The first pose filter operates based on a set of vectorial measurements coupled with a group of velocity vectors and requires preliminary pose reconstruction. The second filter, on the contrary, is able to perform its function using a set of vectorial measurements and a group of velocity vectors directly. Both proposed filters provide reasonable pose estimates with superior convergence properties while being able to use measurements obtained from low-cost inertial measurement, landmark measurement, and velocity measurement units. Simulation results demonstrate effectiveness and robustness of the proposed filters considering large error in initialization and high level of uncertainties in velocity vectors as well as in the set of vector measurements.

Section: B Prescribed Performancementioning

confidence: 76%

Nonlinear Pose Filters on the Special Euclidean Group SE(3) With Guaranteed Transient and Steady-State Performance

IEEE Trans. Syst. Man Cybern, Syst.

Brown

McIsaac

2021

Self Cite

“…Thus,ξ/ξ ≤ 0. According to the equation (20) of Lemma 1, the expression in (77) is negative semidefinite. Thus, the inequality in (76) becomes…”

Section: B Direct Stochastic Estimator With Prescribed Performancementioning

confidence: 99%

“…This transformation enables to maintain the error within dynamically reducing sets enabling the attainment of the prescribed performance measures. The systematic convergence with predefined measures has been applied successfully in different applications, for instance 2 DOF planar robot [19], unknown high-order nonlinear networked systems [20], event-triggered control [21].…”

Section: Introductionmentioning

confidence: 99%

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

Intl J Robust & Nonlinear

2020

Self Cite

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group SO (3) with the tracking error of the normalized Euclidean distance meeting predefined transient and steady-state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from lowcost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.

“…Remark 3. As detailed in [7,11,15], knowing the sign of e i (0) is sufficient to maintain the same robust controller for all t > 0 and satisfy the performance constraints since switching does not occur after t = 0.…”

Section: Prescribed Performancementioning

confidence: 99%

“…Multi-agent distributed control in a way addresses many problems such as nonlinearities, unmodeled dynamics, uncertainties, and disturbances. It is often conceived that closed loop characteristics (transient and steady state error for instance) are analytically rigorous [7,11,15]. With prescribed performance however, such characteristics have been mapped to a relatively smaller set with constrained convergence.…”

Section: Introductionmentioning

confidence: 99%

Adaptive synchronisation of unknown nonlinear networked systems with prescribed performance

International Journal of Systems Science

El-Férik

Lewis

2016

Self Cite

Adaptive cooperative tracking control with prescribed performance function (PPF) is proposed for high-order nonlinear multi-agent systems. The tracking error originally within a known large set is confined to a smaller predefined set using this approach. Using output error transformation, the constrained system is relaxed and mapped to an unconstrained one. The controller is conceived under the assumption that the agents' nonlinear dynamics are unknown and the perceived network is structured and strongly connected. Under the proposed controller, all agents track the trajectory of the leader node with guaranteed uniform ultimately bounded transformed error and bounded adaptive estimate of unknown parameters and dynamics. In addition, the proposed controllers with PPF are distributed such that each follower agent requires information between its own state relative to connected neighbors. Proposed controller is validated for robustness and smoothness using highly nonlinear heterogeneous networked system with uncertain timevarying parameters and external disturbances.