Applying negative imaginary systems theory to non-square systems with polytopic uncertainty

Bhowmick, Parijat; Lanzon, Alexander

doi:10.1016/j.automatica.2021.109570

Cited by 19 publications

(3 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In future scope, the proposed control scheme can be modified by incorporating adaptive control techniques to further improve its performance. The scheme may also be extended to develop a GFT scheme for multiple networked Negative Imaginary systems using previous studies [21][22][23][24][25][26][27].…”

Section: Discussionmentioning

confidence: 99%

A two‐loop group formation tracking control scheme for networked tri‐rotor UAVs using an ARE‐based approach

Bhowmick

Bhadra²,

Panda

2022

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

Cooperative control of networked unmanned aerial vehicles (UAVs) has received significant research interest over the last decade due to its potential applications in military security and surveillance, search and rescue, planetary exploration, precision agriculture, and so on. Many of these practical activities can be formulated as a group formation tracking problem with multiple targets to track. This paper aims to address such problems via designing a cooperative control scheme for networked tri‐rotor UAVs connected with directed graph topology. The proposed methodology consists of a two‐loop control scheme—the inner loop applies a robust feedback linearization technique to linearize the coupled, nonlinear dynamics of the tri‐rotor UAVs; while the outer loop facilitates an ARE‐based cooperative group formation tracking scheme. Tri‐rotor UAVs are considered in this paper instead of quad‐rotor UAVs, which are more common in drone applications, to conquer a major limitation of the quad‐rotor UAVs that it cannot alter its attitude independently while hovering at a particular height. A rigorous theoretical proof is given to establish the two‐loop control scheme exploiting the Lyapunov stability approach and algebraic Riccati equation (ARE)‐based optimal control policy. An in‐depth case study on a multitarget surveillance mission has been performed in this paper using a virtual reality software simulation platform to demonstrate the usefulness and efficacy of the proposed scheme.

show abstract

Section: Discussionmentioning

confidence: 99%

A two‐loop group formation tracking control scheme for networked tri‐rotor UAVs using an ARE‐based approach

Bhowmick

Bhadra²,

Panda

2022

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…This paper aims to design a simple yet effective cooperative controller for a group of networked tricopter drones utilising the NI theory, characteristic loci technique and SMC-based linearisation principles. Negative Imaginary (NI) systems theory has attracted the interest of control theorists and practising engineers due to its potential to solve various real-life engineering challenges, like vibration control of lightly-damped systems [4], cantilever beams [5], [6]; nano-positioning applications [7]; cooperative train platooning [8]; control of dissipative systems [9]- [11]; etc. Due to a simple robust stability criterion depending only on the loop gain at zero frequency (known as the DC loop gain condition [4]), NI theory has gained a lot of traction.…”

Section: Introductionmentioning

confidence: 99%

Cooperative Control of Multi-Tilt Tricopter Drones Applying a ‘Mixed’ Negative Imaginary and Strict Passivity Technique

Abara,

Bhowmick,

Lanzon

2023

2023 European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

This paper develops a cooperative controller for a fleet of multi-tilt tricopter drones modelled as Negative Imaginary (NI) systems via closed-loop linearisation exploiting Sliding-Mode Control (SMC) technique. The multi-tilt tricopter model is derived from the first principles, and the SMC method is invoked to obtain a closed-loop linear model of the tricopter plant with six outputs and six inputs. A subspacebased system identification algorithm is developed to identify the linearised drone model enforcing the NI property. The primary control objective is to design a distributed 'mixed' NI and strictly Passive control protocol so that the tricopter agents asymptotically reach the desired formation and keep tracking the target. Instead of the Lyapunov approach, the characteristic loci method is used to prove the asymptotic convergence of the trajectory tracking error. Finally, an exhaustive simulation case study is carried out on a fleet of six multi-tilt tricopter drones to demonstrate the feasibility of the cooperative controller presented in this work.

show abstract

“…N EGATIVE Imaginary (NI) systems theory has already established its worth due to its potential applications in real-world engineering problems, such as, in vibration control of lightly-damped mechanical systems [1]- [6], cantilever beam [7], large space structures [8] and robotic manipulators [8]; nano-positioning applications [9]; vehicle platooning; etc. NI theory was introduced in [1] and was primarily inspired by the positive position feedback control of highly resonant mechanical structures with colocated position sensors and force actuators.…”

Section: Introductionmentioning

confidence: 99%

On Discrete-Time Output Negative Imaginary Systems

Bhowmick

Lanzon

2022

IEEE Control Syst. Lett.

Self Cite

View full text Add to dashboard Cite

This letter introduces the notion of linear Discrete-time Output Negative Imaginary (D-ONI) systems. The D-ONI class is defined in the z-domain and it includes the systems having poles on the unit circle. The proposed definition involves a real parameter δ ≥ 0, which indicates the strictness properties. δ > 0 specifies the strict subset, Discrete-time Output Strictly Negative Imaginary (D-OSNI), within the stable D-ONI class. Interestingly, the new D-ONI class captures the existing D-NI systems while restricted to discrete-time LTI systems having a real, rational and proper transfer function. However, the D-OSNI systems are not identical to the existing strictly D-NI (D-SNI) subset. Instead, these two subsets intersect each other. An LMIbased state-space characterisation is derived to check the strict/non-strict D-ONI properties of a given system relying on the value of δ. The paper also establishes the connections between the discrete-time Passive and discretetime NI systems. Finally, a closed-loop stability result is proposed for a positive feedback interconnection of two D-ONI systems without poles at z = −1 and z = +1.

show abstract

Applying negative imaginary systems theory to non-square systems with polytopic uncertainty

Cited by 19 publications

References 41 publications

A two‐loop group formation tracking control scheme for networked tri‐rotor UAVs using an ARE‐based approach

A two‐loop group formation tracking control scheme for networked tri‐rotor UAVs using an ARE‐based approach

Cooperative Control of Multi-Tilt Tricopter Drones Applying a ‘Mixed’ Negative Imaginary and Strict Passivity Technique

On Discrete-Time Output Negative Imaginary Systems

Contact Info

Product

Resources

About