Linear Differential Algebraic Equations and Observers

In this paper we propose a method for adaptive sampling using Unmanned Aerial Vehicles (UAVs) in oil spill management. The goal is to measure and estimate oil spill concentrations at the sea surface, while at the same time identify the leak rates of sources at known positions. First we construct a cost which approximates the benefit of sampling locations at specific times. This cost is based on measures of observability and of persistency of excitation for the oil spill model. A receding horizon Mixed-Integer Linear Programming (MILP) problem is solved in order to find UAV trajectories which are optimal with respect to the cost. For UAV trajectory tracking we use a Lyapunov based controller. The oil spill concentration measurements taken by the UAVs by following these tracks are used in an adaptive observer, which provides state (concentration) and parameter (leak rate) estimates. Under the assumption that the sampling strategy described above lead to uniform complete observability and persistency of excitation, we prove Uniform Global Asymptotic Stability (UGAS) of the state estimation, parameter identification and UAV trajectory tracking errors. Finally, we provide a simulation of the proposed strategy, and compare it with two other strategies.

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“…where Φ(T H , T H ) being the identity matrix is used as initial condition, similar to what is done in [19,Page 21].…”

Section: E Cost Approximatormentioning

confidence: 99%

Adaptive sampling for UAV sensor network in oil spill management

Grøtli

Haugen

Johansen

et al. 2021

2021 American Control Conference (ACC)

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“…49, St. Petersburg, 197101, Russia (nikona@yandex.ru) other applications like fault detection and isolation [3]. A lot of research has been reported in the last few years on the development of state observers for this kind of systems, see e.g., [4]- [8]. In this paper we are particularly interested in the case of linear time-varying (LTV) descriptor systemssee [9] for an early reference on this topic and [4], [10] for more recent references.…”

Section: Introductionmentioning

confidence: 99%

Distributed Observers for LTI Systems With Finite Convergence Time: A Parameter-Estimation-Based Approach

Nuño

Bobtsov

2021

IEEE Trans. Automat. Contr.

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“…Specifically, the above referred to descriptor systems can be found in several areas, such as economics and population dynamics-for instance, the singular Leontief dynamic model of a multi-sector economy and the Leslie population model with uncertain parameters; see, e.g., [14,15] and references therein. These models also appear when discretising continuous time-varying descriptor systems arising in power system networks whose circuit elements (e.g., transmission lines and load impedances) may vary within known intervals (see, e.g., [16]) and in mechanical systems, such as robotic manipulators [17], dynamic models of parallel robots [18,19] and uncertain two-mass systems with flexible shafts [20]. However, despite the practical interest, few references deal with control and estimation problems related to LPV discrete-time descriptor systems-see [21] which proposed a gain scheduled approach to the admissibilisation of LPV descriptor systems.…”

Section: Introductionmentioning

confidence: 99%

Robust Filtering for Discrete-Time Linear Parameter-Varying Descriptor Systems

2020

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This paper deals with robust state estimation for discrete-time, linear parameter varying (LPV) descriptor systems. It is assumed that all the system state-space matrices are affine functions of the uncertain parameters and both the parameters and their variations are bounded functions of time with known minimum and maximum values. First, necessary and sufficient conditions are proposed for admissibility and bounded realness for discrete linear time-varying (DLTV) descriptor systems. Next, two convex optimisation based methods are proposed for designing admissible stationary linear descriptor filters for LPV descriptor systems which ensure a prescribed upper bound on the ℓ2-induced gain from the noise signal to the estimation error regardless of model uncertainties. The proposed filter design results were based on parameter-dependent generalised Lyapunov functions, and full-order, augmented-order and reduced-order filters were considered. Numerical examples are presented to show the effectiveness of the proposed filtering scheme. In particular, the proposed approach was used to estimate the state variables of a controlled horizontal 2-DOF robotic manipulator based on noisy measurements.

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Linear Differential Algebraic Equations and Observers

Cited by 8 publications

References 120 publications

Adaptive sampling for UAV sensor network in oil spill management

Adaptive sampling for UAV sensor network in oil spill management

Distributed Observers for LTI Systems With Finite Convergence Time: A Parameter-Estimation-Based Approach

Robust Filtering for Discrete-Time Linear Parameter-Varying Descriptor Systems

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