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Nonlinear observers based on the well-known concept of minimum energy estimation are discussed. The approach relies on an output injection operator determined by a Hamilton-Jacobi-Bellman equation and is subsequently approximated by a neural network. A suitable optimization problem allowing to learn the network parameters is proposed and numerically investigated for linear and nonlinear oscillators.
In this paper, we investigate a constrained optimal coordination problem for a class of heterogeneous nonlinear multi-agent systems described by high-order dynamics subject to both unknown nonlinearities and external disturbances. Each agent has a pr
This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global exponential
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)times mathbb{R}^{15}$ relying on body-frame acceleration, angular v
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while th