Related papers: Stabilizing of a Class of Underactuated Euler Lagr…
Stabilization of a quadrotor without a controller based on cascade structure is a challenging problem. Besides, due to the dynamics and the number of underactuation, an energy shaping controller has not been designed in 3D for a quadrotor.…
Optimal control schemes have achieved remarkable performance in numerous engineering applications. However, they typically require high computational cost, which has limited their use in real-world engineering systems with fast dynamics…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
This Technical Note presents a simple control approach for global trajectory tracking and formation control of underactuated surface vessels equipped with only two propellers. The control approach exploits the inherent cascaded structure of…
The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of…
We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known when the initial vorticity is in $L^p$ with $1\leq p\leq…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
This paper presents a novel extremum seeking control (ESC) approach for the vibrational stabilization of a class of mechanical systems (e.g., systems characterized by equations of motion resulting from Newton second law or Euler-Lagrange…
We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion…
Lagrangian of electronic liquid in magneto-inhomogeneous micro-conductor has been constructed. A corresponding Euler-Lagrange equation has been solved. It was shown that the described system has eigenmodes of spin polarization and total…
In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…
We propose an Eulerian-Lagrangian (EL) Runge-Kutta (RK) discontinuous Galerkin (DG) method for wave equations. The method is designed based on the ELDG method for transport problems [J. Comput. Phy. 446: 110632, 2021.], which tracks…
This paper proposes an imitation learning (IL) framework for synthesizing neural network (NN) controllers that achieve boundary stabilization of systems governed by reaction-diffusion partial differential equations (PDEs). The plant is…
Power grids normally operate at some stable operating condition where power supply and demand are balanced. In response to emergency situations, load shedding is a prevailing approach where local protective devices are activated to cut a…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
This paper proposes an adaptive control allocation approach for uncertain over-actuated systems with actuator saturation. The proposed method does not require uncertainty estimation or a persistent excitation assumption. Using the…