this paper presents a simplifiedlagrangian multiplier based algorithm to solve the fixed head hydrothermalscheduling problem. in fixed head hydrothermal scheduling problem, waterdischarge rate is modeled as quadratic function of hydropower generation andfuel cost is modeled as quadratic function of thermal power generation. thepower output of each hydro unit varies with the rate of water discha...

Abstract Lagrangian models use calculus to solve multi-variable non-linear constrained optimization of problems and for identifying the marginal changes (‘shadow prices’) optimal solutions in constraint bounds. This is especially useful when constraints represent resource limitations.

In this thesis we are going to study the energy shaping problem on controlled Lagrangian systems with degree of underactuation less than or equal to two. Energy shaping is a method of stabilization by designing a suitable feedback control force on the given controlled Lagrangian system so that the total energy of the feedback equivalent system has a non-degenerate minimum at the equilibrium. Th...

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In th...

The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential--computed approximately to be practical in high-dimensional systems--influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys. 132, 014112 (2010)]. For a no...