1,225 research outputs found
Recommended from our members
Optimal Regulator Transparency
Private investment activity is regulated by two semi-independent agencies: an enforcement authority and an appeals authority. Once undertaken, an investment project may be interdicted by the enforcement authority before its final payoff is realized. The investor may refer an interdiction to the appeals authority, who upholds or voids the interdiction according to a privately known rule of law. The appeals authority determines the degree of regulatory transparency by issuing more or less revealing guidelines describing the operation of the rule of law in various circumstances. In this setting, the appeals authority maximizes its ability to extract rents from investors by issuing weakly differentiated guidelines which yield the highest possible rate of interdiction by the enforcement authority, together with the highest possible likelihood that interdiction will be overturned on appeal
Improving stability margins in discrete-time LQG controllers
Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics
Chiral extrapolation beyond the power-counting regime
Chiral effective field theory can provide valuable insight into the chiral
physics of hadrons when used in conjunction with non-perturbative schemes such
as lattice QCD. In this discourse, the attention is focused on extrapolating
the mass of the rho meson to the physical pion mass in quenched QCD (QQCD).
With the absence of a known experimental value, this serves to demonstrate the
ability of the extrapolation scheme to make predictions without prior bias. By
using extended effective field theory developed previously, an extrapolation is
performed using quenched lattice QCD data that extends outside the chiral
power-counting regime (PCR). The method involves an analysis of the
renormalization flow curves of the low energy coefficients in a finite-range
regularized effective field theory. The analysis identifies an optimal
regulator, which is embedded in the lattice QCD data themselves. This optimal
regulator is the regulator value at which the renormalization of the low energy
coefficients is approximately independent of the range of quark masses
considered. By using recent precision, quenched lattice results, the
extrapolation is tested directly by truncating the analysis to a set of points
above 380 MeV, while being blinded of the results probing deeply into the
chiral regime. The result is a successful extrapolation to the chiral regime.Comment: 8 pages, 18 figure
The linear regulator problem for parabolic systems
An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems
The inverse problem of the optimal regulator
Inverse problem of optimal regulator for class of systems with integral type performance indice
QRnet: optimal regulator design with LQR-augmented neural networks
In this paper we propose a new computational method for designing optimal
regulators for high-dimensional nonlinear systems. The proposed approach
leverages physics-informed machine learning to solve high-dimensional
Hamilton-Jacobi-Bellman equations arising in optimal feedback control.
Concretely, we augment linear quadratic regulators with neural networks to
handle nonlinearities. We train the augmented models on data generated without
discretizing the state space, enabling application to high-dimensional
problems. We use the proposed method to design a candidate optimal regulator
for an unstable Burgers' equation, and through this example, demonstrate
improved robustness and accuracy compared to existing neural network
formulations.Comment: Added IEEE accepted manuscript with copyright notic
Geometric existence theory for the control-affine nonlinear optimal regulator
AbstractFor infinite horizon nonlinear optimal control problems in which the control term enters linearly in the dynamics and quadratically in the cost, well-known conditions on the linearised problem guarantee existence of a smooth globally optimal feedback solution on a certain region of state space containing the equilibrium point. The method of proof is to demonstrate existence of a stable Lagrangian manifold M and then construct the solution from M in the region where M has a well-defined projection onto state space. We show that the same conditions also guarantee existence of a nonsmooth viscosity solution and globally optimal set-valued feedback on a much larger region. The method of proof is to extend the construction of a solution from M into the region where M no-longer has a well-defined projection onto state space
- …