Approximate Closed-Form Solution to a Linear Quadratic Optimal Control Problem with Disturbance

Closed Form Solution of Nonlinear-Quadratic Optimal Control Problem by State-control Parameterization using Chebyshev Polynomials

In this paper the quasilinearization technique along with the Chebyshev polynomials of the first type are used to solve the nonlinear-quadratic optimal control problem with terminal state constraints. The quasilinearization is used to convert the nonlinear quadratic optimal control problem into sequence of linear quadratic optimal control problems. Then by approximating the state and control va...

Optimal Mortgage Refinancing: A Closed Form Solution.

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W(.) is the Lambert W-function, [Formula: see text]ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of ...

Optimal Linear Quadratic Control

Linear Quadratic Optimal Control

In previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the feedback gain to achieve this is unique (as long as the system is controllable). For multi-input systems, the feedback gain is not unique, so there is additional design freedom. How does one utilize this...

A Closed-Form Solution to the Ramification Problem

Our general concern is with how to integrate a representation of action into an existing set of state constraints. As has been observed in the literature, state constraints implicitly define indirect effects of actions as well as indirectly imposing further preconditions on the performance of actions. Thus, any representation scheme we propose must address the ramification and qualification pro...