Initial values for Riccati ODEs from variational PDEs

Costanza, Vicente; Rivadeneira, Pablo S.

doi:10.1590/s1807-03022011000200005

Cited by 2 publications

(1 citation statement)

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“…In the infinite‐horizon, bilinear‐quadratic regulator and change of set‐point servo, there also exists an attempt to find the missing initial condition for the costate variable from the data of each particular problem, which allows to integrate the equations in real time with the underlying control process . For nonlinear systems, this line is in its beginnings .…”

Section: Introductionmentioning

confidence: 99%

Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems

Costanza

Rivadeneira

González

2013

Optim Control Appl Methods

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SUMMARYMinimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%