17,866 research outputs found
Final-State Constrained Optimal Control via a Projection Operator Approach
In this paper we develop a numerical method to solve nonlinear optimal
control problems with final-state constraints. Specifically, we extend the
PRojection Operator based Netwon's method for Trajectory Optimization (PRONTO),
which was proposed by Hauser for unconstrained optimal control problems. While
in the standard method final-state constraints can be only approximately
handled by means of a terminal penalty, in this work we propose a methodology
to meet the constraints exactly. Moreover, our method guarantees recursive
feasibility of the final-state constraint. This is an appealing property
especially in realtime applications in which one would like to be able to stop
the computation even if the desired tolerance has not been reached, but still
satisfy the constraints. Following the same conceptual idea of PRONTO, the
proposed strategy is based on two main steps which (differently from the
standard scheme) preserve the feasibility of the final-state constraints: (i)
solve a quadratic approximation of the nonlinear problem to find a descent
direction, and (ii) get a (feasible) trajectory by means of a feedback law
(which turns out to be a nonlinear projection operator). To find the (feasible)
descent direction we take advantage of final-state constrained Linear Quadratic
optimal control methods, while the second step is performed by suitably
designing a constrained version of the trajectory tracking projection operator.
The effectiveness of the proposed strategy is tested on the optimal state
transfer of an inverted pendulum
Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
This article provides a review of recent developments in the formulation and
execution of optimal control strategies for the dynamics of quantum systems. A
brief introduction to the concept of optimal control, the dynamics of of open
quantum systems, and quantum information processing is followed by a
presentation of recent developments regarding the two main tasks in this
context: state-specific and state-independent optimal control. For the former,
we present an extension of conventional theory (Pontryagin's principle) to
quantum systems which undergo a non-Markovian time-evolution. Owing to its
importance for the realization of quantum information processing, the main body
of the review, however, is devoted to state-independent optimal control. Here,
we address three different approaches: an approach which treats dissipative
effects from the environment in lowest-order perturbation theory, a general
method based on the time--evolution superoperator concept, as well as one based
on the Kraus representation of the time-evolution superoperator. Applications
which illustrate these new methods focus on single and double qubits (quantum
gates) whereby the environment is modeled either within the Lindblad equation
or a bath of bosons (spin-boson model). While these approaches are widely
applicable, we shall focus our attention to solid-state based physical
realizations, such as semiconductor- and superconductor-based systems. While an
attempt is made to reference relevant and representative work throughout the
community, the exposition will focus mainly on work which has emerged from our
own group.Comment: 27 pages, 18 figure
Stochastic model predictive control of LPV systems via scenario optimization
A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system's matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios') are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example
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