Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMeasurement-based feedback control of linear quantum stochastic systems with quadratic-exponential criteria
192
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper is concerned with a risk-sensitive optimal control problem for a feedback connection of a quantum plant with a measurement-based classical controller. The plant is a multimode open quantum harmonic oscillator driven by a multichannel quantum Wiener process, and the controller is a linear time invariant system governed by a stochastic differential equation. The control objective is to stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional (QEF) which penalizes the plant variables and the controller output. We combine a frequency-domain representation of the QEF growth rate, obtained recently, with variational techniques and establish first-order necessary conditions of optimality for the state-space matrices of the controller.
rate research
Read More
This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a bounded time interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its asymptotic infinite-horizon growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formulas express the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide two illustrations including a numerical example with a two-mode oscillator.
This paper is concerned with multimode open quantum harmonic oscillators and quadratic-exponential functionals (QEFs) as quantum risk-sensitive performance criteria. Such systems are described by linear quantum stochastic differential equations driven by multichannel bosonic fields. We develop a finite-horizon expansion for the system variables using the eigenbasis of their two-point commutator kernel with noncommuting position-momentum pairs as coefficients. This quantum Karhunen-Loeve expansion is used in order to obtain a Girsanov type representation for the quadratic-exponential functions of the system variables. This representation is valid regardless of a particular system-field state and employs the averaging over an auxiliary classical Gaussian random process whose covariance operator is defined in terms of the quantum commutator kernel. We use this representation in order to relate the QEF to the moment-generating functional of the system variables. This result is also specified for the invariant multipoint Gaussian quantum state when the oscillator is driven by vacuum fields.
This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust performance criteria in control problems for open quantum harmonic oscillators (OQHOs) driven by bosonic fields. We develop a randomised representation for the QEF using a Karhunen-Loeve expansion of the quantum process on a bounded time interval over the eigenbasis of its two-point commutator kernel, with noncommuting position-momentum pairs as coefficients. This representation holds regardless of a particular quantum state and employs averaging over an auxiliary classical Gaussian random process whose covariance operator is specified by the commutator kernel. This allows the QEF to be related to the moment-generating functional of the quantum process and computed for multipoint Gaussian states. For stationary Gaussian quantum processes, we establish a frequency-domain formula for the QEF rate in terms of the Fourier transform of the quantum covariance kernel in composition with trigonometric functions. A differential equation is obtained for the QEF rate with respect to the risk sensitivity parameter for its approximation and numerical computation. The QEF is also applied to large deviations and worst-case mean square cost bounds for OQHOs in the presence of statistical uncertainty with a quantum relative entropy description.
In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.
We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This problem has been studied from different perspectives by different communities. However, the existing theory deals only with the case of quadratic costs (the LQ problem), which limits applications to stabilisation and tracking tasks only. In order to handle more general (non-convex) costs that naturally arise in many practical problems, we carefully select and bring together several tools from different communities, namely non-asymptotic linear regression, recent results in interval prediction, and tree-based planning. Combining and adapting the theoretical guarantees at each layer is non trivial, and we provide the first end-to-end suboptimality analysis for this setting. Interestingly, our analysis naturally adapts to handle many models and combines with a data-driven robust model selection strategy, which enables to relax the modelling assumptions. Last, we strive to preserve tractability at any stage of the method, that we illustrate on two challenging simulated environments.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
