Finite Horizon $H^\infty$ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach

Maalouf, Aline I.; Petersen, Ian R.

doi:10.1137/120866348

Cited by 10 publications

(19 citation statements)

References 26 publications

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“…Similarly, if the LMIs (35) and (36) have feasible solutions and the controller is defined as in (37)- (39), then the closedloop system (20) is strictly bounded real with the disturbance attenuation g. Proof. According to Theorem 4, this theorem can be proved in a straightforward way using the corresponding classical H ∞ control results in [47].…”

Section: A(f(t)) Takes Finite Values Inmentioning

confidence: 99%

“…While [23] only considered the cases of time-invariant quantum systems, in practical applications, time-varying linear quantum systems are often encountered. A dynamic game approach to designing a classical H ∞ controller for a class of timevarying linear quantum systems has been proposed in [35], by recognising the equivalence between a quantum system and a corresponding auxiliary classical stochastic system. A linear quadratic Gaussian (LQG) optimal controller has been designed in [36] to optimize the squeezing level achieved in one of the quadratures of the fundamental optical field for the time-varying quantum systems.…”

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confidence: 99%

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Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Liu¹,

Dong²,

Petersen³

et al. 2020

Preprint

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Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and H ∞ disturbance attenuation performance. This paper first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault tolerant H ∞ control problem to the dissipation properties and the solutions of Riccati differential equations, an H ∞ controller for the quantum system is then designed by solving a set of linear matrix inequalities (LMIs). In particular, an algorithm is employed to introduce additional noises and to construct the corresponding input matrices to ensure the physical realizability of the quantum controller. For real applications of the developed fault-tolerant control strategy, we present a linear quantum system example from quantum optics, where the amplitude of the pumping field randomly jumps among different values. It is demonstrated that a quantum H ∞ controller can be designed and implemented using some basic optical components to achieve the desired control goal.

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Section: A(f(t)) Takes Finite Values Inmentioning

confidence: 99%

mentioning

confidence: 99%

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Liu¹,

Dong²,

Petersen³

et al. 2020

Preprint

Self Cite

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“…For the same plant, the finite horizon dynamic game theory approach was applied in [94], and the solving process was proved equivalent to solving a corresponding deterministic continuous-time problem with imperfect state information. The finite horizon H ∞ control problem in [94] was then extended to the case of delayed measurements in [95]. …”

Section: Robust Controlmentioning

confidence: 99%

Closed‐Loop and Robust Control of Quantum Systems

Chen

Wang

2013

The Scientific World Journal

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For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H ∞ control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention.

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“…Thus, more and more attention has been paid to it by researchers from different perspectives. Some of the previous researches have focused on the H ∞ control/filtering problem for time-varying system [20]- [26], and several kinds of approaches have been used for solving this problem, including the game theoretical approach [21], [22], the differential/difference linear matrix inequality (DLMI) and recursive linear matrix inequality(RLMI) approach [23], [24], and the backward recursive Riccati difference equation approach [23], [25], [26]. On the other hand, the control objects sometimes are required to be completed in a limited time, such as missile interception, satellite orbit, etc..…”

Section: Introductionmentioning

confidence: 99%

H _∞ Control for Time-Varying Cyber-Physical System Under Randomly Occurring Hybrid Attacks: The Output Feedback Case

Liu

et al. 2020

IEEE Access

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In this paper, the H ∞ control problem for a class of linear time-varying cyber-physical system (CPS) under randomly occurring hybrid attacks in a finite horizon is investigated. The hybrid attacks, including denial of service (DoS) attacks on both sensor-to-controller and controller-to-actuator communication channels and false data injection (FDI) attacks on sensors and actuators, aim to destroy the measurement data and control data in order to endanger the functionality of the closed-loop system. The purpose of this paper is to study the relationship between the attack injected signals and the controlled output, and to design the output feedback controller gains so that the H ∞ performance of the closed-loop system is guaranteed over a given finite horizon, meanwhile, the impact of attack signals in the worst case on the linear quadratic performance can be reduced. In order to solve the above problems, both the methods of stochastic analysis and completing squares are utilized to establish the sufficient conditions for the existence of the desired controller, and a finite-horizon controller design algorithm is presented by solving two coupled backward recursive Riccati difference equations (RDEs) subject to some scheduled conditions. At last, the numerical simulation and experimental results are given out to demonstrate the effectiveness of the proposed approach. INDEX TERMS Cyber-physical system, hybrid attacks, time-varying systems, H ∞ control, Riccati equations.

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Finite Horizon $H^\infty$ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach

Cited by 10 publications

References 26 publications

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Closed‐Loop and Robust Control of Quantum Systems

H _∞ Control for Time-Varying Cyber-Physical System Under Randomly Occurring Hybrid Attacks: The Output Feedback Case

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Finite Horizon $H^\infty$ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach

Cited by 10 publications

References 26 publications

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Fault-tolerant Coherent H-infinity Control for Linear Quantum Systems

Closed‐Loop and Robust Control of Quantum Systems

H ∞ Control for Time-Varying Cyber-Physical System Under Randomly Occurring Hybrid Attacks: The Output Feedback Case

Contact Info

Product

Resources

About

H _∞ Control for Time-Varying Cyber-Physical System Under Randomly Occurring Hybrid Attacks: The Output Feedback Case