Hendra G. Harno

Coherent control of linear quantum systems: A differential evolution approach

In this paper, we propose a new method to construct an optimal coherent quantum controller, which is required to be physically realizable. This method is based on an evolutionary optimization method, namely the Differential Evolution approach. The aim is to provide a straightforward algorithm to deal with both nonlinear and nonconvex constraints arising in the quantum controller design. The solution to our problem involves the solutions of a complex algebraic Riccati equation and a Lyapunov equation. The efficacy of the proposed method is demonstrated through a case study on an entanglement control problem for an ideal quantum network comprising two cascaded optical parametric amplifiers.

Synthesis of Linear Coherent Quantum Control Systems Using A Differential Evolution Algorithm

We propose a new method to construct an optimal linear coherent quantum controller based on an evolutionary optimization method, namely a differential evolution algorithm. The aim is to provide a straightforward approach to deal with both nonlinear and nonconvex constraints arising in the coherent quantum controller synthesis. The solution to this control problem involves a complex algebraic Riccati equation, which corresponds to a physical realizability condition for the coherent quantum controller. The proposed method is demonstrated through an example of an entanglement control problem for a quantum network comprising two cascaded optical parametric amplifiers.

Robust H ∞ control of a nonlinear uncertain system via a stable nonlinear output feedback controller

A new approach to solving a nonlinear robust H ∞ control problem using a stable nonlinear output feedback controller is presented in this article. The class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global Lipschitz conditions describing the admissible uncertainties and nonlinearities, respectively. The nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller. The H ∞ control objective is to obtain an absolutely stable closed-loop system with a specified disturbance attenuation level. The solution to this control problem involves stabilising solutions to parametrised algebraic Riccati equations. We apply a differential evolution algorithm to solve a non-convex nonlinear optimisation problem arising in the controller synthesis.

Stochastic diagonal approximate greatest descent in neural networks

Optimization is important in neural networks to iteratively update weights for pattern classification. Existing optimization techniques suffer from suboptimal local minima and slow convergence rate. In this paper, stochastic diagonal Approximate Greatest Descent (SDAGD) algorithm is proposed to optimize neural network weights using multi-stage backpropagation manner. SDAGD is derived from the operation of a multi-stage decision control system. It uses the concept of control system consisting of: (1) when the local search region does not contain a minimum point, the iteration shall be defined at the boundary of the local search region, (2) when the local region contains a minimum point, the Newton method is used to search for the optimum solution. The implementation of SDAGD on Multilayer perceptron (MLP) is investigated with the goal of improving the learning ability and structural simplicity. Simulation results showed that two layer MLP with SDAGD achieved a misclassification rate of 4.7% on MNIST dataset.

Decentralized coherent robust H ∞ control of a class of large-scale uncertain linear complex quantum stochastic systems

This paper presents a procedure to synthesize a decentralized coherent robust H∞ quantum controller for a class of large-scale uncertain linear complex quantum stochastic systems with a norm-bounded unstructured uncertainty. The H∞ control objective is to obtain a strictly bounded real closed loop uncertain quantum system with a specified disturbance attenuation level g > 0. The main idea is that instead of treating the interconnections between quantum subsystems as uncertainties, we consider the neglected off-diagonal blocks of the transfer function matrix of the corresponding non-decentralized quantum controller as additional uncertainties. The resulting decentralized coherent quantum controller is required to satisfy a physical realizability condition.

Nonlinear robust H ∞ control via a stable decentralized nonlinear output feedback controller

This paper presents a procedure to solve a decentralized robust H∞; control problem for a nonlinear uncertain system. The admissible uncertainties and nonlinearities of the system satisfy Integral Quadratic Constraints and Global Lipschitz Conditions, respectively. The decentralized controller is required to be stable and is constructed by exploiting the interconnections between subsystems without treating them as uncertainties. Instead, additional uncertainties are introduced due to the discrepancies between each local controller and the full nonlinear output feedback controller. The solution to this problem involves the solutions of Algebraic Riccati Equations. Also, the closed loop system is required to be absolutely stabilized with a specified disturbance attenuation level.

Robust H ∞ stabilization of a nonlinear uncertain system via a stable nonlinear output feedback controller

A new approach to solving a nonlinear robust H∞ control problem using a stable nonlinear output feedback controller is presented in this paper. The particular class of nonlinear uncertain systems being considered is characterized in terms of Integral Quadratic Constraints and Global Lipschitz Conditions describing the admissible uncertainty and nonlinearity, respectively. The nonlinear controller is then constructed by including a copy of the system nonlinearity in the structure of the linear controller. The aim is to enable the controller to exploit the nonlinearity of the system such that it will absolutely stabilize the closed loop nonlinear system and achieve a specified disturbance attenuation level. This method involves the stabilizing solutions of a pair of algebraic Riccati equations.

Approximate greatest descent in neural network optimization

Numerical optimization is required in artificial neural network to update weights iteratively for learning capability. In this paper, we propose the use of Approximate Greatest Descent (AGD) algorithm to optimize neural network weights using long-term backpropagation manner. The modification and development of AGD into stochastic diagonal AGD (SDAGD) algorithm could improve the learning ability and structural simplicity for deep learning neural networks. It is derived from the operation of a multi-stage decision control system which consists of two phases: (1) when local search region does not contain the minimum point, iteration shall be defined at the boundary of the local search region, (2) when local region contains the minimum point, Newton method is approximated for faster convergence. The integration of SDAGD into Multilayered perceptron (MLP) network is investigated with the goal of improving the learning ability and structural simplicity. Simulation results showed that two-layer MLP with SDAGD achieved a misclassification rate of 9.4% on a smaller mixed national institute of national and technology (MNIST) dataset. MNIST is a database equipped with handwritten digits images suitable for algorithm prototyping in artificial neural networks.

Strict Bounded Real Decentralized Coherent Quantum Robust H∞ Control

Abstract We present a systematic method to synthesize a decentralized coherent quantum robust H ∞ controller for a class of large-scale linear complex quantum stochastic systems with norm-bounded structured uncertainties. The H ∞ control objective is to obtain a closed loop uncertain quantum system, which is strict bounded real with a specified disturbance attenuation level. The solution to this quantum control problem involves stabilizing solutions to parameterized complex Riccati equations.