Optimal Rejection of Stochastic and Deterministic Disturbances

1997 ◽  
Vol 119 (1) ◽  
pp. 140-143 ◽  
Author(s):  
A. G. Sparks ◽  
D. S. Bernstein
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
Necessary Conditions ◽  
Search Algorithm ◽  
Gradient Search ◽  
Feedback Controllers ◽  
Internal Model Principle ◽  
Rejection Cost ◽  
The Cost ◽  
Quasi Newton

The problem of optimal H2 rejection of noisy disturbances while asymptotically rejecting constant or sinusoidal disturbances is considered. The internal model principle is used to ensure that the expected value of the output approaches zero asymptotically in the presence of persistent deterministic disturbances. Necessary conditions are given for dynamic output feedback controllers that minimize an H2 disturbance rejection cost plus an upper bound on the integral square output cost for transient performance. The necessary conditions provide expressions for the gradients of the cost with respect to each of the control gains. These expressions are then used in a quasi-Newton gradient search algorithm to find the optimal feedback gains.

K-Fold Exosystem and the Robust Nonlinear Servomechanism Problem

1998 ◽  
Vol 120 (1) ◽  
pp. 149-153 ◽  
Author(s):  
Jie Huang
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Disturbance Rejection ◽  
Internal Model ◽  
Output Feedback Control ◽  
Uncertain Nonlinear Systems ◽  
Internal Model Principle ◽  
Asymptotic Tracking

Asymptotic tracking and disturbance rejection in uncertain nonlinear systems is studied in the context of output feedback control. This study is facilitated by formalizing the notion of k-fold exosystem and generalizing the internal model principle to the nonlinear setting.

scholarly journals A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE

2020 ◽  
Vol 15 (1) ◽  
pp. 143-156
Author(s):  
Jean-François Biasse ◽  
Benjamin Pring
Keyword(s):  
Search Algorithm ◽  
Circuit Complexity ◽  
Quantum Circuit ◽  
Grover’S Algorithm ◽  
Search Problems ◽  
Trade Offs ◽  
Single Target ◽  
Grover's Algorithm ◽  
Quantum Oracle ◽  
The Cost

AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].

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