arXiv subjects

Saman Cyrus

Publications and source records attributed to Saman Cyrus.

4 recordsLinked to original sources

arXiv2022

Generalized Necessary and Sufficient Robust Boundedness Results for Feedback Systems

Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for arbitrary semi-inner product spaces. Our result is purely algebraic, and holds even when the conventional discrete or continuous-time causal dynamical systems are replaced by general nonlinear relations, where there need not exist a notion of time. Our result clarifies when the sufficient conditions for robust stability are also necessary, and explains why stronger assumptions such as linearity and time-invariance are typically needed to prove necessity in the conventional dynamical systems setting.

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arXiv2019

A Revised Mehrotra Predictor-Corrector algorithm for Model Predictive Control

Input constrained Model predictive control (MPC) includes an optimization problem which should iteratively be solved at each time-instance. The well-known drawback of model predictive control is the computational cost of the optimization problem. This results in restriction of the application of MPC to systems with slow dynamics, e.g., process control systems and small-scale problems. Therefore, implementing fast numerical optimization algorithms has been a point of interest. Interior-point methods are proved to be appropriate algorithms, from computational cost point-of-vie, to solve input-constrained MPC. In this paper first a modified version of Mehrotra's predictor-corrector algorithm, a famous interior-point algorithm, is extended for quadratic programming problems and then is applied to the constrained model predictive control problems. Results show that as expected, the new algorithm is faster than Matlab solver's algorithm.

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arXiv2018

Unified Necessary and Sufficient Conditions for the Robust Stability of Interconnected Sector-Bounded Systems

Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition, but expressed in terms of relations defined on a general semi-inner product space. This increased generality leads to a clean result that can be specialized in a variety of ways. First, we show how to recover both sufficient and necessary-and-sufficient versions of the aforementioned classical results. Second, we show that suitably choosing the semi-inner product space leads to a new necessary and sufficient condition for weighted stability, which is in turn sufficient for exponential stability.

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arXiv2017

A Robust Accelerated Optimization Algorithm for Strongly Convex Functions

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient noise versus worst-case convergence rate. At one extreme, the algorithm is faster than Nesterov's Fast Gradient Method by a constant factor but more fragile to noise. At the other extreme, the algorithm reduces to the Gradient Method and is very robust to noise. The algorithm design technique is inspired by methods from classical control theory and the resulting algorithm has a simple analytical form. Algorithm performance is verified on a series of numerical simulations in both noise-free and relative gradient noise cases.

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