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LMI tests for positive definite polynomials: Slack variable approach
 IEEE Trans. on Automatic Control
"... The considered problem is assessing nonnegativity of a function’s values when indeterminates are in domains constrained by scalar polynomial inequalities. The tested functions are multiindeterminates polynomial matrices which are required to be positive semidefinite. For such problems new tests b ..."
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The considered problem is assessing nonnegativity of a function’s values when indeterminates are in domains constrained by scalar polynomial inequalities. The tested functions are multiindeterminates polynomial matrices which are required to be positive semidefinite. For such problems new tests based on linear matrix inequalities are provided in a Slack Variables type approach. The results are compared to those obtained via the SumOfSquares approach, are proved to be equivalent in case of unbounded domains and less conservative if polytopictype bounds are known.
Global Stability Analysis of Fluid Flows using SumofSquares
, 2011
"... This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sumofsquares decomposition to constr ..."
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This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sumofsquares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite dimensional NavierStokes systems using robust optimization techniques. Crucially, this extension requires only the solution of infinitedimensional linear eigenvalue problems and finitedimensional sumofsquares optimization problems. We further show that subject to minor technical constraints, a general polynomial Lyapunov function is always guaranteed to provide better results than the classical energy methods in determining a lowerbound on the maximum Reynolds number for which a flow is globally stable, if the flow does remain globally stable for Reynolds numbers at least slightly beyond the energy stability limit. Such polynomial functions can be searched for efficiently using the SOS technique we propose.
Switched Control of Mechanical Systems by Using Musculotendon Actuators∗
"... Abstract — This paper addresses the problem of modeling, control, and simulation of a mechanical system actuated by an agonistantagonist musculotendon subsystem. Contraction dynamics is given by case I of Zajac’s model. Saturated semi– positive PDtype controllers with switching as neural excitatio ..."
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Abstract — This paper addresses the problem of modeling, control, and simulation of a mechanical system actuated by an agonistantagonist musculotendon subsystem. Contraction dynamics is given by case I of Zajac’s model. Saturated semi– positive PDtype controllers with switching as neural excitation inputs are proposed. Linear approaches of nonlinear systems, root locus, switched systems control and SOSTOOLS are used to determine the stability for the obtained closedloop system. To corroborate the obtained theoretical results numerical simulations have been performed with help of Matlab. I.
rsta.royalsocietypublishing.org Research
"... One contribution of 15 to a Theme Issue ‘Stability, separation and close body interactions’. Subject Areas: fluid mechanics, applied mathematics ..."
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One contribution of 15 to a Theme Issue ‘Stability, separation and close body interactions’. Subject Areas: fluid mechanics, applied mathematics
Timedomain performance based nonlinear state feedback control of constrained
, 2008
"... linear systems ..."
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OptimizationBased Control Methodologies with Applications to Autonomous Vehicle
, 2010
"... and submitted in partial fulfilment of the requirements for the degree of ..."
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and submitted in partial fulfilment of the requirements for the degree of
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, 2015
"... Sumofsquares of polynomials approach to nonlinear stability of fluid flows: an example of application. Proc. R. Soc. A 471: 20150622. ..."
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Sumofsquares of polynomials approach to nonlinear stability of fluid flows: an example of application. Proc. R. Soc. A 471: 20150622.
Demonstrating Passivity and Dissipativity using Computational Methods
, 2013
"... Passivity and dissipativity are energy based properties of dynamical systems that may be used for the analysis and synthesis of linear and nonlinear systems. The two properties provide valuable stability results as well as compositional results for the analysis of interconnected systems. Using both ..."
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Passivity and dissipativity are energy based properties of dynamical systems that may be used for the analysis and synthesis of linear and nonlinear systems. The two properties provide valuable stability results as well as compositional results for the analysis of interconnected systems. Using both the stability and compositionality results, large scale systems can be determined to be stable by analyzing the components in terms of energy dissipation and then sequentially analyzing the system interconnections. One of the drawbacks of this approach is that demonstrating that a system is passive or dissipative typically requires finding an energy storage function, which is analogous to a Lyapunov function. As with Lyapunov stability, the search for a storage function to show dissipativity is in general an openended search. This paper surveys computational methods for finding energy storage functions. This includes linear matrix inequality (LMI) methods for linear systems and sum of squares (SOS) methods for polynomial nonlinear systems. When these methods are applicable, the search for storage functions can be automated to greatly simplify analysis and synthesis of linear and nonlinear systems. New material is provided on the application of these methods to find passivity indices for dynamical systems. Additional material is provided on using SOS methods to demonstrate dissipativity for switched systems. Examples are provided to illustrate how these methods may be used in practice. 1 1