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Stabilization And Robustness Analysis For Time-Varying Systems With Time-Varying Delays Using A Sequential Subpredictors Approach, Frédéric Mazenc, Michael Malisoff
Stabilization And Robustness Analysis For Time-Varying Systems With Time-Varying Delays Using A Sequential Subpredictors Approach, Frédéric Mazenc, Michael Malisoff
Faculty Publications
We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems. Our method circumvents the problem of constructing and estimating distributed terms in the control laws, and allows arbitrarily large input delay bounds, pointwise time-varying input delays, and uncertainties. Instead of using distributed terms, our approach to handling longer delays is to increase the number of predictors. We obtain explicit formulas to find lower bounds for the number of required predictors. The formulas involve bounds on the delays and on the derivatives of the delays. We illustrate our method in three examples.
Stability And Robustness Analysis For A Multi-Species Chemostat Model With Uncertainties, Frederic Mazenc, Michael Malisoff, Gonzalo Robledo
Stability And Robustness Analysis For A Multi-Species Chemostat Model With Uncertainties, Frederic Mazenc, Michael Malisoff, Gonzalo Robledo
Faculty Publications
We prove stability and robustness results for chemostat models with one substrate, an arbitrary number of species, a constant dilution rate, and constant inputs of the species. Unlike all previous works, we prove input-to-state stability under uncertainties in important cases where the controls are the input nutrient concentration and the species inputs. Our assumptions ensure global asymptotic stability for an equilibrium, which can allow persistence of multiple species, when the uncertainties are zero. We allow arbitrarily large bounds on the uncertainties in the species dynamics, and equilibria that can be in the boundary of the state space.
Stabilization Of Nonlinear Time-Varying Systems Through A New Prediction Based Approach, Frederic Mazenc, Michael Malisoff
Stabilization Of Nonlinear Time-Varying Systems Through A New Prediction Based Approach, Frederic Mazenc, Michael Malisoff
Faculty Publications
We propose a prediction based stabilization approach for a general class of nonlinear time-varying systems with pointwise delay in the input. It is based on a recent new prediction strategy, which makes it possible to circumvent the problem of constructing and estimating distributed terms in the expression for the stabilizing control laws. Our result applies in cases where other recent results do not.
Extensions Of Razumikhin's Theorem And Lyapunov–Krasovskii Functional Constructions For Time-Varying Systems With Delay, Frédéric Mazenc, Michael Malisoff
Extensions Of Razumikhin's Theorem And Lyapunov–Krasovskii Functional Constructions For Time-Varying Systems With Delay, Frédéric Mazenc, Michael Malisoff
Faculty Publications
We prove extensions of Razumikhin's theorem for time-varying continuous and discrete time nonlinear systems. Our results include a novel ‘strictification’ technique for converting a nonstrict Lyapunov function into a strict one. We also provide new constructions of Lyapunov–Krasovskii functionals that can be used to prove robustness to perturbations. Our examples include a key model from identification theory, and they show how our method can sometimes allow broader classes of delays than the results in the literature.
Stability And Robustness Analysis For Human Pointing Motions With Acceleration Under Feedback Delays, Paul Varnell, Michael Malisoff, Fumin Zhang
Stability And Robustness Analysis For Human Pointing Motions With Acceleration Under Feedback Delays, Paul Varnell, Michael Malisoff, Fumin Zhang
Faculty Publications
Pointer acceleration is often used in computer mice and other interfaces to increase the range and speed of pointing motions without sacrificing precision during slow movements. However, the effects of pointer acceleration are not yet well understood. We use a system perspective and feedback control to analyze the effects of pointer acceleration. We use a new pointer acceleration model connected in feedback with the vector integration to endpoint model for pointing motions. When there are no feedback delays, we prove global asymptotic stability of the closed loop system for a general class of acceleration profiles. We also prove robustness under …
Adaptive Planar Curve Tracking Control And Robustness Analysis Under State Constraints And Unknown Curvature, Michael Malisoff, Robert Sizemore, Fumin Zhang
Adaptive Planar Curve Tracking Control And Robustness Analysis Under State Constraints And Unknown Curvature, Michael Malisoff, Robert Sizemore, Fumin Zhang
Faculty Publications
We provide adaptive controllers for curve tracking in the plane, under unknown curvatures and control uncertainty, which is a central problem in robotics. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature, to form the augmented error dynamics. We prove input-to-state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control, under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this gives tracking of the curve …