arXiv subjects

Anusree Rajan

Publications and source records attributed to Anusree Rajan.

5 recordsLinked to original sources

arXiv2025

Event-Triggered Polynomial Control for Trajectory Tracking by Unicycle Robots

This paper proposes an event-triggered polynomial control method for trajectory tracking by unicycle robots. In this method, each control input between two consecutive events is a polynomial and its coefficients are chosen to minimize the error in approximating a continuous-time control signal. We design an event-triggering rule that guarantees uniform ultimate boundedness of the tracking error and non-Zeno behavior of inter-event times. We illustrate our results through a suite of numerical simulations and experiments, which indicate that the number of events generated by the proposed controller is significantly less compared to that by a time-triggered controller or a event-triggered controller based on zero-order hold while guaranteeing similar tracking performance.

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arXiv2024

A Control Lyapunov Function Approach to Event-Triggered Parameterized Control for Discrete-Time Linear Systems

This paper proposes an event-triggered parameterized control method using a control Lyapunov function approach for discrete time linear systems with external disturbances. In this control method, each control input to the plant is a linear combination of a fixed set of linearly independent scalar functions. The controller updates the coefficients of the parameterized control input in an event-triggered manner so as to minimize a quadratic cost function subject to quadratic constraints and communicates the same to the actuator. We design an event-triggering rule that guarantees global uniform ultimate boundedness of trajectories of the closed loop system and non-trivial inter-event times. We illustrate our results through numerical examples and we also compare the performance of the proposed control method with other existing control methods in the literature.

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arXiv2024

Event-Triggered Parameterized Control of Nonlinear Systems

This paper deals with event-triggered parameterized control (ETPC) of nonlinear systems with external disturbances. In this control method, between two successive events, each control input to the plant is a linear combination of a set of linearly independent scalar functions. At each event, the controller updates the coefficients of the parameterized control input so as to minimize the error in approximating a continuous time control signal and communicates the same to the actuator. We design an event-triggering rule (ETR) that guarantees global uniform ultimate boundedness of trajectories of the closed loop system. We also ensure the absence of Zeno behavior by showing the existence of a uniform positive lower bound on the inter-event times (IETs). We illustrate our results through numerical examples.

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arXiv2024

Asymptotic Behavior of Inter-Event Times in Planar Systems under Event-Triggered Control

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of the angle of the state at an event. This viewpoint allows us to analyze the inter-event times by studying the fixed points of the angle map, which represents the evolution of the angle of the state from one event to the next. We provide a sufficient condition for the convergence or non-convergence of inter-event times to a steady state value under a scale-invariant event-triggering rule. Following up on this, we further analyze the inter-event time behavior in the special case of threshold based event-triggering rule and we provide various conditions for convergence or non-convergence of inter-event times to a constant. We also analyze the asymptotic average inter-event time as a function of the angle of the initial state of the system. With the help of ergodic theory, we provide a sufficient condition for the asymptotic average inter-event time to be a constant for all non-zero initial states of the system. Then, we consider a special case where the angle map is an orientation-preserving homeomorphism. Using rotation theory, we comment on the asymptotic behavior of the inter-event times, including on whether the inter-event times converge to a periodic sequence. We illustrate the proposed results through numerical simulations.

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arXiv2023

Analysis of Inter-Event Times in Linear Systems under Region-Based Self-Triggered Control

This paper analyzes the evolution of inter-event times (IETs) in linear systems under region-based self-triggered control (RBSTC). In this control method, the state space is partitioned into a finite number of conic regions and each region is associated with a fixed IET. In this framework, studying the steady state behavior of the IETs is equivalent to studying the existence of a conic subregion that is positively invariant under the map that gives the evolution of the state from one event to the next. We provide necessary conditions and sufficient conditions for the existence of a positively invariant subregion (PIS). We also provide necessary and sufficient conditions for a PIS to be asymptotically stable. Indirectly, they provide necessary and sufficient conditions for local convergence of IETs to a constant or to a given periodic sequence. We illustrate the proposed method of analysis and results through numerical simulations.

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