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

Anusree Rajan, Kushagra Parmeshwar, Pavankumar Tallapragada

Abstract

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.

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

Abstract

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.

Paper Structure

This paper contains 11 sections, 4 theorems, 33 equations, 2 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Literature Review
  3. Contributions
  4. Notation
  5. PROBLEM SETUP
  6. DESIGN OF EVENT-TRIGGERED CONTROLLER
  7. Design of Parameterized Control Law
  8. Design of Event-Triggering Rule
  9. ANALYSIS OF THE EVENT-TRIGGERED CONTROLLER
  10. NUMERICAL EXAMPLES
  11. CONCLUSION

Key Result

Proposition 4

(Sufficient condition to ensure the feasibility of eq:QCQP). The optimization problem eq:QCQP is feasible if there exists a solution $C \in \mathbb{R}^{m(p+1) \times n}$ for the following linear matrix inequality (LMI), $\forall \tau \in [0,M]_{{\mathbb{Z}}}$, where $c_{ij}$ denotes the $\{i,j\}^{^\text{th}}$ element of $C$, and Here, $Q_{ij}(\tau)$ is the matrix formed by multiplying the $i{^\

Figures (2)

  • Figure 2: Event-triggered parameterized control configuration
  • Figure 3: Simulation results of Example 1 for $p=3$, $N=25$ and $x(0)=[2\quad5\quad6]^{\top}$.

Theorems & Definitions (12)

  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 4
  • proof
  • Remark 5
  • Lemma 6
  • proof
  • Lemma 7
  • proof
  • ...and 2 more