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Data-Based Control of Continuous-Time Linear Systems with Performance Specifications

Victor G. Lopez, Matthias A. Müller

TL;DR

This work develops a data-driven framework for continuous-time linear systems with performance requirements, leveraging a continuous-time Willems-type representation to design state-feedback controllers directly from data. It solves three problems—trajectory-reference control, data-based CT LQR, and data-based robust pole placement—each formulated to respect stability and performance using Hankel-like data structures and persistently exciting inputs. The results establish data-based stability conditions, provide procedures to obtain LQR gains from data, and introduce a robust pole-placement method that achieves exact pole placement despite measurement noise. The approach is demonstrated through simulations on CT linear models, illustrating practical viability for stabilization, optimal control, and pole placement without explicit system identification. This work thus offers a cohesive, data-driven pathway for CT control design with concrete performance guarantees and robustness to noise, potentially extendable to discrete-time and nonlinear CT systems.

Abstract

The design of direct data-based controllers has become a fundamental part of control theory research in the last few years. In this paper, we consider three classes of data-based state feedback control problems for linear systems. These control problems are such that, besides stabilization, some additional performance requirements must be satisfied. First, we formulate and solve a trajectory-reference control problem, on which desired closed-loop trajectories are known and a controller that allows the system to closely follow those trajectories is computed. Then, the solution of the LQR problem for continuous-time systems is presented. Finally, we consider the case in which the precise position of the desired poles of the closed-loop system is known, and introduce a data-based variant of a robust pole-placement procedure. The applicability of the proposed methods is tested using numerical simulations.

Data-Based Control of Continuous-Time Linear Systems with Performance Specifications

TL;DR

This work develops a data-driven framework for continuous-time linear systems with performance requirements, leveraging a continuous-time Willems-type representation to design state-feedback controllers directly from data. It solves three problems—trajectory-reference control, data-based CT LQR, and data-based robust pole placement—each formulated to respect stability and performance using Hankel-like data structures and persistently exciting inputs. The results establish data-based stability conditions, provide procedures to obtain LQR gains from data, and introduce a robust pole-placement method that achieves exact pole placement despite measurement noise. The approach is demonstrated through simulations on CT linear models, illustrating practical viability for stabilization, optimal control, and pole placement without explicit system identification. This work thus offers a cohesive, data-driven pathway for CT control design with concrete performance guarantees and robustness to noise, potentially extendable to discrete-time and nonlinear CT systems.

Abstract

The design of direct data-based controllers has become a fundamental part of control theory research in the last few years. In this paper, we consider three classes of data-based state feedback control problems for linear systems. These control problems are such that, besides stabilization, some additional performance requirements must be satisfied. First, we formulate and solve a trajectory-reference control problem, on which desired closed-loop trajectories are known and a controller that allows the system to closely follow those trajectories is computed. Then, the solution of the LQR problem for continuous-time systems is presented. Finally, we consider the case in which the precise position of the desired poles of the closed-loop system is known, and introduce a data-based variant of a robust pole-placement procedure. The applicability of the proposed methods is tested using numerical simulations.
Paper Structure (14 sections, 48 equations, 1 figure, 2 tables)

This paper contains 14 sections, 48 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. A continuous-time version of Willems' lemma
  5. Conditions for stabilizing control of continuous-time systems
  6. Data-based control design with performance specifications
  7. Trajectory-reference control
  8. Data-based optimal control for CT systems
  9. Data-based robust pole placement
  10. Simulation examples
  11. Trajectory-reference control
  12. Data-based optimal control
  13. Robust pole placement
  14. Conclusion

Figures (1)

  • Figure 1: A trajectory (blue) for each state is given as reference for problem (\ref{['optprobbc']}). The states of the system (dashed red) closely follow the desired references.