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Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints

The problem of finding a feedback law that drives the state of a linear discrete-time system to the origin in minimum-time subject to state-control constraints is considered. Algorithms are given to obtain facial descriptions of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -step admissible sets. These descriptions are then used to characterize the complete class of minimum-time feedback laws. Moreover, the characterization leads to a conceptually simple on-line implementation. The main ideas are illustrated with two simple examples.

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S.S. Keerthi · · 1 min read · 3 views
#Advanced Control Systems Optimization #Stability and Control of Uncertain Systems #Adaptive Control of Nonlinear Systems

The problem of finding a feedback law that drives the state of a linear discrete-time system to the origin in minimum-time subject to state-control constraints is considered. Algorithms are given to obtain facial descriptions of the M -step admissible sets. These descriptions are then used to characterize the complete class of minimum-time feedback laws. Moreover, the characterization leads to a conceptually simple on-line implementation. The main ideas are illustrated with two simple examples.

Executive Summary

This article presents algorithms for computing minimum-time feedback control laws for discrete-time systems with state-control constraints. The authors provide facial descriptions of the M-step admissible sets, which are used to characterize the complete class of minimum-time feedback laws. The main contribution of the article is the development of a conceptually simple on-line implementation of the minimum-time feedback laws. The authors illustrate the main ideas with two simple examples. The article has significant implications for the control of discrete-time systems with state-control constraints, particularly in applications where real-time implementation is critical. The results presented in the article have the potential to improve the performance of control systems in various fields, including robotics, aerospace, and process control.

Key Points

  • ▸ The article presents algorithms for computing minimum-time feedback control laws for discrete-time systems with state-control constraints.
  • ▸ The authors provide facial descriptions of the M-step admissible sets, which are used to characterize the complete class of minimum-time feedback laws.
  • ▸ The article develops a conceptually simple on-line implementation of the minimum-time feedback laws.

Merits

Contribution to Control Theory

The article presents new algorithms for computing minimum-time feedback control laws, which is a significant contribution to the field of control theory. The development of these algorithms has the potential to improve the performance of control systems in various applications.

Practical Implementation

The article provides a conceptually simple on-line implementation of the minimum-time feedback laws, which is a significant advantage for practical applications where real-time implementation is critical.

Demerits

Limited Scope

The article is limited to discrete-time systems with state-control constraints, which may not be applicable to other types of systems or control problems.

Complexity of Algorithms

The algorithms presented in the article may be complex and difficult to implement in practice, particularly for large-scale systems.

Expert Commentary

The article presents a significant contribution to the field of control theory, with the development of new algorithms for computing minimum-time feedback control laws. The conceptually simple on-line implementation of the minimum-time feedback laws is a significant advantage for practical applications. However, the article is limited to discrete-time systems with state-control constraints, which may not be applicable to other types of systems or control problems. The complexity of the algorithms presented in the article may also be a challenge for practical implementation. Nevertheless, the article has significant implications for the control of discrete-time systems with state-control constraints, and the results presented have the potential to improve the performance of control systems in various fields.

Recommendations

  • ✓ The article is recommended for researchers and practitioners in the field of control theory, particularly those working on discrete-time systems with state-control constraints.
  • ✓ The algorithms presented in the article may be of interest to developers of control systems in various fields, including robotics, aerospace, and process control.

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