<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.</p></abstract>

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

Fundamental Limitations of the Decay of Generalized Energy in Controlled (Discrete–Time) Nonlinear Systems Subject to State and Input Constraints

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard...

Fundamental Limitations of the Decay of Generalized Energy in Controlled (Discrete–Time) Nonlinear Systems Subject to State and Input Constraints

Published Online: Dec 31, 2019

Page range: 629 - 639

Received: Nov 30, 2018

Accepted: Jul 25, 2019

DOI: https://doi.org/10.2478/amcs-2019-0046

Keywords
decay rate maximization, Lyapunov function, nonlinear control systems

© 2019 István Selek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fundamental Limitations of the Decay of Generalized Energy in Controlled (Discrete–Time) Nonlinear Systems Subject to State and Input Constraints

Published Online: Dec 31, 2019

Page range: 629 - 639

Received: Nov 30, 2018

Accepted: Jul 25, 2019

DOI: https://doi.org/10.2478/amcs-2019-0046

Keywordsdecay rate maximization, Lyapunov function, nonlinear control systems

© 2019 István Selek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
decay rate maximization, Lyapunov function, nonlinear control systems