Regular Papers

International Journal of Control, Automation and Systems 2014; 12(4): 722-732

Published online July 1, 2014

https://doi.org/10.1007/s12555-013-0234-2

© The International Journal of Control, Automation, and Systems

Optimal Time-varying P-controller for a Class of Uncertain Nonlinear Systems

M. Suruz Miah* and Wail Gueaieb

University of Ottawa

Abstract

In this manuscript, an optimal time-varying P-controller is presented for a class of continuous-time underactuated nonlinear systems in the presence of process noise associated with systems’ inputs. This is a state feedback control strategy where the optimization is performed on a time-varying feedback operator (herein called the feedback control gain). The main goal of the current manuscript is to provide a framework for multi-input multi-output nonlinear systems which yields a satisfactory tracking performance based on the optimal time-varying feedback control gain. Unlike other feedback control techniques that perform dynamic linearization of system models, the proposed time-varying P-controller provides the full-state feedback control to the original nonlinear system model. Hence, this P-controller guarantees global asymptotic state-tracking. Furthermore, the bounded system’s process noise is taken into consideration to measure the controller’s robustness. The proposed P-controller is tested for its nonlinear trajectory tracking and fixed-point stabilization capabilities with two non-holonomic systems in the presence of input noise.

Keywords Feedback control gain, gradient descent, hamiltonian, lagrange multipliers, mobile robots, optimal control, robustness.

Article

Regular Papers

International Journal of Control, Automation and Systems 2014; 12(4): 722-732

Published online August 1, 2014 https://doi.org/10.1007/s12555-013-0234-2

Copyright © The International Journal of Control, Automation, and Systems.

Optimal Time-varying P-controller for a Class of Uncertain Nonlinear Systems

M. Suruz Miah* and Wail Gueaieb

University of Ottawa

Abstract

In this manuscript, an optimal time-varying P-controller is presented for a class of continuous-time underactuated nonlinear systems in the presence of process noise associated with systems’ inputs. This is a state feedback control strategy where the optimization is performed on a time-varying feedback operator (herein called the feedback control gain). The main goal of the current manuscript is to provide a framework for multi-input multi-output nonlinear systems which yields a satisfactory tracking performance based on the optimal time-varying feedback control gain. Unlike other feedback control techniques that perform dynamic linearization of system models, the proposed time-varying P-controller provides the full-state feedback control to the original nonlinear system model. Hence, this P-controller guarantees global asymptotic state-tracking. Furthermore, the bounded system’s process noise is taken into consideration to measure the controller’s robustness. The proposed P-controller is tested for its nonlinear trajectory tracking and fixed-point stabilization capabilities with two non-holonomic systems in the presence of input noise.

Keywords: Feedback control gain, gradient descent, hamiltonian, lagrange multipliers, mobile robots, optimal control, robustness.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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