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

M. Suruz Miah* and Wail Gueaieb
International Journal of Control, Automation, and Systems, vol. 12, no. 4, pp.722-732, 2014

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.

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

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