Grimble, M.J. and Martin, P. (2003) *Time varying optimal control of a non-linear system.* In: 42nd IEEE Conference on Decision and Control 2003, 2003-12-09 - 2003-12-12, Maui.

## Abstract

The solution is given to a time-varying optimal state feedback problem with stochastic disturbances. The system is composed of a plant and disturbance model represented by polynomials in the delay operator, z(-1), leading to a solution involving spectral factorisation of operator equations and Diophantine operator equations. The cost function is over infinite time and the assumption is made that the system is time-varying for T steps into the future from the current sample and time-invariant thereafter. For a time-invariant system over infinite time, the optimal controller is a constant state-feedback matrix gain. Thus, with the assumption of time-invariance from T to, the feedback gain may be calculated using constant system polynomials. The solution of the spectral factors and Diophantine equations may then be computed recursively, for a scalar plant, working from T steps ahead to the current time. The controller calculated for the current time is then applied to the system. If the input non-linearity of a plant is represented in time-varying form, the time-varying ideas may be used to produce a nonlinear controller for the system. The example in this paper is for a smooth saturation non-linearity represented by a tanh function. Simulation results are given and it is clear that performance gains over a time-invariant controller are possible.

Item type: | Conference or Workshop Item (Paper) |
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ID code: | 39323 |

Keywords: | time varying, optimal control, non-linear system, control systems, time varying systems , stochastic processes , state feedback , polynomials, nonlinear equations, nonlinear control systems, delay, cost function, Electrical engineering. Electronics Nuclear engineering |

Subjects: | Technology > Electrical engineering. Electronics Nuclear engineering |

Department: | Faculty of Engineering > Electronic and Electrical Engineering |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 24 Apr 2012 10:57 |

Last modified: | 17 Jul 2013 15:13 |

URI: | http://strathprints.strath.ac.uk/id/eprint/39323 |

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