### Abstract

In this paper, we formulate a general class of Adaptive FSI (full-state information) optimal control problems, and develop a constructive method to solve it. An Adaptive FSI problem is defined in terms of state dynamics which are linear in the unknown constant parameters and additive state disturbances, but nonlinear otherwise, and a soft-constrained performance function that is quadratic in disturbances and the unknown parameters, but non-quadratic otherwise. In this formulation, the controller is assumed to have access to the current and past values of both the state and its derivative. Using the cost-to-come method, we show that the original problem with partial information can be converted into an equivalent full information (FI) minimax control problem of higher dimension, which can be solved using Dynamic Programming (DP) methods. Both the finite-and-infinite-horizon problems are considered, and in each case, a set of necessary and sufficient conditions are obtained. The methodology is illustrated on a numerical example.

Original language | English (US) |
---|---|

Pages (from-to) | 2839-2844 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 3 |

State | Published - Dec 1 1994 |

Event | Proceedings of the 2nd IEEE International Symposium on Requirements Engineering - York, Engl Duration: Mar 27 1995 → Mar 29 1995 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*3*, 2839-2844.

**Minimax adaptive control of uncertain plants.** / Didinsky, Garry; Basar, M Tamer.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 3, pp. 2839-2844.

}

TY - JOUR

T1 - Minimax adaptive control of uncertain plants

AU - Didinsky, Garry

AU - Basar, M Tamer

PY - 1994/12/1

Y1 - 1994/12/1

N2 - In this paper, we formulate a general class of Adaptive FSI (full-state information) optimal control problems, and develop a constructive method to solve it. An Adaptive FSI problem is defined in terms of state dynamics which are linear in the unknown constant parameters and additive state disturbances, but nonlinear otherwise, and a soft-constrained performance function that is quadratic in disturbances and the unknown parameters, but non-quadratic otherwise. In this formulation, the controller is assumed to have access to the current and past values of both the state and its derivative. Using the cost-to-come method, we show that the original problem with partial information can be converted into an equivalent full information (FI) minimax control problem of higher dimension, which can be solved using Dynamic Programming (DP) methods. Both the finite-and-infinite-horizon problems are considered, and in each case, a set of necessary and sufficient conditions are obtained. The methodology is illustrated on a numerical example.

AB - In this paper, we formulate a general class of Adaptive FSI (full-state information) optimal control problems, and develop a constructive method to solve it. An Adaptive FSI problem is defined in terms of state dynamics which are linear in the unknown constant parameters and additive state disturbances, but nonlinear otherwise, and a soft-constrained performance function that is quadratic in disturbances and the unknown parameters, but non-quadratic otherwise. In this formulation, the controller is assumed to have access to the current and past values of both the state and its derivative. Using the cost-to-come method, we show that the original problem with partial information can be converted into an equivalent full information (FI) minimax control problem of higher dimension, which can be solved using Dynamic Programming (DP) methods. Both the finite-and-infinite-horizon problems are considered, and in each case, a set of necessary and sufficient conditions are obtained. The methodology is illustrated on a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=0028738651&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028738651&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0028738651

VL - 3

SP - 2839

EP - 2844

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -