# Output feedback optimal control with contraints

Perez, Tristan & Haimovich, Hernan
(2005)
Output feedback optimal control with contraints.
In
Goodwin, Graham C, Seron , Maria M, & Doná, José A (Eds.) *Constrained Control and Estimation : An Optimisation Approach (Part II).*
Springer London, The United Kingdom, pp. 279-294.

## Abstract

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.)

When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.

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ID Code: | 70634 |
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Item Type: | Book Chapter |

Keywords: | Control Engineering , Systems Theory, Control , Optimization , Control Structures and Microprogramming |

DOI: | 10.1007/1-84628-063-X_12 |

ISBN: | 9781846280634 (online) 9781852335489 (print) |

ISSN: | 0178-5354 |

Divisions: | Current > Schools > School of Electrical Engineering & Computer Science Current > QUT Faculties and Divisions > Science & Engineering Faculty |

Copyright Owner: | Copyright 2005 Springer-Verlag London Limited |

Deposited On: | 30 Apr 2014 23:48 |

Last Modified: | 25 Jun 2016 03:52 |

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