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| Author(s): |
Diego de Sousa Madeira
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação |
| Defense date: | 2012-03-29 |
| Examining board members: |
João Bosco Ribeiro do Val;
Marcelo Dutra Fragoso;
Paulo Augusto Valente Ferreira
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| Advisor: | João Bosco Ribeiro do Val |
| Abstract | |
The main contributions of this work are that the necessary and sufficient optimality conditions for the control problem of discrete linear deterministic systems and some classes of linear stochastic systems are obtained. We adopted the output feedback control method, a finite horizon control and a cost function that is quadratic in the state and control vectors. The deterministic problem is completely solved, that is, we prove that for any MIMO system the necessary optimality conditions are also sufficient. To do so, a formulation of the Discrete Maximum Principle is used. Furthermore, we analyze the stochastic case with additive noise and prove that the discrete maximum principle provides the necessary optimality conditions, though they are not sufficient. Finally, in a particular two-stage scenario, we apply a parametrization technique of the cost function associated with the linear stochastic system with additive noise and prove that, for SISO systems with orthogonal matrices C (output) and B (input) so that CB = 0, the necessary optimality conditions are sufficient too. We prove that under the underlined context the previous statement is also valid in the case of the Markov Jump Linear Systems (MJLS). In order to illustrate the theoretical results obtained, some numerical examples are given (AU) | |
| FAPESP's process: | 09/12511-4 - Control of Markov Jump Systems under the Long Run Average Criteria |
| Grantee: | Diego de Sousa Madeira |
| Support Opportunities: | Scholarships in Brazil - Master |