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| Author(s): |
Filipe de Carvalho Pedrosa
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: | 2018-05-24 |
| Examining board members: |
João Bosco Ribeiro do Val;
Marcos Garcia Todorov;
Alim Pedro de Castro Gonçalves
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| Advisor: | João Bosco Ribeiro do Val |
| Abstract | |
This master's thesis deals with the paradigm of optimal control for stochastic systems whose dynamics are poorly known and impossible to be fully determined. To this end, we introduce the CVIU principle (Control Variation Increases Uncertainty) and devise the controls accordingly. The CVIU model comes in handy particularly in situations where a full dynamic model is not available and the employment of systems identification techniques is prohibitive. Consequently, only a rough model is available for control design. The conception of the CVIU approach is developed from the standpoint of one moderately known equilibrium point and an alternative way to account for the inherent model uncertainties. Interesting solution characteristics emerge from the optimal control problem. For instance, the existence of a delimited region on the state space within which the optimal control action is to remain idle - the so called inaction region. This feature, peculiar to the CVIU approach, has ties to cautionary control policies with occurrences in the context of economics. The infinite horizon, discounted control problem with quadratic cost function admits solutions in closed form inside the inaction region, given by a linearly perturbed Lyapunov equation, and asymptotically in far-off regions by a rational Riccati equation. The complete solution is comprised of an anlytical part and a numerical one, to be considered in the intermediate regions stretching from the inaction region to the asymptotic ones in the infinity. Additionally, existence conditions and solution methods for these algebraic equations are explored as they are of utmost importance when deriving the solution to the CVIU control problem. Moreover, as a last contribution of this work, a stochastic stability analysis is carried out for the CVIU controlled model. In the final chapter of this manuscript, three numerical experiments illustrate the application of the CVIU controller in distinct scenarios. Firstly, a CVIU control policy is applied in an optimal fish harvesting problem. In a second moment, the experiment proposes a comparison between the average incurred costs associated to the CVIU and LQG policies for an uncertain system with mismatched parameters. This experiments points to case scenarios where the use of the CVIU policy is more advantageous than that of the LQG regulator. At last, an example of a two-dimensional CVIU system in the states and control is brought about and interesting features of the technique become visually perceptible (AU) | |
| FAPESP's process: | 16/13508-0 - Modeling and control of discrete stochastic systems with poorly known dynamics |
| Grantee: | Filipe de Carvalho Pedrosa |
| Support Opportunities: | Scholarships in Brazil - Master |