In the thesis, two different model predictive control (MPC) strategies are investigated for linear systems with uncertainty in the presence of constraints: namely robust MPC and stochastic MPC. Firstly, a Youla Parameter is integrated into an efficient robust MPC algorithm. It is demonstrated that even in the constrained cases, the use of the Youla Parameter can desensitize the costs to the effect of uncertainty while not affecting the nominal performance, and hence it strengthens the robustness of the MPC strategy. Since the controller u = K x + c can offer many advantages and is used across the thesis, the work provides two solutions to the problem when the unconstrained nominal LQ-optimal feedback K cannot stabilise the whole class of system models. The work develops two stochastic tube approaches to account for probabilistic constraints. By using a semi closed-loop paradigm, the nominal and the error dynamics are analyzed separately, and this makes it possible to compute the tube scalings offline. First, ellipsoidal tubes are considered. The evolution for the tube scalings is simplified to be affine and using Markov Chain model, the probabilistic tube scalings can be calculated to tighten the constraints on the nominal. The online algorithm can be formulated into a quadratic programming (QP) problem and the MPC strategy is closed-loop stable. Following that, a direct way to compute the tube scalings is studied. It makes use of the information on the distribution of the uncertainty explicitly. The tubes do not take a particular shape but are defined implicitly by tightened constraints. This stochastic MPC strategy leads to a non-conservative performance in the sense that the probability of constraint violation can be as large as is allowed. It also ensures the recursive feasibility and closed-loop stability, and is extended to the output feedback case.

For traditional wireless communication systems, static spectrum allocation is the major spectrum allocation methodology. However, according to the recent investigations by the FCC, this has led to more than 70 percent of the allocated spectrum in the United States being under-utilized. Cognitive radio (CR) technology, which supports opportunistic spectrum sharing, is one idea that is proposed to improve the overall utilization efficiency of the radio spectrum. In this thesis we consider a CR communication system based on spectrum sharing schemes, where we have a secondary user (SU) link with multiple transmitting antennas and a single receiving antenna, coexisting with a primary user (PU) link with a single receiving antenna. At the SU transmitter (SU-Tx), the channel state information (CSI) of the SU link is assumed to be perfectly known; while the interference channel from the SU-Tx to the PU receiver (PU-Rx) is not perfectly known due to less cooperation between the SU and the PU. As such, the SU-Tx is only assumed to know that the interference channel gain can take values from a finite set with certain probabilities. Considering a SU transmit power constraint, our design objective is to determine the transmit covariance matrix that maximizes the SU rate, while we protect the PU by enforcing both a PU average interference constraint and a PU outage probability constraint. This problem is first formulated as a non-convex optimization problem with a non-explicit probabilistic constraint, which is then approximated as a mixed binary integer programming (MBIP) problem and solved with the Branch and Bound (BB) algorithm. The complexity of the BB algorithm is analyzed and numerical results are presented to validate the eff ectiveness of the proposed algorithm. A key result proved in this thesis is that the rank of the optimal transmit covariance matrix is one, i.e., CR beamforming is optimal under PU outage constraints. Finally, a heuristic algorithm is proposed to provide a suboptimal solution to our MBIP problem by efficiently (in polynomial time) solving a particularly-constructed convex problem.

ARARUMA Arthur Rodrigues. Caminho mínimo com restrição probabilística de atraso máximo. 2013. 89 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2013. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-08T19:26:26Z No. of bitstreams: 1 2013_dis_arararuna.pdf: 2167566 bytes, checksum: cd1f84fd0b24a51bd2b955d8e18a7ea1 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-13T13:35:18Z (GMT) No. of bitstreams: 1 2013_dis_arararuna.pdf: 2167566 bytes, checksum: cd1f84fd0b24a51bd2b955d8e18a7ea1 (MD5) / Made available in DSpace on 2016-07-13T13:35:18Z (GMT). No. of bitstreams: 1 2013_dis_arararuna.pdf: 2167566 bytes, checksum: cd1f84fd0b24a51bd2b955d8e18a7ea1 (MD5) Previous issue date: 2013 / In the Probabilistic Delay Constrained Shortest Path problem we aim to consider the time factor in the design of cargo routing paths in road networks at minimum cost, considering the increasing uncertainty in travel times of these routes in real networks, and keeping in mind strategies of quality of service, in order to obtain a compromise between the travel costs and the compliance of the arrival time at the destination. We conducted a study of related problems in the literature of transport networks optimization, in order to better understand the problem to be addressed, about which we are not aware of existing works. We developed a scheme for enumerating partitions of the solution space of this problem, which uses an L decomposition to select these partitions wisely, and is aided by solutions to relaxations of the problem to obtain bounds for the optimal cost. In addition, we developed some branching and pruning strategies for a Branch-and-Bound scheme, with a pre-processing phase, in order to try and solve the problem directly. The computational results show that we are competitive with the commercial tool used for comparison in the smaller instances. For the remaining instances, this tool is more efficient in the time required for solving the problem. / No problema do Caminho Mínimo com Restrição Probabilística de Atraso Máximo visamos considerar o fator tempo no projeto de rotas de transporte de cargas em malhas viárias a custo mínimo, atentando à crescente incerteza nos tempos de percurso dessas rotas em malhas reais, e observá-lo tendo em mente estratégias de qualidade de serviço, de forma a obtermos um compromisso entre o custo de percurso e a conformidade ao prazo de chegada ao destino. Realizamos um estudo de problemas relacionados na literatura da área de otimização em redes de transporte, de forma a tentarmos conhecer melhor o problema a ser estudado, sobre o qual não tomamos conhecimento de trabalhos existentes. Desenvolvemos um esquema para enumeração de partições do espaço de soluções do problema, que utiliza uma decomposição em L para selecionar partições de forma inteligente, e que é auxiliado por soluções de relaxações do problema de forma a obter cotas para o custo ótimo. Além disso, desenvolvemos algumas estratégias de ramificação e de poda para um esquema de Branch-and-Bound, com uma fase de pré-processamento, de forma a tentar resolver o problema diretamente. Os resultados computacionais obtidos demonstram que somos competitivos com a ferramenta comercial utilizada para comparação em instâncias de menor porte para o problema. Para as demais instâncias, essa ferramenta se mostrou mais eficiente quanto ao tempo necessário para a resolução.

ARARUNA, Arthur Rodrigues. Caminho mínimo com restrição probabilística de atraso máximo. 2013. 88 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2013. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-06-01T19:53:59Z No. of bitstreams: 1 2013_dis_arararuna.pdf: 2167566 bytes, checksum: cd1f84fd0b24a51bd2b955d8e18a7ea1 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-06-01T19:54:22Z (GMT) No. of bitstreams: 1 2013_dis_arararuna.pdf: 2167566 bytes, checksum: cd1f84fd0b24a51bd2b955d8e18a7ea1 (MD5) / Made available in DSpace on 2016-06-01T19:54:22Z (GMT). No. of bitstreams: 1 2013_dis_arararuna.pdf: 2167566 bytes, checksum: cd1f84fd0b24a51bd2b955d8e18a7ea1 (MD5) Previous issue date: 2013 / In the Probabilistic Delay Constrained Shortest Path problem we aim to consider the time factor in the design of cargo routing paths in road networks at minimum cost, considering the increasing uncertainty in travel times of these routes in real networks, and keeping in mind strategies of quality of service, in order to obtain a compromise between the travel costs and the compliance of the arrival time at the destination. We conducted a study of related problems in the literature of transport networks optimization, in order to better understand the problem to be addressed, about which we are not aware of existing works. We developed a scheme for enumerating partitions of the solution space of this problem, which uses an L decomposition to select these partitions wisely, and is aided by solutions to relaxations of the problem to obtain bounds for the optimal cost. In addition, we developed some branching and pruning strategies for a Branch-and-Bound scheme, with a pre-processing phase, in order to try and solve the problem directly. The computational results show that we are competitive with the commercial tool used for comparison in the smaller instances. For the remaining instances, this tool is more efficient in the time required for solving the problem. / No problema do Caminho Mínimo com Restrição Probabilística de Atraso Máximo visamos considerar o fator tempo no projeto de rotas de transporte de cargas em malhas viárias a custo mínimo, atentando à crescente incerteza nos tempos de percurso dessas rotas em malhas reais, e observá-lo tendo em mente estratégias de qualidade de serviço, de forma a obtermos um compromisso entre o custo de percurso e a conformidade ao prazo de chegada ao destino. Realizamos um estudo de problemas relacionados na literatura da área de otimização em redes de transporte, de forma a tentarmos conhecer melhor o problema a ser estudado, sobre o qual não tomamos conhecimento de trabalhos existentes. Desenvolvemos um esquema para enumeração de partições do espaço de soluções do problema, que utiliza uma decomposição em L para selecionar partições de forma inteligente, e que é auxiliado por soluções de relaxações do problema de forma a obter cotas para o custo ótimo. Além disso, desenvolvemos algumas estratégias de ramificação e de poda para um esquema de Branch-and-Bound, com uma fase de pré-processamento, de forma a tentar resolver o problema diretamente. Os resultados computacionais obtidos demonstram que somos competitivos com a ferramenta comercial utilizada para comparação em instâncias de menor porte para o problema. Para as demais instâncias, essa ferramenta se mostrou mais eficiente quanto ao tempo necessário para a resolução.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / No problema do Caminho MÃnimo com RestriÃÃo ProbabilÃstica de Atraso MÃximo visamos considerar o fator tempo no projeto de rotas de transporte de cargas em malhas viÃrias a custo mÃnimo, atentando à crescente incerteza nos tempos de percurso dessas rotas em malhas reais, e observÃ-lo tendo em mente estratÃgias de qualidade de serviÃo, de forma a obtermos um compromisso entre o custo de percurso e a conformidade ao prazo de chegada ao destino. Realizamos um estudo de problemas relacionados na literatura da Ãrea de otimizaÃÃo em redes de transporte, de forma a tentarmos conhecer melhor o problema a ser estudado, sobre o qual nÃo tomamos conhecimento de trabalhos existentes. Desenvolvemos um esquema para enumeraÃÃo de partiÃÃes do espaÃo de soluÃÃes do problema, que utiliza uma decomposiÃÃo em L para selecionar partiÃÃes de forma inteligente, e que à auxiliado por soluÃÃes de relaxaÃÃes do problema de forma a obter cotas para o custo Ãtimo. AlÃm disso, desenvolvemos algumas estratÃgias de ramificaÃÃo e de poda para um esquema de Branch-and-Bound, com uma fase de prÃ-processamento, de forma a tentar resolver o problema diretamente. Os resultados computacionais obtidos demonstram que somos competitivos com a ferramenta comercial utilizada para comparaÃÃo em instÃncias de menor porte para o problema. Para as demais instÃncias, essa ferramenta se mostrou mais eficiente quanto ao tempo necessÃrio para a resoluÃÃo. / In the Probabilistic Delay Constrained Shortest Path problem we aim to consider the time factor in the design of cargo routing paths in road networks at minimum cost, considering the increasing uncertainty in travel times of these routes in real networks, and keeping in mind strategies of quality of service, in order to obtain a compromise between the travel costs and the compliance of the arrival time at the destination. We conducted a study of related problems in the literature of transport networks optimization, in order to better understand the problem to be addressed, about which we are not aware of existing works. We developed a scheme for enumerating partitions of the solution space of this problem, which uses an L decomposition to select these partitions wisely, and is aided by solutions to relaxations of the problem to obtain bounds for the optimal cost. In addition, we developed some branching and pruning strategies for a Branch-and-Bound scheme, with a pre-processing phase, in order to try and solve the problem directly. The computational results show that we are competitive with the commercial tool used for comparison in the smaller instances. For the remaining instances, this tool is more efficient in the time required for solving the problem.

This dissertation addresses a fundamental question of multi-agent coordination: what infor- mation should be sent to whom and when, with the limited resources available to each agent? Communication requirements for multi-agent systems can be rather high when an accurate picture of the environment and the state of other agents must be maintained. To reduce the impact of multi-agent coordination on networked systems, e.g., power and bandwidth, this dissertation introduces new concepts to enable Intelligent Knowledge Distribution (IKD), including Constrained-action POMDPs (CA-POMDP) and concurrent decentralized (CoDec) POMDPs for an agnostic plug-and-play capability for fully autonomous systems. Each agent runs a CoDec POMDP where all the decision making (motion planning, task allocation, asset monitoring, and communication) are separated into concurrent individual MDPs to reduce the combinatorial explosion of the action and state space while maintaining dependencies between the models. We also introduce the CA-POMDP with action-based constraints on partially observable Markov decision processes, rewards driven by the value of information, and probabilistic constraint satisfaction through discrete optimization and Markov chain Monte Carlo analysis. IKD is adapted real-time through machine learning of the actual environmental impacts on the behavior of the system, including collaboration strategies between autonomous agents, the true value of information between heterogeneous systems, observation probabilities and resource utilization. / Doctor of Philosophy / This dissertation addresses a fundamental question behind when multiple autonomous sys- tems, like drone swarms, in the field need to coordinate and share data: what information should be sent to whom and when, with the limited resources available to each agent? Intelligent Knowledge Distribution is a framework that answers these questions. Communication requirements for multi-agent systems can be rather high when an accurate picture of the environment and the state of other agents must be maintained. To reduce the impact of multi-agent coordination on networked systems, e.g., power and bandwidth, this dissertation introduces new concepts to enable Intelligent Knowledge Distribution (IKD), including Constrained-action POMDPs and concurrent decentralized (CoDec) POMDPs for an agnostic plug-and-play capability for fully autonomous systems. The IKD model was able to demonstrate its validity as a "plug-and-play" library that manages communications between agents that ensures the right information is being transmitted at the right time to the right agent to ensure mission success.