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This thesis explores the attitude estimation and control problem of a magnetically controlled small satellite in initial acquisition phase. During this phase, large data uncertainties pose estimation challenges, while highly nonlinear dynamics and inherent limitations of the magnetic actuation are primary issues in control. We aim to design algorithms, which can improve performance compared to the state of the art techniques and remain tractable for practical applications. Static attitude estimation, which is an essential part of a satellite control system, uses vector information and solves a constrained weighted least-square problem. With large data uncertainties, this technique results in large errors rendering divergence or infeasibility in dynamic filtering and control. When static estimation is the primary source of attitude, these errors become critical; for example in low budget small satellites. To address this issue, we formulate a robust static estimation problem with norm-bounded uncertainties, which is a difficult optimization problem due to its unfavorable convexity properties and nonlinear constraints. By deriving an analytical upper bound for the convex maximization, the robust min-max problem is approximated with a minimization problem with quadratic cost and constraints (a QCQP), which is non-convex. Semidefinite relaxation is used to upper bound the non-convex QCQP with a semi-definite program, which can efficiently be solved in a polynomial time. Furthermore, it is shown that the derived upper bound has no gap in solving the robust problem in practice. Semi-definite relaxations are also applied to solve the robust formulations of a more general class of problems known as the orthogonal Procrustes problem (OPP). It is shown that the solution of the relaxed OPP is exact when no uncertainties are considered; however, for the robust case, only a sub-optimal solution can be obtained. Finally, a satellite rate damping in initial acquisition phase is addressed by using nonlinear model predictive control (NMPC). Standard NMPC schemes with guaranteed stability show superior performance than existing techniques; however, they are computationally expensive. With large initial rates, the computational burden of NMPC becomes prohibitively excessive. For these cases, an algorithm is presented with an additional constraint on the cost reduction that allows an early termination of the optimizer based on the available computational resources. The presented algorithm significantly reduces the de-tumbling time due to the imposed cost reduction constraint.

Stream water quality and ecosystem health are controlled by a multitude of complex, interacting anthropogenic and natural processes. A generalized understanding of stream water quality dynamics under diverse hydro-climatic and biogeochemical conditions therefore still remains elusive, particularly in the context of coastal urban/natural environments. This dissertation focuses to investigate the major spatiotemporal controls of stream water quality, and leverages the knowledge to investigate stream biogeochemical-ecological similitude (parametric reduction), scaling, and emergent patterns across the East Coast of U.S.A. Total nitrogen (TN), total phosphorus (TP), chlorophyll-a (Chla), and dissolved oxygen (DO) were used to represent the stream water quality. Pearson correlation matrix, principal component analysis, and factor analysis were used to analyze the interrelations and groupings among the environmental drivers alongside tracking their individual linkages with the stream water quality. Partial least squares regression models were then developed to directly estimate the linkages by appropriately resolving multicollinearity among the predictor variables. Spatial analytics on 6 major streams in southeast Florida indicated the external sources (e.g., Everglades) and draining watershed's agricultural lands as the major drivers of in-stream TN, TP, and Chla. However, stream DO was most strongly influenced by the adjacent groundwater depth and watershed (agricultural and built-up) land uses. Spatio-temporal analytics on 50 stream sites across the East Coast showed strong controls of climatic (stream temperature) and biogeochemical (pH and salinity) drivers on stream DO. The dominant drivers were then involved in dimensional analysis to formulate mechanistically meaningful dimensionless numbers, which represented the contrasting as well as the collective influence of different hydro-climatic and biogeochemical drivers on stream water quality. A graphical exploration of the driver (predictor) numbers and stream DO number unraveled emergent patterns by collapsing observations from diverse environmental conditions into single dimensionless curves. Two environmental regimes ('climatic' versus 'metabolic' controls) were identified based on the critical threshold of the driver dimensionless number. The dimensionless numbers and emergent patterns led to the estimation of a scaling relationship, which was robust across the different environmental regimes. The scaling relationship was then utilized as a non-linear empirical model to successfully predict DO from numerous streams across the East Coast of U.S.A. (Nash-Sutcliffe Efficiency = 0.82). The research findings and insights are expected to guide effective water resources management for maintaining healthy stream water quality across the U.S. East Coast and similar regions around the world.