In the study of multi-agent systems (MASs), cooperative control is one of the most fundamental issues. As it covers a broad spectrum of applications in many industrial areas, there is a desire to design cooperative control protocols for different system and network setups. Motivated by this fact, in this thesis we focus on elaborating consensus protocol design, via model predictive control (MPC), under two different scenarios: (1) general constrained linear MASs with bounded additive disturbance; (2) linear MASs with input constraints underlying distributed communication networks. In Chapter 2, a tube-based robust MPC consensus protocol for constrained linear MASs is proposed. For undisturbed linear MASs without constraints, the results on designing a centralized linear consensus protocol are first developed by a suboptimal linear quadratic approach. In order to evaluate the control performance of the suboptimal consensus protocol, we use an infinite horizon linear quadratic objective function to penalize the disagreement among agents and the size of control inputs. Due to the non-convexity of the performance function, an optimal controller gain is difficult or even impossible to find, thus a suboptimal consensus protocol is derived. In the presence of disturbance, the original MASs may not maintain certain properties such as stability and cooperative performance. To this end, a tube-based robust MPC framework is introduced. When disturbance is involved, the original constraints in nominal prediction should be tightened so as to achieve robust constraint satisfaction, as the predicted states and the actual states are not necessarily the same. Moreover, the corresponding robust constraint sets can be determined offline, requiring no extra iterative online computation in implementation. In Chapter 3, a novel distributed MPC-based consensus protocol is proposed for general linear MASs with input constraints. For the linear MAS without constraints, a pre-stabilizing distributed linear consensus protocol is developed by an inverse optimal approach, such that the corresponding closed-loop system is asymptotically stable with respect to a consensus set. Implementing this pre-stabilizing controller in a distributed digital setting is however not possible, as it requires every local decision maker to continuously access the state of their neighbors simultaneously when updating the control input. To relax these requirements, the assumed neighboring state, instead of the actual state of neighbors, is used. In our distributed MPC scheme, each local controller minimizes a group of control variables to generate control input. Moreover, an additional state constraint is proposed to bound deviation between the actual and the assumed state. In this way, consistency is enforced between intended behaviors of an agent and what its neighbors believe it will behave. We later show that the closed-loop system converges to a neighboring set of the consensus set thanks to the bounded state deviation in prediction. In Chapter 4, conclusions are made and some research topics for future exploring are presented. / Graduate / 2021-03-31

We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear. / Master of Science

Item Response Theory (IRT) Models, like the one parameter, two parameters, or normal Ogive, have been discussed for many years. These models represent a rich area of investigation due to their complexity as well as the large amount of data collected in relationship to model parameter estimation. Here we propose a new way of looking at IRT models using I-projections and duality. We use convex optimization methods to derive these models. The Kullback-Leibler divergence is used as a metric and specific constraints are proposed for the various models. With this approach, the dual problem is shown to be much easier to solve than the primal problem. In particular when there are many constraints, we propose the application of a projection algorithm for solving these types of problems. We also consider re-framing the problem and utilizing a decomposition algorithm to solve for parameters as well. Both of these methods will be compared to the Rasch and 2-Parameter Logistic models using established computer software where estimation of model parameters are done under Maximum Likelihood Estimation framework. We will also compare the appropriateness of these techniques on multidimensional item response data sets and propose new models with the use of I-projections.

Nonsmoothness appears in various applications in chemical engineering, including multi-stream heat exchangers, nonsmooth flash calculation, process integration. In terms of numerical approaches, convex/concave relaxations of static and dynamic systems may also exhibit nonsmoothness. These relaxations are used in deterministic methods for global optimization. This thesis presents several new theoretical results for nonsmooth sensitivity analysis, with an emphasis on convex relaxations. Firstly, the "compass difference" and established ODE results by Pang and Stewart are used to describe a correct subgradient for a nonsmooth dynamic system with two parameters. This sensitivity information can be computed using standard ODE solvers. Next, this thesis also uses the compass difference to obtain a subgradient for the Tsoukalas-Mitsos convex relaxations of composite functions of two variables. Lastly, this thesis develops a new general subgradient result for Tsoukalas-Mitsos convex relaxations of composite functions. This result does not limit on the dimensions of input variables. It gives the whole subdifferential of Tsoukalas-Mitsos convex relaxations. Compare to Tsoukalas-Mitsos’ previous subdifferential results, it does not require additionally solving a dual optimization problem as well. The new subgradient results are extended to obtain directional derivatives for Tsoukalas-Mitsos convex relaxations. The new subgradient results and directional derivative results are computationally approachable: subgradients in this article can be calculated both by the vector forward AD mode and reverse AD mode. A proof-of-concept implementation in Matlab is discussed. / Thesis / Master of Applied Science (MASc)

This thesis gives a unified framework to formulate and solve resource management problems in radar systems. / As a crucial factor in improving radar performance for multiple target tracking (MTT), resource management problems are analyzed in this thesis with regard to sensor platform path planning, beam scheduling, and burst parameter design. This thesis addresses problems to deploy or adapt radar configurations for multisensor-multitarget tracking, including 1) the path planning of movable receivers and power allocation of transmitted signals, 2) the optimal beam steering of high-precision pencil beams, and 3) the pulsed repetition frequency (PRF) set selection and waveform design. Firstly, the coordinated sensor management on the ends of both receivers and transmitters for a multistatic radar is studied. A multistatic radar system consists of fixed transmitters and movable receivers. To form better transmitter-target-receiver geometry and to establish an effective power allocation scheme to illuminate targets with different priorities, a joint path planning and power allocation problems, which determines the moving trajectories of receivers mounted on unmanned airborne vehicles (UAVs) and the power allocation scheme of transmitted signals over a limited time horizon, is formulated as a weighted-sum optimization. The problem is solved with a genetic algorithm (GA) with a novel pre-selection operator. The pre-selection operator, which takes advantage of the receding horizon control (RHC) framework to improve population structures prior to the next generation, can accelerate the convergence of GA. Secondly, the beam steering strategies for a cooperative phased array radar system with high-precision beams are developed. Pencil beams with narrow beamwidth, which are designated to track targets for a phased array radar, offer efficient performance in an energy-saving design, but can cause partial observations. The novel concept of expected Cramér-Rao lower bound (EPCRLB) is proposed to model partial observations. A formulation based on PCRLB is given and solved with a hierarchical genetic algorithm (HGA). An optimal strategy based on EPCRLB, which is effective in performance and efficient in time, is proposed. Finally, a joint pulsed repetition frequency (PRF) set selection and waveform design is studied. The problem tries to improve blind zone maps while preventing targets from falling into blind zones. Waveform parameters are then optimized for the system to provide better tracking accuracy. The problem is first formulated as a bi-objective optimization problem and solved with a multiple-objective genetic algorithm. Then, a two-step strategy that prioritizes the visibility of targets is developed. Numerical results demonstrate the effectiveness of proposed strategies over simple approaches. / Thesis / Doctor of Philosophy (PhD) / This thesis formulates resource management problems in various radar systems. The problems use PCRLB, a theoretically achievable lower bound for estimators, as a metric to optimize, and help the configuration of radar resources in an efficient manner. Effective strategies and improved algorithms are proposed to solve the problems.

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