Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we developed a new neuroadaptive control architecture for nonlinear uncertain dynamical systems as well as nonlinear nonnegative uncertain dynamical systems. Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A subclass of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this research, we developed a direct adaptive and neuroadaptive control framework for stabilization, disturbance rejection and noise suppression for nonnegative and compartmental dynamical systems with exogenous system disturbances. Furthermore, we developed a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. Specifically, the proposed framework involves a new and novel controller architecture involving additional terms, or Q-modification terms, in the update laws that are constructed using a moving time window of the integrated system uncertainty. The Q-modification terms can be used to identify the ideal neural network system weights which can be used in the adaptive law. In addition, these terms effectively suppress system uncertainty. Finally, neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. This architecture is used to control lung volume and minute ventilation with input pressure constraints that also accounts for spontaneous breathing by the patient. Specifically, we develop a pressure- and work-limited neuroadaptive controller for mechanical ventilation based on a nonlinear multi-compartmental lung model. The control framework does not rely on any averaged data and is designed to automatically adjust the input pressure to the patient's physiological characteristics capturing lung resistance and compliance modeling uncertainty. Moreover, the controller accounts for input pressure constraints as well as work of breathing constraints. The effect of spontaneous breathing is incorporated within the lung model and the control framework.

In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics: direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances; direct discrete-time adaptive control with guaranteed parameter error convergence; and hybrid adaptive control for nonlinear uncertain impulsive dynamical systems.

Modern complex dynamical systems typically possess a multiechelon hierarchical hybrid structure characterized by continuous-time dynamics at the lower-level units and logical decision-making units at the higher-level of hierarchy. Hybrid dynamical systems involve an interacting countable collection of dynamical systems defined on subregions of the partitioned state space. Thus, in addition to traditional control systems, hybrid control systems involve supervising controllers which serve to coordinate the (sometimes competing) actions of the lower-level controllers. A subclass of hybrid dynamical systems are impulsive dynamical systems which consist of three elements, namely, a continuous-time differential equation, a difference equation, and a criterion for determining when the states of the system are to be reset. One of the main topics of this dissertation is the development of stability analysis and control design for impulsive dynamical systems. Specifically, we generalize Poincare's theorem to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of left-continuous, hybrid, and impulsive dynamical systems. For nonlinear impulsive dynamical systems, we present partial stability results, that is, stability with respect to part of the system's state. Furthermore, we develop adaptive control framework for general class of impulsive systems as well as energy-based control framework for hybrid port-controlled Hamiltonian systems. Extensions of stability theory for impulsive dynamical systems with respect to the nonnegative orthant of the state space are also addressed in this dissertation. Furthermore, we design optimal output feedback controllers for set-point regulation of linear nonnegative dynamical systems. Another main topic that has been addressed in this research is the stability analysis of large-scale dynamical systems. Specifically, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. Moreover, we develop vector dissipativity theory for large-scale dynamical systems based on vector storage functions and vector supply rates. Finally, using a large-scale dynamical systems perspective, we develop a system-theoretic foundation for thermodynamics. Specifically, using compartmental dynamical system energy flow models, we place the universal energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation laws of thermodynamics on a system-theoretic basis.