Control of nonlinear systems with applications

In practical applications of feedback control, most actuators exhibit physical constraints that limit the control amplitude and/or rate. The principal challenge of control design problem for linear systems with input constraints is to ensure closed-loop stability and yield a good transient performance in the presence of amplitude and/or rate-limited control. Since actuator saturation manifests itself as a nonlinear behavior in an otherwise linear system, the development of a nonconservative saturation control design methodology poses a significant challenge. In particular, it is well known that unstable linear systems can be stabilized using smooth controllers only in a local sense in the presence of actuator saturation. Thus, it is of paramount importance to develop a saturation control design methodology that yields a nonconservative estimate of the stability domain for closed-loop system.; The first part of this research focuses on a numerically tractable formulation of the control synthesis problem for linear systems with actuator amplitude and rate saturation nonlinearity using a linear-matrix-inequality (LMI) framework. Following the recent trend in the actuator saturation control research, we (i) utilize absolute stability theory to ensure closed-loop stability and (ii) minimize a quadratic cost to account for the closed-loop system performance degradation. In order to reduce the inherent conservatism of the absolute stability based saturation control framework, we exploit stability multipliers (of, e.g., weighted circle criterion, Popov criterion, etc.). For the control of linear systems with simultaneous actuator amplitude and rate saturation nonlinearities, by virtue of a rate limiter that is predicated on designing the control amplitude and then computing the control rates, we directly account for rate constraints. Both continuous- and discrete-time systems with actuator saturation are considered. A number of design examples are presented to demonstrate the efficacy of our proposed saturation control design framework.; The second part of this research addresses adaptive nonlinear control designs for nonlinear systems, with application to several real-world problems. This research is motivated by the inherent nonlinear characteristics of most physical plants. Although control theory for linear systems is quite mature and has been successful in practice, it is often inadequate when dealing with nonlinear systems. In addition, inaccurately known and often unknown plant parameter/plant and unpredictable environmental changes render the nonlinear control design problems more complicated. In this research, we utilize a Lyapunov framework combined with the backstepping methodology to design adaptive full-state feedback controllers for several interesting real-world problems. First, we consider a liquid level control problem in a state-coupled water tank system. Next, we address the combined orbit and attitude modeling and adaptive control design problems for a 6 degree of freedom (DOF) spacecraft. We also consider a spacecraft formation control problem with combined orbit and attitude dynamics. For each problem, all control designs are validated via experimentation or simulation studies.