Data-Driven Nonlinear Control Designs for Constrained Systems

Systems with nonlinear dynamics are theoretically constrained to the realm of nonlinear analysis and design, while explicit constraints are expressed as equalities or inequalities of state, input, and output vectors of differential equations. Few control designs exist for systems with such explicit constraints, and no generalized solution has been provided. This dissertation presents general techniques to design stabilizing controls for a specific class of nonlinear systems with constraints on input and output, and verifies that such designs are straightforward to implement in selected applications. Additionally, a closed-form technique for an open-loop problem with unsolvable dynamic equations is developed. Typical optimal control methods cannot be readily applied to nonlinear systems without heavy modification. However, by embedding a novel control framework based on barrier functions and feedback linearization, well-established optimal control techniques become applicable when constraints are imposed by the design in real-time. Applications in power systems and aircraft control often have safety, performance, and hardware restrictions that are combinations of input and output constraints, while cryogenic memory applications have design restrictions and unknown analytic solutions. Most applications fall into a broad class of systems known as passivity-short, in which certain properties are utilized to form a structural framework for system interconnection with existing general stabilizing control techniques. Previous theoretical contributions are extended to include constraints, which can be readily applied to the development of scalable system networks in practical systems, even in the presence of unknown dynamics. In cases such as these, model identification techniques are used to obtain estimated system models which are guaranteed to be at least passivity-short. With numerous analytic tools accessible, a data-driven nonlinear control design framework is developed using model identification resulting in passivity-short systems which handles input and output saturations. Simulations are presented that prove to effectively control and stabilize example practical systems

Coordinated Optimal Control Of Constrained Ders

In this paper, a coordinated optimal control is designed to simultaneously satisfy multiple power system objectives at the distribution network level. With high penetration of renewables, traditional generation and control may not be enough to compensate for intermittent changes in net load. Dynamic coordination of battery storage devices and demand response at aggregated distributed energy resource (DER) sites becomes necessary to maintain power system operation, however, each dynamic power component operates at different time scales. Frequency stabilization can be achieved by designing optimal controls for traditional generation, storage devices and demand response. The proposed optimal controls naturally render frequency separation of these load balancing mechanisms. Given a 24-hour net load forecast, optimal tracking control inputs are designed subject to constraints of selected system elements to ensure optimal performance of the power system. Simulation results are presented and discussed