In many existing and emerging engineering systems there is an inherent tendency of process variables to drift. In some systems this drift is caused by large, persistent disturbances due to interactions with the external environment. In other systems, similar drift is caused by finite resources (fuel, energy, component life etc.) being continuously depleted. The operating objectives for such systems with drift are reflected in a set of constraints that must be satisfied for as long as possible by countering the drift, rather than in terms of usual set-point command tracking requirements. This research project advances theory and methods for designing control algorithms that perform drift counteraction thereby establishing a foundation for addressing practical drift counteraction applications, and for incorporating drift counteraction technology into industrial products. These advances will represent contributions to several areas of control theory including stochastic control, set-theoretic control, game-theoretic control, constrained control, and nonlinear control. The developments in theory will proceed in close synergy with the demonstration of their benefits in several engineering applications to automotive and aerospace systems and dynamic motion simulators. The research results will be integrated into university courses for graduate students, short courses for industrial and academic audiences, and into the computational software package implementing drift counteraction control design techniques. The drift counteraction control is based primarily on constraints and does not use conventional set-points, differently from most of the traditional control theory. The development of effective techniques for drift counteraction will be based on treating external disturbances causing drift and constraint violation first in the stochastic and then in the deterministic setting. In the stochastic setting, advances in Stochastic Drift Counteraction Optimal Control (SDCOC) that maximizes the expected cost before the imposed constraints are violated will be pursued. Stability and boundness conditions for closed-loop trajectories of systems operating under SDCOC control laws when disturbances settle to constant values or vary within a subset of the full range will be derived. Sub-optimality and convergence properties of receding horizon and reinforcement learning variants of SDCOC will be studied. Advances in SDCOC computational procedures will be made, firstly, by exploiting decomposition of the system dynamics into slow and fast subsystems and, secondly, based on Markov Chain models that use Fuzzy Encoding (MCFE). By combining SDCOC and MCFE, evidence based control framework for drift counteraction in uncertain systems will be defined and complemented with estimation algorithms. In the deterministic setting, set-theoretic, game-theoretic and disturbance estimation/cancellation based approaches to drift counteraction problems will be pursued. The advances will focus on formulation and derivation of algorithms, the improvements in their off-board and on-board computations, and characterization of closed-loop properties (constraint violation time, ability to prevent constraint violation over an infinite time interval, trajectory bounds, etc.). Synergistically with the theoretical advances, several practical applications of drift counteraction control will be considered. These applications will include increasing comfort and fuel efficiency of adaptive cruise control systems for conventional and hybrid passenger vehicles, extending range and life of electric and hybrid electric vehicles and their batteries, improving the ability to replicate motions in small scale dynamic motion simulators, and improving the capability and efficiency of spacecraft attitude control using momentum exchange devices. For each application, its requirements will be reflected in a drift counteraction problem formulation, appropriate models will be established, drift counteraction control algorithms will be designed, and performance benefits will be quantified. To ensure practical relevance of the results and facilitate their experimental validation in the vehicle adaptive cruise control case, interactions and collaborations with industry partners will be leveraged.
